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OptiSystemComponent Library
Optical Communication System Design Software
Version 3.0for Windows® 2000/XP
OptiSystemComponent LibraryOptical Communication System Design Software
Copyright © 2003 Optiwave CorporationAll rights reserved.
All OptiSystem documents, including this one, and the information contained therein, is copyright material.
No part of this document may be reproduced, stored in a retrieval system, or transmitted in any form or by any means whatsoever, including recording, photocopying, or faxing, without prior written approval of Optiwave Corporation.
DisclaimerOptiwave Corporation makes no representation or warranty with respect to the adequacy of this documentation or the programs which it describes for any particular purpose or with respect to its adequacy to produce any particular result. In no event shall Optiwave Corporation, its employees, its contractors or the authors of this documentation, be liable for special, direct, indirect, or consequential damages, losses, costs, charges, claims, demands, or claim for lost profits, fees, or expenses of any nature or kind.
9/30/03
Technical support
If you purchased Optiwave software from a distributor that is not listed here, please send technical questions to your distributor.
Optiwave Corporation Canada/USTel (613) 224-4700 E-mail [email protected]
Fax (613) 224-4706 URL www.optiwave.com
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Fax +81 (03) 5978-6082 URL www.cybernet.co.jp
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Fax +33 494 12 18 49 URL www.lighttec.fr
Table of contents
Transmitters Library
Pulse GeneratorsElectrical
Duobinary Pulse Generator........................................................................................3Electrical Jitter............................................................................................................5Noise Source..............................................................................................................7RZ Pulse Generator ...................................................................................................9NRZ Pulse Generator...............................................................................................13Gaussian Pulse Generator.......................................................................................15Hyperbolic-Secant Pulse Generator.........................................................................17Sine Generator.........................................................................................................19Triangle Pulse Generator .........................................................................................21Saw-Up Pulse Generator .........................................................................................23Saw-Down Pulse Generator.....................................................................................25Impulse Generator ...................................................................................................27Raised Cosine Pulse Generator...............................................................................29Sine Pulse Generator...............................................................................................31Measured Pulse .......................................................................................................33Measured Pulse Sequence ......................................................................................35Bias Generator .........................................................................................................37
Optical
Optical Gaussian Pulse Generator...........................................................................39Optical Sech Pulse Generator..................................................................................43Optical Impulse Generator .......................................................................................47Measured Optical Pulse ...........................................................................................51Measured Optical Pulse Sequence..........................................................................55Time Resolve Chirp (TRC) Measurement Data .......................................................59
Optical SourcesCW Laser .................................................................................................................63Laser Rate Equations...............................................................................................67Laser Measured .......................................................................................................71LED ..........................................................................................................................77White Light Source...................................................................................................79Pump Laser..............................................................................................................81Pump Laser Array ....................................................................................................83CW Laser Array........................................................................................................87CW Laser Array ES..................................................................................................91CW Laser Measured ................................................................................................95Directly Modulated Laser Measured ......................................................................101WDM Transmitter ...................................................................................................107
Bit Sequence GeneratorsPseudo-Random Bit Sequence Generator.............................................................115User-Defined Bit Sequence Generator ..................................................................117Mach-Zehnder Modulator.......................................................................................119
ModulatorsOptical
Electroabsorption Modulator ..................................................................................121Amplitude Modulator ..............................................................................................123Phase Modulator ....................................................................................................125Frequency Modulator .............................................................................................127Dual Drive Mach-Zehnder Modulator Measured ....................................................129Electroabsorption Modulator Measured .................................................................133Single Drive Mach-Zehnder Modulator Measured .................................................137Dual Port Dual Drive Mach-Zehnder Modulator Measured ....................................141LiNbO3 Mach-Zehnder Modulator..........................................................................145
Optical Fibers Library
Optical fiber data ....................................................................................................151Optical fiber ............................................................................................................159Linear Multimode fiber............................................................................................187Nonlinear Dispersive fiber ......................................................................................193
Receivers Library
RegeneratorsElectrical
Clock Recovery ......................................................................................................211Data Recovery .......................................................................................................2123R Regenerator......................................................................................................214
OpticalDemodulators
Ideal Frequency Demodulator................................................................................217Ideal Phase Demodulator.......................................................................................219
PhotodetectorsPhotodetector PIN..................................................................................................221Photodetector APD ................................................................................................228
Amplifiers Library
OpticalRaman
Raman Amplifier.....................................................................................................235Raman Amplifier—Average power model ..............................................................251Raman Amplifier—Dynamic model ........................................................................261
EDFA
EDFA Black Box.....................................................................................................271EDF Dynamic — Full model...................................................................................283EDF Dynamic — Analytical model .........................................................................289EDFA......................................................................................................................295EDFA Ideal.............................................................................................................303EDFA Measured.....................................................................................................309Erbium doped fiber.................................................................................................315Er-Yb codoped fiber ...............................................................................................353Er-Yb codoped waveguide amplifier ......................................................................363
SOA
Semiconductor Optical Amplifier ............................................................................381
Electrical
Limiting Amplifier....................................................................................................387Electrical Amplifier..................................................................................................389Transimpedance Amplifier .....................................................................................391AGC Amplifier ........................................................................................................393
Filters Library
OpticalOptical IIR filter.......................................................................................................397Measured Optical filter ...........................................................................................400Measured Group Delay Optical filter ......................................................................404Rectangle Optical filter ...........................................................................................409Trapezoidal Optical filter ........................................................................................411Gaussian Optical filter ............................................................................................413Butterworth Optical filter.........................................................................................415Bessel Optical filter ................................................................................................417Fabry Perot Optical filter ........................................................................................420Acousto Optical filter ..............................................................................................422Mach-Zehnder Interferometer ................................................................................425Inverted Optical IIR filter.........................................................................................427Inverted Rectangle Optical filter .............................................................................430Inverted Trapezoidal Optical filter ..........................................................................432Inverted Gaussian Optical filter ..............................................................................434Inverted Butterworth Optical filter...........................................................................436Inverted Bessel Optical filter ..................................................................................438
FBGFiber Bragg Grating (FBG).....................................................................................440Uniform Fiber Bragg Grating ..................................................................................446Ideal Dispersion Compensation FBG.....................................................................448
ElectricalLow Pass IIR filter (Electrical) ................................................................................453Low Pass Rectangle filter (Electrical).....................................................................456Low Pass Gaussian filter (Electrical)......................................................................458Low Pass Butterworth filter (Electrical) ..................................................................460Low Pass Bessel filter (Electrical) ..........................................................................462Low Pass Chebyshev filter (Electrical) ...................................................................464Low Pass RC filter (Electrical)................................................................................466Low Pass Raised Cosine filter (Electrical) .............................................................468Low Pass Cosine Roll Off filter (Electrical).............................................................470Low Pass Squared Cosine Roll Off filter (Electrical) ..............................................472
Band Pass IIR filter (Electrical) ..............................................................................474Measured filter (Electrical) .....................................................................................477Band Pass Rectangle filter (Electrical) ...................................................................481Band Pass Gaussian filter (Electrical)....................................................................483Band Pass Butterworth filter (Electrical).................................................................485Band Pass Bessel filter (Electrical) ........................................................................487Band Pass Chebyshev filter (Electrical) .................................................................489Band Pass RC filter (Electrical)..............................................................................491Band Pass Raised Cosine filter (Electrical)............................................................493Band Pass Cosine Roll Off filter (Electrical) ...........................................................495Band Pass Square Cosine Roll Off filter (Electrical) ..............................................497S Parameters Measured filter (Electrical) ..............................................................499
Filter AnalyzersOptical Filter analyzer ............................................................................................503Electrical Filter analyzer .........................................................................................505
WDM Multiplexers Library
Add and DropWDM Add...............................................................................................................509WDM Drop .............................................................................................................511WDM Add and Drop ...............................................................................................513
DemultiplexersWDM Demux 1x2 ...................................................................................................517WDM Demux 1x4 ...................................................................................................521WDM Demux 1x8 ...................................................................................................525WDM Demux..........................................................................................................529WDM Demux ES ....................................................................................................533Ideal Demux ...........................................................................................................535
MultiplexersWDM Mux 2x1........................................................................................................536WDM Mux 4x1........................................................................................................539WDM Mux 8x1........................................................................................................543WDM Mux ..............................................................................................................547WDM Mux ES.........................................................................................................551Ideal Mux................................................................................................................553
Network Library
Optical SwitchesDynamic Y Select Nx1 Measured ..........................................................................557Dynamic Y Switch 1xN Measured..........................................................................560Dynamic Y Switch 1xN...........................................................................................563Dynamic Y Select Nx1 ...........................................................................................567Dynamic Space Switch Matrix NxM Measured ......................................................571Dynamic Space Switch Matrix NxM .......................................................................575Optical Switch ........................................................................................................579Digital Optical Switch .............................................................................................581Optical Y Switch .....................................................................................................583Optical Y Select......................................................................................................585Ideal Switch 2x2 .....................................................................................................587Ideal Y Switch ........................................................................................................589Ideal Y Select .........................................................................................................591Ideal Y Switch 1x4..................................................................................................593Ideal Y Select 4x1 ..................................................................................................595Ideal Y Switch 1x8..................................................................................................597Ideal Y Select 8x1 ..................................................................................................599Ideal Y Select Nx1..................................................................................................601Ideal Y Switch 1xN .................................................................................................603
Frequency ConvertersIdeal Frequency Converter.....................................................................................605
Passives Library
ElectricalElectrical Signal Time Delay ..................................................................................609
OpticalOptical Attenuator ..................................................................................................611Phase Shift .............................................................................................................613PMD Emulator........................................................................................................615Time Delay .............................................................................................................619
Couplers
X Coupler ...............................................................................................................621Pump Coupler Co-Propagating ..............................................................................623Pump Coupler Counter-Propogating......................................................................625
Power Splitters
Power Splitter 1x2 ..................................................................................................627Power Splitter 1x4 ..................................................................................................629Power Splitter 1x8 ..................................................................................................631Power Splitter.........................................................................................................633
Power Combiners
Power Combiner 2x1..............................................................................................635Power Combiner 4x1..............................................................................................637Power Combiner 8x1..............................................................................................639Power Combiner ....................................................................................................641
Polarization
Linear Polarizer ......................................................................................................643Circular Polarizer....................................................................................................645Polarization Attenuator...........................................................................................647Polarization Combiner............................................................................................649Polarization Controller............................................................................................651Polarization Rotator................................................................................................653Polarization Splitter ................................................................................................655
Isolators
Isolator ...................................................................................................................657Ideal Isolator...........................................................................................................659
Circulators
Circulator................................................................................................................661Ideal Circulator .......................................................................................................663
Signal Processing Library
ArithmeticElectrical
Electrical Gain ........................................................................................................667Electrical Adder ......................................................................................................668Electrical Subtractor ...............................................................................................669Electrical Multiplier .................................................................................................670Electrical Bias.........................................................................................................671Electrical Norm.......................................................................................................672Electrical Differentiator ...........................................................................................673Electrical Integrator ................................................................................................674Electrical Limiter.....................................................................................................675
Optical
Optical Gain ...........................................................................................................677Optical Adder .........................................................................................................678Optical Subtractor ..................................................................................................679Optical Bias ............................................................................................................680Optical Multiplier.....................................................................................................681
ToolsOptical
Merge Optical Signal Bands...................................................................................682Convert to Parameterized ......................................................................................683Convert to Noise Bins ............................................................................................684
LogicBinary
Binary NOT ............................................................................................................685Binary AND ............................................................................................................686Binary OR...............................................................................................................687Binary XOR ............................................................................................................688Binary NAND..........................................................................................................689Binary NOR ............................................................................................................690Binary XNOR..........................................................................................................691Binary Delay...........................................................................................................692Duobinary precoder................................................................................................693
Tools Library
Switch.....................................................................................................................697Select .....................................................................................................................699Fork 1x2 .................................................................................................................701Loop Control...........................................................................................................702Ground ...................................................................................................................703Buffer Selector .......................................................................................................704Fork 1xN.................................................................................................................705Binary Null..............................................................................................................706Optical Null .............................................................................................................707Electrical Null .........................................................................................................708Binary Delay...........................................................................................................709Optical Delay..........................................................................................................710Electrical Delay ......................................................................................................711Optical Ring Controller ...........................................................................................713Electrical Ring Controller........................................................................................715Limiter ....................................................................................................................719
Initializer .................................................................................................................721Load from file .........................................................................................................724Command Line Application ....................................................................................725
Optiwave Software Tools
OptiAmplifier...........................................................................................................731IFO_Gratings..........................................................................................................739WDM_Phasar Demux 1xN .....................................................................................743WDM_Phasar Mux Nx1..........................................................................................745OptiBPM Component NxM.....................................................................................747
MATLAB Library
MATLAB Filter Component ....................................................................................753MATLAB Optical Filter Component ........................................................................757MATLAB Component .............................................................................................761
EDA Cosimulation Library
Save ADS File........................................................................................................777Load ADS File ........................................................................................................779Save Spice Stimulus File .......................................................................................783Load Spice CSDF File............................................................................................789Triggered Save Spice Stimulus File .......................................................................793Triggered Load Spice CSDF File ...........................................................................797
Cable Access Library
Carrier GeneratorsCarrier Generator ...................................................................................................803Carrier Generator Measured ..................................................................................805
TransmittersModulators
Electrical Amplitude Modulator (AM)......................................................................807Electrical Frequency Modulator (FM) .....................................................................809Electrical Phase Modulator ....................................................................................811Quadrature Modulator ............................................................................................813PAM Modulator ......................................................................................................815QAM Modulator ......................................................................................................817PSK Modulator .......................................................................................................819
DPSK Modulator ....................................................................................................821OQPSK Modulator .................................................................................................823MSK Modulator ......................................................................................................825FSK Modulator .......................................................................................................827CPFSK Modulator ..................................................................................................829
Pulse Generators
M-ary Pulse Generator...........................................................................................831PAM Pulse Generator ............................................................................................833QAM Pulse Generator............................................................................................835PSK Pulse Generator.............................................................................................839DPSK Pulse Generator ..........................................................................................841OQPSK Pulse Generator .......................................................................................843MSK Pulse Generator ............................................................................................845
Sequence Generators
PAM Sequence Generator .....................................................................................849QAM Sequence Generator.....................................................................................853PSK Sequence Generator......................................................................................857DPSK Sequence Generator ...................................................................................861
ReceiversDemodulators
Electrical Amplitude Demodulator ..........................................................................865Electrical Phase Demodulator................................................................................867Electrical Frequency Demodulator .........................................................................869Quadrature Demodulator .......................................................................................871
Decoders
PAM Sequence Decoder........................................................................................873QAM Sequence Decoder .......................................................................................877PSK Sequence Decoder ........................................................................................881DPSK Sequence Decoder......................................................................................885
Detectors
M-ary Threshold Detector ......................................................................................889
Visualizer Library
OpticalOptical Spectrum Analyzer (OSA)..........................................................................893Optical Time Domain Visualizer (OTDV)................................................................897Optical Power Meter Visualizer ..............................................................................903WDM Analyzer (WDMA) ........................................................................................905Dual Port WDM Analyzer (DPWDMA) ...................................................................911
ElectricalOscilloscope Visualizer ..........................................................................................919RF Spectrum Analyzer (RFSA) .............................................................................923Eye Diagram Analyzer ...........................................................................................927BER Analyzer.........................................................................................................937Electrical Power Meter ...........................................................................................951Electrical Carrier Analyzer (ECAN) ........................................................................953Electrical Constellation Visualizer ..........................................................................959
Transmitters LibraryThis section contains information on the following transmitters.
Pulse Generators
Electrical
• Duobinary Pulse Generator• Electrical Jitter• Noise Source• RZ Pulse Generator• NRZ Pulse Generator• Gaussian Pulse Generator• Hyperbolic-Secant Pulse Generator• Sine Generator• Triangle Pulse Generator• Saw-Up Pulse Generator• Saw-Down Pulse Generator• Impulse Generator• Raised Cosine Pulse Generator• Sine Pulse Generator• Measured Pulse• Measured Pulse Sequence• Bias Generator
Optical
• Optical Gaussian Pulse Generator• Optical Sech Pulse Generator• Optical Impulse Generator• Measured Optical Pulse
1
• Measured Optical Pulse Sequence• Time Resolve Chirp (TRC) Measurement Data
Optical Sources
• CW Laser• Laser Rate Equations• Laser Measured• LED• White Light Source• Pump Laser• Pump Laser Array• CW Laser Array• CW Laser Array ES• CW Laser Measured• Directly Modulated Laser Measured• WDM Transmitter
Bit Sequence Generators
• Pseudo-Random Bit Sequence Generator• User-Defined Bit Sequence Generator
Modulators
Optical
• Mach-Zehnder Modulator• Electroabsorption Modulator• Amplitude Modulator• Phase Modulator• Frequency Modulator• Dual Drive Mach-Zehnder Modulator Measured• Electroabsorption Modulator Measured• Single Drive Mach-Zehnder Modulator Measured• Dual Port Dual Drive Mach-Zehnder Modulator Measured• LiNbO3 Mach-Zehnder Modulator
Duobinary Pulse Generator
Used for duobinary modulation schemes. It is equivalent to a subsystem based on an electrical delay and adder. It can be used together with any electrical pulse generator.
Ports
Parameters
Simulation
Name and description Port type Signal type
Input Input Electrical
Clock Input Binary
Output Output Electrical
Name and description Default value Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
DUOBINARY PULSE GENERATOR
Technical backgroundThe equivalent subsystem is:
Figure 1 Duobinary Pulse Generator subsystem
4
Electrical Jitter
Inserts jitter in the input signal.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Clock Input Binary
Output Output Electrical
Name and description Default value
Default unit Units Value range
FrequencyJitter frequency
100 MHz Hz, MHz, GHz, THz
[0,+INF[
Jitter amplitudeJitter amplitude range
0.1 UI — [0,+INF[
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
ELECTRICAL JITTER
Technical backgroundThe jitter is a short-term, non-cumulative variation of the significant instants of a digital signal from their positions in time. Jitter amplitude is measured in unit intervals (UI), where 1 UI is the phase deviation of one clock period. The peak-to-peak UI deviation of the phase function with respect to time is referred as jitter amplitude. The output signal is:
where A is the jitter amplitude, B is the bit rate, and f is the jitter frequency.
Eout t( ) Ein t A2B------- 2πft( )sin+
=
6
NOISE SOURCE
Noise Source
Source of thermal noise.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Output Output Electrical
Name and description Default value
Default unit Units Value range
PSDDetermines whether the power is defined as PSD or as the average power in time
True — — True, False
Noise PowerValue of the PSD or the average power
–60 dBm W, mW, dBm ]-INF,+INF[
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
IterationsNumber of times to repeat the calculation
Iterations — — [1,+INF[
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
7
NOISE SOURCE
Noise
Random numbers
Technical backgroundThe average output Power or Power spectral density are parameters that you specify. This model generates electrical sampled signals or electrical sampled noise according to:
A Gaussian distribution describes the probability density function for the real and imaginary part of E. P is the average power when PSD parameter is false, if PSD is true then P is calculated from the power spectral density multiplied by the Sample rate.
Name and description Default value
Units Value range
Add noise to signalDetermines whether the noise will propagate separately from the signal or will be added to the signal
False — True, False
Name and description Default value
Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0, 4999]
Eout x t( ) jy t( )+[ ] P 2⁄=
8
RZ PULSE GENERATOR
RZ Pulse Generator
Generates a Return to Zero (RZ) coded signal.
Ports
Parameters
Main
Name and description Port type Signal type
Bit sequence Input Binary
Output Output Electrical
Name and description Default value
Default unit Value range
Rectangle shapeDetermines the shape for the edges of the pulse
Exponential — Exponential, Gaussian, Linear, Sine
AmplitudePeak-to-peak amplitude of the pulse
1 a.u. ]-INF,+INF[
BiasDC Offset of the pulse
0 a.u. ]-INF,+INF[
Duty cycleDuration of the high level bit
0.5 bit [0,1]
Position 0 bit
Rise timeDefined as the time from when the rising edge reaches 10% of the amplitude to the time it reaches 90% of the amplitude
0.05 bit [0,1]
Fall timeDefined as the time from when the falling edge reaches 90% of the amplitude to the time it reaches 10% of the amplitude
0.05 bit [0,1]
9
RZ PULSE GENERATOR
Simulation
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
10
RZ PULSE GENERATOR
Technical backgroundAccording to the parameter Rectangle shape, this model can produce pulses with different edge shapes:
Exponential
Gaussian
Linear
E t( )
1 et cr⁄( )–
0 t t1<≤,–
1 t1 t t2<≤,
et cf⁄( )–
t2 t tc<≤,
0 tc t T<≤,
=
E t( )
1 et cr⁄( )2–
0 t t1<≤,–
1 t1 t t2<≤,
et cf⁄( )2–
t2 t tc<≤,
0 t, c t T<≤
=
E t( )
t cr 0 t t1<≤,⁄
1 t1 t t2<≤,
t cf t2 t tc<≤,⁄
0 tc t T<≤,
=
11
RZ PULSE GENERATOR
Sine
where cr is the rise time coefficient and cf is the fall time coefficient. t1 and t2, together with cr and cf , are numerically determinate to generate pulses with the exact values of the parameters Rise time and Fall time. tc is the duty cycle duration, and T is the bit period.
E t( )
π.t cr⁄( ) 0 t t1<≤,sin
1 t1 t t2<≤,
π.t c⁄ f( ) t2 t tc<≤,sin
0 tc t T<≤,
=
12
NRZ PULSE GENERATOR
NRZ Pulse Generator
Generates a Non Return to Zero (NRZ) coded signal.
Ports
Parameters
Main
Name and description Port type Signal type
Bit sequence Input Binary
Output Output Electrical
Name and description Default value
Default unit Value range
Rectangle shapeDetermines the shape for the edges of the pulse
Exponential — Exponential, Gaussian, Linear, Sine
AmplitudePeak-to-peak amplitude of the pulse
1 a.u. ]-INF,+INF[
BiasDC Offset of the pulse
0 a.u. ]-INF,+INF[
Position 0 bit
Rise timeDefined as the time from when the rising edge reaches 10% of the amplitude to the time it reaches 90% of the amplitude
0.05 bit [0,1]
Fall timeDefined as the time from when the falling edge reaches 90% of the amplitude to the time it reaches 10% of the amplitude
0.05 bit [0,1]
13
NRZ PULSE GENERATOR
Simulation
Technical backgroundAccording to the parameter Rectangle shape, this model can produce pulses with different edge shapes:
Exponential
Gaussian
Linear
Sine
where cr is the rise time coefficient and cf is the fall time coefficient. t1 and t2, together with cr and cf, are numerically determined to generate pulses with the exact values of the parameters Rise time and Fall time, and T is the bit period.
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
E t( )
1 et cr⁄( )–
0 t t1<≤,–
1 t1 t t2<≤,
et cf⁄( )–
t2 t T<≤,
=
E t( )
et cr⁄( )2–
0 t t1<≤,
1 t1 t t2<≤,
et cf⁄( )2–
t2 t T<≤( ),
=
E t( )
t cr 0 t t1<≤,⁄
1 t1 t t2<≤,
t cf t2 t T<≤,⁄
=
E t( )
π.t cr⁄( ) 0 t t1<≤,sin
1 t1 t t2<≤,
π.t c⁄ f( ) t2 t T<≤,sin
=
14
GAUSSIAN PULSE GENERATOR
Gaussian Pulse Generator
Generates an electrical Gaussian-pulsed signal.
Ports
Parameters
Main
Name and description Port type Signal type
Bit sequence Input Binary
Output Output Electrical
Name and description Default value
Default unit Value range
AmplitudePeak-to-peak amplitude of the pulse
1 a.u. ]-INF,+INF[
BiasDC Offset of the pulse
0 a.u. ]-INF,+INF[
WidthFWHM of the pulse amplitude
0.5 bit [0,1]
Position 0 bit
OrderOrder of the function
1 — [1,100]
TruncatedDetermines whether or not the pulses overlap with each other
False — True, False
15
GAUSSIAN PULSE GENERATOR
Simulation
Technical backgroundThis model generates Gaussian or super-Gaussian electrical pulses according to the bit sequence at the input. For each bit
where Ap is the parameter peak-to-peak Amplitude, and Abias is the parameter Bias. B is the bit value (1 or 0) and depends on the input bit sequence. k is the fitting coefficient determined numerically to generate pulses with the exact values of the parameter Width TFWHM, and N is the Order of the Gaussian (N=1) or super-Gaussian pulses (N>1).
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
E t( ) B. Ap.e
12--- t.k
TFWHM----------------
2N–
Abias+
=
16
HYPERBOLIC-SECANT PULSE GENERATOR
Hyperbolic-Secant Pulse Generator
Generates a hyperbolic-secant pulsed signal.
Ports
Parameters
Main
Name and description Port type Signal type
Bit sequence Input Binary
Output Output Electrical
Name and description Default value
Default unit Value range
AmplitudePeak-to-peak amplitude of the pulse
1 a.u. ]-INF,+INF[
BiasDC Offset of the pulse
0 a.u. ]-INF,+INF[
WidthFWHM of the pulse amplitude
0.5 bit [0,1]
Position 0 bit
TruncatedDefinea whether or not the pulses overlap with each other
False — True, False
17
HYPERBOLIC-SECANT PULSE GENERATOR
Simulation
Technical backgroundThis model generates electrical pulses according to the bit sequence at the input. For each bit:
where Ap is the parameter peak-to-peak Amplitude, and Abias is the parameter Bias. B is the bit value (1 or 0) and depends on the input bit sequence. k is the fitting coefficient determined numerically to generate pulses with the exact values of the parameter Width, TFWHM.
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
E t( ) B. Apt.k
TFWHM-----------------
2cosh⁄ Abias+
=
18
SINE GENERATOR
Sine Generator
Generates an electrical sine waveform signal.
Ports
Parameters
Main
Name and description Port type Signal type
Output Output Electrical
Name and description Default value
Default unit Units Value range
FrequencyFrequency simulation window
32 GHz Hz, MHz, GHz, THz
]0,+INF[
AmplitudePeak-to-peak amplitude of the pulse
1 a.u. — ]-INF,+INF[
BiasDC Offset of the pulse
0 a.u. — ]-INF,+INF[
PhaseInitial phase of the signal
0 deg — ]-INF,+INF[
19
SINE GENERATOR
Simulation
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
IterationsNumber of times to repeat the calculation
Iterations — — [1,+INF[
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
20
TRIANGLE PULSE GENERATOR
Triangle Pulse Generator
Generates an electrical triangle-pulsed signal.
Ports
Parameters
Main
Name and description Port type Signal type
Bit sequence Input Binary
Output Output Electrical
Name and description Default value
Default unit Value range
AmplitudePeak-to-peak amplitude of the pulse
1 a.u. ]-INF,+INF[
BiasDC Offset of the pulse
0 a.u. ]-INF,+INF[
WidthFWHM of the pulse amplitude
0.5 bit [0,1]
Position 0 bit
TruncatedDetermines whether or not the pulses overlap with each other
False — True, False
21
TRIANGLE PULSE GENERATOR
Simulation
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
22
SAW-UP PULSE GENERATOR
Saw-Up Pulse Generator
Generates a saw-up signal.
Ports
Parameters
Main
Name and description Port type Signal type
Bit sequence Input Binary
Output Output Electrical
Name and description Default value
Default unit Value range
AmplitudePeak-to-peak amplitude of the pulse
1 a.u. ]-INF,+INF[
BiasDC Offset of the pulse
0 a.u. ]-INF,+INF[
WidthFWHM of the pulse amplitude
0.5 bit [0,1]
Position 0 bit
TruncatedDetermines whether or not the pulses overlap with each other
False — True, False
23
SAW-UP PULSE GENERATOR
Simulation
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
24
SAW-DOWN PULSE GENERATOR
Saw-Down Pulse Generator
Generates a saw-down pulsed signal.
Ports
Parameters
Main
Name and description Port type Signal type
Bit sequence Input Binary
Output Output Electrical
Name and description Default value
Default unit Value range
AmplitudePeak-to-peak amplitude of the pulse
1 a.u. ]-INF,+INF[
BiasDC Offset of the pulse
0 a.u. ]-INF,+INF[
WidthFWHM of the pulse amplitude
0.5 bit [0,1]
Position 0 bit [-1, 1]
TruncatedDetermines whether or not the pulses overlap with each other
False — True, False
25
SAW-DOWN PULSE GENERATOR
Simulation
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
26
IMPULSE GENERATOR
Impulse Generator
Generates an electrical signal composed by a sequence of Impulses.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Bit sequence Input Binary
Output Output Electrical
Name and description Default value
Default unit Value range
AmplitudePeak-to-peak amplitude of the pulse
1 a.u. ]-INF,+INF[
BiasDC Offset of the pulse
0 a.u. ]-INF,+INF[
PositionRelative position of the impulse
0.5 bit [0,1]
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
27
IMPULSE GENERATOR
Notes:
28
RAISED COSINE PULSE GENERATOR
Raised Cosine Pulse Generator
Generates a raised-cosine pulsed signal.
Ports
Parameters
Main
Name and description Port type Signal type
Bit sequence Input Binary
Output Output Electrical
Name and description Default value
Default unit Value range
AmplitudePeak-to-peak amplitude of the pulse
1 a.u. ]-INF,+INF[
BiasDC Offset of the pulse
0 a.u. ]-INF,+INF[
WidthFWHM of the pulse amplitude
0.5 bit [0,1]
Position 0 bit
TruncatedDetermines whether or not the pulses overlap with each other
False — True, False
29
RAISED COSINE PULSE GENERATOR
Simulation
Technical backgroundThis model generates electrical pulses according to the bit sequence at the input. For each bit:
where Ap is the parameter peak-to-peak Amplitude, and Abias is the parameter Bias. B is the bit value (1 or 0) and depends on the input bit sequence. k is the fitting coefficient determined numerically to generate pulses with the exact values of the parameter Width, TFWHM.
Name and description Default value
Default unit Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
E t( ) B. Ap. t.kTFWHM-----------------
2cos Abias+
=
30
SINE PULSE GENERATOR
Sine Pulse Generator
Generates a sine-pulsed signal.
Ports
Parameters
Main
Name and description Port type Signal type
Bit sequence Input Binary
Output Output Electrical
Name and description Default value
Default unit Value range
AmplitudePeak-to-peak amplitude of the pulse
1 a.u. ]-INF,+INF[
BiasDC Offset of the pulse
0 a.u. ]-INF,+INF[
WidthFWHM of the pulse amplitude
0.5 bit [0,1]
Position 0 bit
TruncatedDetermines whether or not the pulses overlap with each other
False — True, False
31
SINE PULSE GENERATOR
Simulation
Technical backgroundThis model generates electrical pulses according to the bit sequence at the input. For each bit:
where Ap is the parameter peak-to-peak Amplitude, and Abias is the parameter Bias. B is the bit value (1 or 0) and depends on the input bit sequence. k is the fitting coefficient numerically determinate to generate pulses with the exact values of the parameter Width TFWHM.
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
E t( ) B. Ap. t.kTFWHM-----------------
cos Abias+ =
32
MEASURED PULSE
Measured Pulse
Generates an electrical pulse based on measurements according to the bit sequence at the input port.
Ports
Parameters
Main
Numerical
Name and description Port type Signal type
Bit sequence Input Binary
Output Output Electrical
Name and description Default value Default unit Value range
AmplitudePeak-to-peak amplitude of the pulse
1 a.u. ]-INF,+INF[
BiasDC Offset of the pulse
0 a.u. ]-INF,+INF[
Position 0 bit
FilenameFilename with the measured data
Pulse.dat — —
Name and description Default value Units Value range
InterpolationDetermines the interpolation algorithm for the measured data
Linear — Linear, Cubic
33
MEASURED PULSE
Simulation
Graphs
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
Name and description X Title Y Title
Measured data Time period (a.u.) Amplitude (a.u.)
34
MEASURED PULSE SEQUENCE
Measured Pulse Sequence
Generates an electrical signal based on measurements.
Ports
Parameters
Main
Numerical
Name and description Port type Signal type
Output Output Electrical
Name and description Default value Default unit Value range
ScaleFactor to scale the signal amplitude
1 a.u. ]-INF,+INF[
Start timeInitial part of the signal to be skipped
0 s [0,+INF[
FilenameFilename with the measured data
Sequence.dat — —
Name and description Default value Units Value range
InterpolationDetermines the interpolation algorithm for the measured data
Linear — Linear, Cubic
35
MEASURED PULSE SEQUENCE
Simulation
Graphs
Technical backgroundThis model generates electrical signal loading measurements from a file. The input file is formatted containing two values per line, the time in seconds and signal amplitude in arbitrary units. For example, the file representing one measurement has the following form:
Name and description Default value
Default unit
Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
IterationsNumber of times to repeat the calculation
Iterations — — [1,+INF[
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
Name and description X Title Y Title
Measured data Time (s) Amplitude (a.u.)
0 0
1e-6 0.5
2e-6 0.5
3e-6 0
...
36
BIAS GENERATOR
Bias Generator
A d.c. source.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Output Output Electrical
Name and description Default value
Units Value range
AmplitudeAmplitude of the signal output
1 a.u. ]-INF,+INF[
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
IterationsNumber of times to repeat the calculation
Iterations — — [1,+INF[
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
37
BIAS GENERATOR
Notes:
38
OPTICAL GAUSSIAN PULSE GENERATOR
Optical Gaussian Pulse Generator
Generates a Gaussian-pulsed optical signal.
Ports
Parameters
Main
Name and description Port type Signal type
Bit sequence Input Binary
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency Emission frequency
193.1 THz Hz, THz, nm [0,+INF[
PowerPeak-to-peak power of the pulse
0 dBm W, mW, dBm ]-INF,+INF[
BiasDC Offset of the pulse
–100 dBm W, mW, dBm ]-INF,+INF[
WidthFWHM of the pulse amplitude
0.5 bit — [0,1]
Position 0 bit —
OrderOrder of the function
1 — — [1,100]
TruncatedDetermines whether or not the pulses overlap with each other
False — — True, False
39
OPTICAL GAUSSIAN PULSE GENERATOR
Chirp
Polarization
Simulation
Name and description Default value
Default unit Value range
Chirp definition Linear — Linear, Measured
Chirp factor 0 rad/s
Alpha parameter 0 rad/W
Adiabatic chirpResults from changes in the steady state carrier densities
0 1/s [0,1]
Name and description Default value
Default unit Value range
AzimuthAzimuth angle of output polarization
0 deg ]-90,90]
EllipticityEllipticity angle of output polarization
0 deg [-45,45]
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Parameterized Parameterized — —
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
40
OPTICAL GAUSSIAN PULSE GENERATOR
Technical backgroundThis model generates Gaussian or super-Gaussian optical pulses according to the bit sequence at the input. For each bit, the output optical power is:
where Ap is the parameter peak-to-peak Power, and Abias is the parameter Bias. B is the bit value (1 or 0) and depends on the input bit sequence. k is the fitting coefficient determined numerically to generate pulses with the exact values of the parameter Width, TFWHM, and N is Order of the Gaussian (N=1) or super-Gaussian pulses (N>1).
The chirp is modeled using:
where ϕ is the signal phase, αe is the parameter Linewidth enhancement factor, and is the parameter Adiabatic chirp.
The output is multiplied with a complex vector considering the state of polarization:
where the power splitting k and the phase difference θ are related to the parameters Azimuth and Ellipticity as:
P t( ) B. Ap.e
12--- t.k
TFWHM----------------
2N–
Abias+
=
dϕdt------
αe2------ d
dt----- P t( ) κP t( )+ln=
κ
EX t( )
EY t( ) 1 k–
kejθ
P t( )⋅=
α ε
2α( )tan 2 k 1 k–( ) θ( )cos1 2.k–
-----------------------------------------=
2ε( )sin 2 k 1 k–( ) θ( )sin=
41
OPTICAL GAUSSIAN PULSE GENERATOR
Notes:
42
OPTICAL SECH PULSE GENERATOR
Optical Sech Pulse Generator
Generates a hyperbolic-secant pulsed optical signal.
Ports
Parameters
Main
Name and description Port type Signal type
Bit sequences Input Binary
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency Emission frequency
193.1 THz Hz, THz, nm [0,+INF[
PowerPeak-to-peak power of the pulse
0 dBm W, mW, dBm ]-INF,+INF[
BiasDC Offset of the pulse
–100 dBm W, mW, dBm ]-INF,+INF[
WidthFWHM of the pulse amplitude
0.5 bit — [0,1]
Position 0 bit —
TruncatedDetermines whether or not the pulses overlap with each other
False — — True, False
43
OPTICAL SECH PULSE GENERATOR
Chirp
Polarization
Simulation
Name and description Default value
Default unit Value range
Chirp definition Linear — Linear, Measured
Chirp factor 0 rad/s
Alpha parameter 0 rad/W
Adiabatic chirpResults from changes in the steady state carrier densities
0 1/s [0,1]
Name and description Default value
Units Value range
AzimuthAzimuth angle of output polarization
0 deg ]-90,90]
EllipticityEllipticity angle of output polarization
0 deg [-45,45]
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Parameterized Parameterized — —
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
44
OPTICAL SECH PULSE GENERATOR
Technical backgroundThis model generates optical pulses according to the bit sequence at the input. For each bit, the output optical power is:
where Ap is the parameter peak-to-peak Power, and Abias is the parameter Bias. B is the bit value (1 or 0) and depends on the input bit sequence. k is the fitting coefficient determined numerically to generate pulses with the exact values of the parameter Width, TFWHM.
The chirp is modeled using:
where ϕ is the signal phase, αe is the parameter Linewidth enhancement factor, and is the parameter Adiabatic chirp.
The output is multiplied with a complex vector considering the state of polarization:
The power splitting k and the phase difference θ are related to the parameters Azimuth and Ellipticity as:
P t( ) B. Apt.k
TFWHM
------------- Abias+cosh⁄
=
dϕdt------
αe2------ d
dt----- P t( ) κP t( )+ln=
κ
EX t( )
EY t( ) 1 k–
kejθ
P t( )⋅=
αε
2α( )tan 2 k 1 k–( ) θ( )cos1 2.k–
-----------------------------------------=
2ε( )sin 2 k 1 k–( ) θ( )sin=
45
OPTICAL SECH PULSE GENERATOR
Notes:
46
OPTICAL IMPULSE GENERATOR
Optical Impulse Generator
Generates an optical signal composed by a sequence of Impulses.
Ports
Parameters
Main
Chirp
Name and description Port type Signal type
Bit sequence Input Binary
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency Emission frequency
193.1 THz Hz, THz, nm [0,+INF[
PowerPeak-to-peak power of the pulse
0 dBm W, mW, dBm ]-INF,+INF[
BiasDC Offset of the pulse
–100 dBm W, mW, dBm ]-INF,+INF[
PositionRelative position of the impulse
0 bit [0,1]
Name and description Default value
Units Value range
Alpha parameter 0 rad/W
Adiabatic chirpResults from changes in the steady state carrier densities
0 1/s [0,1]
47
OPTICAL IMPULSE GENERATOR
Polarization
Simulation
Name and description Default value
Units Value range
AzimuthAzimuth angle of output polarization
0 deg ]-90,90]
EllipticityEllipticity angle of output polarization
0 deg [-45,45]
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Parameterized Parameterized — —
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
48
OPTICAL IMPULSE GENERATOR
Technical backgroundThis model generates optical pulses according to the bit sequence at the input. For each bit, the output optical power is:
where Ap is the parameter peak-to-peak Power, and Abias is the parameter Bias. B is the bit value (1 or 0) and depends on the input bit sequence. δ is the impulse function and tP is the parameter Pulse position.
The chirp is modeled using:
where ϕ is the signal phase, αe is the parameter Linewidth enhancement factor, and is the parameter Adiabatic chirp.
The output is multiplied with a complex vector considering the state of polarization:
The power splitting k and the phase difference θ are related to the parameters Azimuth and Ellipticity as:
P t( ) B. Apδ t tp–( ) Abias+( )=
dϕdt------
αe2------ d
dt----- P t( ) κP t( )+ln=
κ
EX t( )
EY t( ) 1 k–
kejθ
P t( )⋅=
αε
2α( )tan 2 k 1 k–( ) θ( )cos1 2.k–
-----------------------------------------=
2ε( )sin 2 k 1 k–( ) θ( )sin=
49
OPTICAL IMPULSE GENERATOR
Notes:
50
MEASURED OPTICAL PULSE
Measured Optical Pulse
Generates a pulse based on measurements.
Ports
Parameters
Main
Name and description Port type Signal type
Bit sequence Input Binary
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency Emission frequency
193.1 THz Hz, THz, nm [0,+INF[
PowerPeak-to-peak power of the pulse
0 dBm W, mW, dBm ]-INF,+INF[
BiasDC Offset of the pulse
–100 dBm W, mW, dBm ]-INF,+INF[
Position 0 bit —
FilenameFilename with the measured data
Optical pulse.dat
— — —
File formatDetermines the format of the file with the measurements
Power — — Power, Power Phase, Real Imag, Phase
51
MEASURED OPTICAL PULSE
Polarization
Numerical
Simulation
Graphs
Name and description Default value
Units Value range
AzimuthAzimuth angle of output polarization
0 deg ]-90,90]
EllipticityEllipticity angle of output polarization
0 deg [-45,45]
Name and description Default value
Units Value range
InterpolationDetermines the interpolation algorithm for the measured data
Linear — Linear, Cubic
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Parameterized Parameterized — —
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
Name and description X Title Y Title
Measured magnitude data Time period (a.u.) Amplitude (V)
Measured phase data Time period (a.u.) Phase (rad)
52
MEASURED OPTICAL PULSE
Technical backgroundThe input file is formatted containing two items per line — the time in seconds and the signal measurement (Power in watts, Phase in radians, Real and Imag in Volts). According to the parameter File format, the second item can be one value (Power or Phase), or two values (Power and Phase or Real and Imag).
Power (Phase will be set to zero)
Power Phase
Real Imag
0 0
1e-6 0.5
2e-6 0.5
3e-6 0
...
0 0 0
1e-6 0.5 3.14
2e-6 0.5 3.14
3e-6 0 0
...
0 0 0
1e-6 –0.5 7.9e-4
2e-6 –0.5 7.9e-4
3e-6 0 0
...
53
MEASURED OPTICAL PULSE
Phase (Power will be set to one)
This model generates optical pulses according to the bit sequence at the input. For each bit, the output optical power is:
where Ap is the parameter peak-to-peak Power, and Abias is the parameter Bias. B is the bit value (1 or 0) and depends on the input bit sequence. M is the measured data.
The output is multiplied with a complex vector considering the state of polarization:
The power splitting k and the phase difference θ are related to the parameters Azimuth and Ellipticity as:
0 0
1e-6 3.14
2e-6 3.14
3e-6 0
...
P t( ) B. ApM t( ) Abias+( )=
EX t( )
EY t( ) 1 k–
kejθ
P t( )⋅=
αε
2α( )tan 2 k 1 k–( ) θ( )cos1 2.k–
-----------------------------------------=
2ε( )sin 2 k 1 k–( ) θ( )sin=
54
MEASURED OPTICAL PULSE SEQUENCE
Measured Optical Pulse Sequence
Generates an optical signal based on measurements.
Ports
Parameters
Main
Polarization
Name and description Port type Signal type
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency Emission frequency
193.1 THz Hz, THz, nm [0,+INF[
ScaleFactor to scale the signal amplitude
1 a.u. — ]-INF,+INF[
Start timeInitial part of the signal to be skipped
0 s — [0,+INF[
FilenameFilename with the measured data
Sequence.dat — — —
File formatDetermines the format of the file with the measurements
Power — — Power, Power Phase, Real Imag, Phase
Name and description Default value
Units Value range
AzimuthAzimuth angle of output polarization
0 deg ]-90,90]
55
MEASURED OPTICAL PULSE SEQUENCE
Numerical
Simulation
Graphs
EllipticityEllipticity angle of output polarization
0 deg [-45,45]
Name and description Default value
Units Value range
InterpolationDetermines the interpolation algorithm for the measured data
Linear — Linear, Cubic
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
IterationsNumber of times to repeat the calculation
Iterations — — [1,+INF[
Parameterized Parameterized — — Sampled, Parameterized
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
Name and description X Title Y Title
Measured magnitude data Time (s) Amplitude (V)
Measured phase data Time (s) Phase (rad)
Name and description Default value
Units Value range
56
MEASURED OPTICAL PULSE SEQUENCE
Technical backgroundThis model generates optical signal loading measurements from a file.
The input file is formatted containing two items per line — the time in seconds and signal measurement (Power in watts, Phase in radians, Real and Imag in Volts). According to the parameter File format, the second item can be one value (Power or Phase) or two values (Power and Phase or Real and Imag).
Power (Phase will be set to zero)
Power Phase
Real Imag
0 0
1e-6 0.5
2e-6 0.5
3e-6 0
...
0 0 0
1e-6 0.5 3.14
2e-6 0.5 3.14
3e-6 0 0
...
0 0 0
1e-6 –0.5 7.9e-4
2e-6 –0.5 7.9e-4
3e-6 0 0
...
57
MEASURED OPTICAL PULSE SEQUENCE
Phase (Power will be set to one)
The output is multiplied with a complex vector considering the state of polarization:
The power splitting k and the phase difference θ are related to the parameters Azimuth and Ellipticity as:
0 0
1e-6 3.14
2e-6 3.14
3e-6 0
...
EX t( )
EY t( ) 1 k–
kejθ
P t( )⋅=
αε
2α( )tan 2 k 1 k–( ) θ( )cos1 2.k–
-----------------------------------------=
2ε( )sin 2 k 1 k–( ) θ( )sin=
58
TIME RESOLVE CHIRP (TRC) MEASUREMENT DATA
Time Resolve Chirp (TRC) Measurement Data
This component is an interface between OptiSystem and time resolve chirp (TRC) [1] measurement instruments, such as the OSA Agilent 86146B with TRC option.
Ports
Parameters
Main
Polarization
Name and description Port type Signal type
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency Emission frequency
193.1 THz Hz, THz, nm [0,+INF[
ScaleFactor to scale the signal amplitude
1 a.u. — ]-INF,+INF[
Start timeInitial part of the signal to be skipped
0 s — [0,+INF[
FilenameFilename with the measured data
Sequence.dat — — —
Name and description Default value
Units Value range
AzimuthAzimuth angle of output polarization
0 deg ]-90,90]
EllipticityEllipticity angle of output polarization
0 deg [-45,45]
59
TIME RESOLVE CHIRP (TRC) MEASUREMENT DATA
Numerical
Simulation
Graphs
Technical backgroundThis component generates optical signal loading measurements from a file. These measurements are TRC data that describe the power and chirp evolution of the optical signal in time [1].
TRC provides frequency vs time information about a modulated lightwave signal. Also called dynamic chirp, the TRC graph provides useful information on the ability of a modulated signal to propagate over long distances in optical fiber.
Using measurement equipment such as the Agilent 86146B, with the filter mode capability, Agilent 86100 Infinium Digital Communications Analyzer (DCA) dedicated software (86146B Option TRL), and a personal computer, the time resolved chirp (TRC) of a modulated laser can be calculated.
From the measurement, a file with the TRC data is generated. OptiSystem can load this file and the effect of laser chirp on a wide variety of system performance metrics
Name and description Default value
Units Value range
InterpolationDetermines the interpolation algorithm for the measured data
Linear — Linear, Cubic
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
IterationsNumber of times to repeat the calculation
Iterations — — [1,+INF[
Parameterized Parameterized — — Sampled, Parameterized
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
Name and description X Title Y Title
Measured power data Time (s) Power (W)
BER measured chirp data Time (s) Chirp (Hz)
60
TIME RESOLVE CHIRP (TRC) MEASUREMENT DATA
- such as the effect on the performance of a long-haul dense wavelength division multiplexed (DWDM) system with EDFA and Raman optical amplification and dispersion compensation - can be studied across an unlimited range of system designs.
The input file is formatted containing three items per line - the time in seconds, the signal power is Watt (Linear scale) or dBm, and the signal chirp (Hz).
The output is multiplied with a complex vector considering the state of polarization:
The power splitting k and the phase difference θ are related to the parameters Azimuth and Ellipticity as:
Time Signal power (W or dBm) Signal chirp
0 1.27617e-006 -7.80425e+009
6.25e-012 1.139e-006 -4.94806e+009
1.25e-011 1.46161e-006 -6.57706e+009
1.875e-011 1.33136e-006 -6.10874e+009
2.5e-011 1.54705e-006 -2.89844e+009
3.125e-011 1.03595e-006 -7.38826e+009
. . . . . . . . .
EX t( )
EY t( ) 1 k–
kejθ
P t( )⋅=
αε
2α( )tan 2 k 1 k–( ) θ( )cos1 2.k–
-----------------------------------------=
2ε( )sin 2 k 1 k–( ) θ( )sin=
61
TIME RESOLVE CHIRP (TRC) MEASUREMENT DATA
Reference:[1] Agilent Technologies, “Making Time-Resolved Chirp Measurements Using the Optical
Spectrum Analyzer and Digital Communications Analyzer”, Agilent Application Note 1550-7, 2002.
62
CW LASER
CW Laser
Generates a continuous wave (CW) optical signal.
Ports
Parameters
Main
Polarization
Name and description Port type Signal type
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency Emission frequency
193.1 THz Hz,THz, nm [0,+INF[
Power 0 dBm W, mW, dBm ]-INF,+INF[
Linewidth 10 MHz — [0,+INF[
Initial phase 0 deg — ]-INF,+INF[
MxN next generation — — — —
StringParameter — — — —
Name and description Default value
Units Value range
Azimuth Azimuth angle of output polarization
0 deg ]-90,90]
EllipticityEllipticity angle of output polarization
0 deg [-45,45]
63
CW LASER
Simulation
Noise
Random numbers
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
IterationsNumber of times to repeat the calculation
Iterations — — [1,+INF[
Parameterized Parameterized — — Sampled, Parameterized
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
Name and description Default value
Default unit Units Value range
Noise bandwidthBandwidth to create noise bins
0 THz Hz, THz, nm [0,+INF[
Noise thresholdMinimum value for adaptation of noise bins
–100 dB — ]-INF,+INF[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB — ]-INF,+INF[
Name and description Default value
Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
64
CW LASER
Technical backgroundIn the CW case, the average output Power is a parameter that you specify. Laser phase noise is modeled using the probability density function:
where is the phase difference between two successive time instants and dt is the time discretization. A Gaussian random variable for the phase difference between two successive time instants with zero mean and a variance equal to has been assumed, with as the laser Linewidth.
The output is multiplied with a complex vector considering the state of polarization:
where the power splitting k and the phase difference θ are related to the parameters Azimuth and Ellipticity as follows:
f ∆ϕ( ) 12π ∆fdt---------------------- e
∆ϕ2
4π∆fdt------------------–
⋅=
∆ϕ
2π ∆f ∆f
EX t( )
EY t( ) 1 k–
kejθ
P t( )⋅=
α ε
2α( )tan 2 k 1 k–( ) θ( )cos1 2.k–
--------------------------------------------=
2ε( )sin 2 k 1 k–( ) θ( )sin=
65
CW LASER
Notes:
66
LASER RATE EQUATIONS
Laser Rate Equations
Utilizes the rate equations to simulate a DFB laser.
Ports
Parameters
Main
Physical
Name and description Port type Signal type
Modulation Input Electrical
Output Output Optical
Name and description Default value
Default unit Unit Value range
Frequency 193.1 THz Hz, THz, nm [30,3e5]
Calculate current True — — True, False
Power 0 dBm W, mW, dBm [-1e100, 1e100]
Power at bias current –30 dBm W, mW, dBm
Bias current 38 mA — [0, 1000]
Modulation peak current 28 mA — [0, 1000]
Threshold current 33.4572 mA — [0, 1000]
Threshold power 0.0155558 mW — [0, 1000]
Name and description Default value
Default unit Value range
Active layer volume 1.5e-010 cm3 0, 1e-3
Quantum efficiency 0.4 — 0, 1
Spontaneous emission factor 3e-005 — 2e-5, 20e-5
67
LASER RATE EQUATIONS
Simulation
Noise
Random numbers
Gain compression coefficient 1e-017 cm3 0.5e-17, 10e-17
Carrier density at transparency 1e+018 cm-3 0, 100e18
Differential gain coefficient 2.5e-016 cm2 0, 50e-16
Group velocity 8.5e+009 cm/s 0, 100e9
Linewidth enhancement factor 5 — –20, 20
Mode confinement factor 0.4 — 0, 1
Carrier lifetime 1e-009 s 0, 50e-9
Photon lifetime 3e-012 s 0, 50e-9
Name and description Default value
Units Value range
Enabled True — True, False
Parameterized Parameterized — —
Name and description Default value
Units Value range
Include noise True — True, False
Include phase noise True — True, False
Name and description Default value
Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
Name and description Default value
Default unit Value range
68
LASER RATE EQUATIONS
Technical backgroundThe modulation dynamics of the laser are modeled by coupled rate equations which describe the relation between the carrier density , photon density , and optical phase
:
where go is the gain slope constant,
The optical power and chirp response of the semiconductor laser to a current waveform is determined by the above equations. A Runge-Kutta algorithm is used to numerically integrate the coupled first order differential equations (2-4). These
(2)
(3)
(4)
ao is the active layer coefficient
vg is the group velocity
is the gain compression factor
Nt is the carrier density at transparency
is the fraction of spontaneous emission coupled into the lasing mode
is the mode confinement factor
V is the active layer volume
is the photon lifetime
is the electron lifetime
is the linewidth enhancement factor
N t( ) S t( )φ t( )
dN t( )dt
-------------- I t( )q V⋅----------- N t( )
τn----------– go N t( ) Nt–( ) 1
1 ε S t( )⋅+( )------------------------------- S t( )⋅ ⋅ ⋅–=
dS t( )dt
------------- Γ go N t( ) Nt–( ) 11 ε S t( )⋅+( )
------------------------------- S t( ) S t( )τp
---------– Γ β N t( )⋅ ⋅τn
--------------------------+⋅ ⋅ ⋅ ⋅=
dφ t( )dt
------------- 12--- α Γ go N t( ) Nt–( ) 1
τp-----–⋅ ⋅⋅ ⋅=
go vg ao⋅=
ε
β
Γ
τp
τn
α
( )tI
69
LASER RATE EQUATIONS
equations apply to a noiseless laser oscillating in a single longitudinal mode above threshold. The photon and electron densities within the active region of the laser are assumed to be uniform. The linewidth enhancement factor and the nonlinear gain compression parameter are taken to be constant for a given structure.
The time variations for the optical and laser chirp are:
where is the differential quantum efficiency
References
[1] J. C. Cartledge and G. S. Burley, “The Effect of the Laser Chirping on Lightwave System Performance”, J. Lightwave Technology, vol. 7, pp. 568-573, March 1989.
(5)
(6)
v is the optical frequency
h is the Planck’s constant
PS V ηo h v⋅ ⋅ ⋅ ⋅
2 Γτp⋅------------------------------------=
∆v 12 π⋅---------- dφ
dt------⋅=
ηo
70
LASER MEASURED
Laser Measured
Extracts values of the rate equation parameters using measurements and simulates a DFB laser.
Ports
Parameters
Main
Measurements
Name and description Port type Signal type
Modulation Input Electrical
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency 193.1 THz Hz, THz, nm [30,3e5]
Calculate current True — — True, False
Power 0 dBm W, mW, dBm [-1e100, 1e100]
Power at bias current –30 dBm W, mW, dBm [-1e100, 1e100]
Bias current 23 mA — [0, 1000]
Modulation peak current 28 mA — [0, 1000]
Name and description Default value
Default unit Units Value range
Damping factor 10.28 1e9 s-1 — ]0, 1000]
Resonance frequency factor 6.43 1e20 Hz2 — ]0, 1000]
Threshold current 18 mA — [0, 1000]
Power bias 0.4 mW W, mW, dBm [1e-100, 1e100]
71
LASER MEASURED
Physical
Initial estimate
Simulation
Name and description Default value Default unit Value range
Calculate parameters True —
Active layer volume 2e-011 cm3 0, 1e-3
Quantum efficiency 0.2 — 0, 1
Spontaneous emission factor 0.0001 — 2e-5, 20e-5
Gain compression coefficient 1.5e-017 cm3 0.5e-17, 10e-17
Carrier density at transparency 1e+018 cm-3 0, 100e18
Differential gain coefficient 1.765e-016 cm2 0, 50e-16
Mode confinement factor 0.2 — 0, 1
Carrier lifetime 1e-009 s 0, 50e-9
Photon lifetime 1e-012 s 0, 50e-9
Group velocity 8.5e+009 cm/s 0, 100e9
Linewidth enhancement factor 5 — –20, 20
Name and description Default value Default unit Value range
Active layer volume estimation 2e-011 cm3 0, 1e-3
Quantum efficiency estimation 0.2 — 0, 1
Spontaneous emission factor estimation 0.0001 — 2e-5, 20e-5
Gain compression coefficient estimation 1.5e-017 cm3 0.5e-17, 10e-17
Carrier density at transparency estimation 1e+018 cm-3 0, 100e18
Differential gain coefficient estimation 1.765e-016 cm2 0, 50e-16
Mode confinement factor estimation 0.2 — 0, 1
Carrier lifetime estimation 1e-009 s 0, 50e-9
Photon lifetime estimation 1e-012 s 0, 50e-9
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
Parameterized Parameterized — —
72
LASER MEASURED
Noise
Random numbers
Name and description Default value Units Value range
Include noise True — True, False
Include phase noise True — True, False
Name and description Default value Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
73
LASER MEASURED
Technical backgroundThe laser measured model extracts values of the rate equation parameters using measurements of the threshold current, optical power, resonance frequency, and damping factor to simulate a DFB laser.
Based on the results featured in [1] , the values of the rate equation parameters are calculated in a way that parameters simultaneously yield the measured values of Y (damping factor), Z (resonance frequency factor), Ith (threshold current), and P (Power bias). The parameter extraction procedure is based on minimization of the sum of squared errors between the measured values of (Y, Z, Ith, P) and values calculated from rate equation parameters. The minimization is over the values of the rate equation parameters which are:
Damping factor
Resonance frequency factor
Threshold current
Power bias
where go is the gain slope constant,
ao is the active layer coefficient
is the gain compression factor
Nt is the carrier density at transparency
is the fraction of spontaneous emission coupled into the lasing mode
is the mode confinement factor
is the differential quantum efficiency
V is the active layer volume
Y g0S
1 ε S⋅+( )------------------------ 1
τn----- Γ g0 N Nt–( ) 1
1 ε S⋅+( )2
-------------------------- 1τp-----+⋅–+=
Z g0S
1 ε S⋅+( )------------------------ 1
τp----- β 1–( ) Γ
g0τn-----g0 N Nt–( ) 1
1 ε S⋅+( )2
-------------------------- 1τp τn⋅--------------+⋅ ⋅+⋅=
Ithq V⋅
τn-----------
1 Nt Γ go τp⋅ ⋅ ⋅+Γ go τp⋅ ⋅
------------------------------------------⋅=
PS V η0 h v⋅ ⋅ ⋅ ⋅
2 Γτp⋅------------------------------------=
go vg ao⋅=
ε
β
Γ
η0
74
LASER MEASURED
The minimization routine finds a local minimum for the equation
where are the measured values and are the calculated values using the initial estimates of the rate equation parameters.
The parameters available in the main tab allow the user to enter the values for current, or for power in steady state. Using these numbers, the model will estimate the values of the current.
Note: It is recommended to enter the values for current, rather than power, when using the measured laser (as this is the realistic case).
The parameters in the measured tab are used to extract the physical/geometrical properties of the laser. This extraction is completely independent of the parameters in the main tab (current/power).
After finding the rate equation parameters, the laser measured works similarly to the DFB laser model.
is the photon lifetime
is the electron lifetime
are the steady-state values of the carrier and photon densities corresponding to the bias current of the laser
v is the unmodulated optical frequency
vg is the group velocity
h is the Planck’s constant
τp
τn
NandS
Func Ymea Ycal–( )2 zmea zcal–( )2 Pmea Pcal–( )2 Imea Ical–( )2+ + +=
Ymea Zmea Pmea Imea,,,( ) Ycal Zcal Pcal Ical,,,( )
75
LASER MEASURED
Reference:[1] Cartledge, J. C. and Srinivasan, R. C. “Extraction of DFB laser rate equation parameters for
system simulation purposes”, J. Light. Techn., 15, 852-860, (1997).
76
LED
LED
Simulates a modulated LED.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Modulation Input Electrical
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency 193.1 THz Hz, THz, nm [30,3e5]
Electron lifetime 1e-009 s — ]0, 1]
RC constant 1e-009 s — ]0, 1]
Quantum efficiency 0.05 — — ]0, 1]
Bandwidth 6 THz Hz, THz, nm ]0, INF ]
Name and description Default value
Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
Parameterized Parameterized — —
Iterations Iterations — [1, 1e+009]
77
LED
Random numbers
Technical backgroundIn this model, the mean of the optical power is a function of the modulation current (input signal). The conversion of the current into optical power is described by the responsivity of the LED:
where is the quantum efficiency
The modulated characteristics depend of the electron lifetime and the device of the diode, and are modeled by the transfer function applied to the current:
where is the Electron life time and is the RC constant.
If the parameter Parameterized is selected, the output consist of a single value representing the average LED output at the frequency output.
Note: The noise bins signals are not produced by this modulator.
Name and description Default value
Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
Yes — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
h is the Planck’s constant
f is the emission frequency
q is the electron charge
i(t) is the modulation current signal
P η h f i t( )q
--------⋅ ⋅ ⋅=
η
H f( ) 11 j 2 π f τn τrc+( )⋅ ⋅ ⋅ ⋅+------------------------------------------------------------=
τn τrc
78
WHITE LIGHT SOURCE
White Light Source
Generates a gaussian distributed optical white noise.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency Emission frequency
193.1 THz Hz, THz, nm [0,+INF[
PSDDetermines whether the Power is the PSD (/Hz) or the average power
True — — True, False
PowerAverage output powers
–30 dBm W, mW, dBm ]-INF,+INF[
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
IterationsNumber of times to repeat the calculation
Iterations — — [1,+INF[
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
79
WHITE LIGHT SOURCE
Noise
Random numbers
Technical backgroundThe average output Power or Power spectral density and Frequency are parameters that you specify. This model generates noise bins or sampled signals at the output according to:
A Gaussian distribution has been assumed to describe the probability density function for the real and imaginary part of Ex and Ey. P is the average power when PSD parameter is false. If PSD is true, then P is calculated from the power spectral density multiplied by the Sample rate.
Name and description Default value
Default unit Units Value range
Noise bins spacing 10 GHz Hz, GHz, THz, nm
[1, 100000]
Convert noise binsDetermines if the generated noise bins are incorporated into the signal
Convert noise bins
— — —
Name and description Default value
Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
80
PUMP LASER
Pump Laser
Generates an optical parameterized signal to be used for optical amplifier pumping.
Ports
Parameters
Main
Polarization
Name and description Port type Signal type
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency Emission frequency
980 nm Hz, THz, nm [0,+INF[
PowerAverage output powers
100 mW W, mW, dBm [0,+INF[
Name and description Default value
Units Value range
Azimuth Azimuth angle of output polarization
0 deg ]-90,90]
EllipticityEllipticity angle of output polarization
0 deg [-45,45]
81
PUMP LASER
Simulation
Technical backgroundIn the CW Laser case, average output Power is a parameter that you specify. This model generates only parameterized signal at the output.
The output is multiplied with a complex vector considering the state of polarization:
where the power splitting k and the phase difference θ are related to the parameters Azimuth and Ellipticity as follows:
Name and description Default value
Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
IterationsNumber of times to repeat the calculation
Iterations — [1, 1e+009]
EX t( )
EY t( ) 1 k–
kejθ
P⋅=
α ε
2α( )tan 2 k 1 k–( ) θ( )cos1 2.k–
--------------------------------------------=
2ε( )sin 2 k 1 k–( ) θ( )sin=
82
PUMP LASER ARRAY
Pump Laser Array
An array of pump lasers.
Ports
Parameters
Main
Frequency
Name and description Port type Signal type
Output 1 Output Optical
Output 2 Output Optical
Output 3 Output Optical
Output 4 Output Optical
Output 5 Output Optical
Output 6 Output Optical
Output 7 Output Optical
Output 8 Output Optical
Name and description Default value Units Value range
Number of output ports 8 — [1, 1000]
Name and description Default value
Default unit Units Value range
Frequency[0]Center frequency for pump 0
1405 nm Hz, THz, nm [100, 2000]
Frequency[1]Center frequency for pump 1
1412.5 nm Hz, THz, nm [100, 2000]
83
PUMP LASER ARRAY
Power
Frequency[2]Center frequency for pump 2
1420 nm Hz, THz, nm [100, 2000]
Frequency[3]Center frequency for pump 3
1427.5 nm Hz, THz, nm [100, 2000]
Frequency[4]Center frequency for pump 4
1435 nm Hz, THz, nm [100, 2000]
Frequency[5]Center frequency for pump 5
1442.5 nm Hz, THz, nm [100, 2000]
Frequency[6]Center frequency for pump 6
1450 nm Hz, THz, nm [100, 2000]
Frequency[7]Center frequency for pump 7
1457.5 nm Hz, THz, nm [100, 2000]
Name and description Default value
Default unit Units Value range
Power[0]Ouptut power for pump 0
100 mW W, mW, dBm [0,+INF[
Power[1]Ouptut power for pump 1
100 mW W, mW, dBm [0,+INF[
Power[2]Ouptut power for pump 2
100 mW W, mW, dBm [0,+INF[
Power[3]Ouptut power for pump 3
100 mW W, mW, dBm [0,+INF[
Power[4]Ouptut power for pump 4
100 mW W, mW, dBm [0,+INF[
Power[5]Ouptut power for pump 5
100 mW W, mW, dBm [0,+INF[
Power[6]Ouptut power for pump 6
100 mW W, mW, dBm [0,+INF[
Power[7]Ouptut power for pump 7
100 mW W, mW, dBm [0,+INF[
Name and description Default value
Default unit Units Value range
84
PUMP LASER ARRAY
Polarization
Simulation
Name and description Default value Units Value range
AzimuthAzimuth angle of output polarization
0 deg ]-90,90]
EllipticityEllipticity angle of output polarization
0 deg [-45,45]
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
IterationsNumber of times to repeat the calculation
Iterations — [1, 1e+009]
85
PUMP LASER ARRAY
Notes:
86
CW LASER ARRAY
CW Laser Array
This component is an array of CW lasers.
Ports
Parameters
Main
Name and description Port type Signal type
Output 1 Output Optical
Output 2 Output Optical
Output 3 Output Optical
Output 4 Output Optical
Output 5 Output Optical
Output 6 Output Optical
Output 7 Output Optical
Output 8 Output Optical
Name and description Default value Default Unit Value range
Number of output ports 8 — [1, 1000]
Linewidth 10 MHz [0, 1e+009[
Initial phase 0 deg [-1e+100,1e+100]
87
CW LASER ARRAY
Frequency
Power
Name and description Default value
Default unit Units Value range
Frequency[0]Center frequency for laser 0
193.1 THz Hz, THz, nm [30, 300000]
Frequency[1]Center frequency for laser 1
193.2 THz Hz, THz, nm [30, 300000]
Frequency[2]Center frequency for laser 2
193.3 THz Hz, THz, nm [30, 300000]
Frequency[3]Center frequency for laser 3
193.4 THz Hz, THz, nm [30, 300000]
Frequency[4]Center frequency for laser 4
193.5 THz Hz, THz, nm [30, 300000]
Frequency[5]Center frequency for laser 5
193.6 THz Hz, THz, nm [30, 300000]
Frequency[6]Center frequency for laser 6
193.7 THz Hz, THz, nm [30, 300000]
Frequency[7]Center frequency for laser 7
193.8 THz Hz, THz, nm [30, 300000]
Name and description Default value
Default unit Units Value range
Power[0]Ouptut power for laser 0
0 dBm W, mW, dBm ]-INF,+INF[
Power[1]Ouptut power for laser 1
0 dBm W, mW, dBm ]-INF,+INF[
Power[2]Ouptut power for laser 2
0 dBm W, mW, dBm ]-INF,+INF[
Power[3]Ouptut power for laser 3
0 dBm W, mW, dBm ]-INF,+INF[
Power[4]Ouptut power for laser 4
0 dBm W, mW, dBm ]-INF,+INF[
Power[5]Ouptut power for laser 5
0 dBm W, mW, dBm ]-INF,+INF[
88
CW LASER ARRAY
Polarization
Simulation
Noise
Power[6]Ouptut power for laser 6
0 dBm W, mW, dBm ]-INF,+INF[
Power[7]Ouptut power for laser 7
0 dBm W, mW, dBm ]-INF,+INF[
Name and description Default value
Units Value range
AzimuthAzimuth angle of output polarization
0 deg ]-90,90]
EllipticityEllipticity angle of output polarization
0 deg [-45,45]
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
IterationsNumber of times to repeat the calculation
Iterations — — [1,+INF[
Parameterized Parameterized — — —
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
Name and description Default value
Default unit Units Value range
Noise bandwidthBandwidth to create noise bins
0 THz Hz, THz, nm [0,+INF[
Noise thresholdMinimum value for adaptation of noise bins
–100 dB — ]-INF,+INF[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB — ]-INF,+INF[
Name and description Default value
Default unit Units Value range
89
CW LASER ARRAY
Random numbers
Name and description Default value
Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
90
CW LASER ARRAY ES
CW Laser Array ES
This component is an array of CW lasers. The emission frequencies are equally spaced (ES).
Ports
Parameters
Main
Name and description Port type Signal type
Output 1 Output Optical
Output 2 Output Optical
Output 3 Output Optical
Output 4 Output Optical
Output 5 Output Optical
Output 6 Output Optical
Output 7 Output Optical
Output 8 Output Optical
Name and description Default value Default Unit Value range
Number of output ports 8 — [1, 1000]
FrequencyEmission frequency of the first laser
193.1 THz, Hz, nm [30,+INF[
Frequency spacingFrequency spacing between adjacent lasers
100 GHz, THZ, Hz, nm
]-INF,+INF[
Linewidth 10 MHz [0, 1e+009[
Initial phase 0 deg [-1e+100,1e+100]
91
CW LASER ARRAY ES
Power
Polarization
Name and description Default value
Default unit Units Value range
Power[0]Ouptut power for laser 0
0 dBm W, mW, dBm ]-INF,+INF[
Power[1]Ouptut power for laser 1
0 dBm W, mW, dBm ]-INF,+INF[
Power[2]Ouptut power for laser 2
0 dBm W, mW, dBm ]-INF,+INF[
Power[3]Ouptut power for laser 3
0 dBm W, mW, dBm ]-INF,+INF[
Power[4]Ouptut power for laser 4
0 dBm W, mW, dBm ]-INF,+INF[
Power[5]Ouptut power for laser 5
0 dBm W, mW, dBm ]-INF,+INF[
Power[6]Ouptut power for laser 6
0 dBm W, mW, dBm ]-INF,+INF[
Power[7]Ouptut power for laser 7
0 dBm W, mW, dBm ]-INF,+INF[
Name and description Default value
Units Value range
AzimuthAzimuth angle of output polarization
0 deg ]-90,90]
EllipticityEllipticity angle of output polarization
0 deg [-45,45]
92
CW LASER ARRAY ES
Simulation
Noise
Random numbers
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
IterationsNumber of times to repeat the calculation
Iterations — — [1,+INF[
Parameterized Parameterized — — —
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
Name and description Default value
Default unit Units Value range
Noise bandwidthBandwidth to create noise bins
0 THz Hz, THz, nm [0,+INF[
Noise thresholdMinimum value for adaptation of noise bins
–100 dB — ]-INF,+INF[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB — ]-INF,+INF[
Name and description Default value
Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
93
CW LASER ARRAY ES
Technical BackgroundThe CW Laser Array ES is equivalent to the conventional CW Laser Array component. However, The CW Laser Array ES model is easier to set up for WDM systems, because it only requires the initial laser emission frequency and the spacing. The signal output power is the same for all the output signals.
94
CW LASER MEASURED
CW Laser Measured
Generates a continuous wave (CW) optical signal based on measurements. You can enter parameters such as linewidth, side mode suppression, and relative intensity noise (RIN).
Ports
Parameters
Main
Side Mode
Name and description Port type Signal type
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency Emission frequency
193.1 THz Hz,THz, nm [0,+INF[
Power 0 dBm W, mW, dBm ]-INF,+INF[
Linewidth 10 MHz — [0,+INF[
Initial phase 0 deg — ]-INF,+INF[
Name and description Default value
Default unit Units Value range
Calculate side modeDetermines if the signal output will have one side mode
False — — —
95
CW LASER MEASURED
RIN
Polarization
SeparationMode frequency separation from the laser center frequency
75 GHz Hz, GHz, THz, nm
[0,+INF[
Suppression ratioAttenuation of the side mode relative to the output power
30 dB — [0,+INF[
Independent side modeWhen enabled, the side mode has an independent power value that can change the total average power
False — — —
Name and description Default value
Default unit Units Value range
RINRelative intensity noise value
–130 dB/Hz — ]-INF,+INF[
Include RINDetermines if the RIN will be added to the output signal
False — — True, False
Measured powerValue of the power during the measurement of RIN
10 dBm W. mW, dBm ]-INF,+INF[
Name and description Default value
Units Value range
Azimuth Azimuth angle of output polarization
0 deg ]-90,90]
EllipticityEllipticity angle of output polarization
0 deg [-45,45]
Polarization filterDetermines the polarization of the filter
None — None, Polarization X, Polarization Y
Name and description Default value
Default unit Units Value range
96
CW LASER MEASURED
Simulation
Noise
Random numbers
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
IterationsNumber of times to repeat the calculation
Iterations — — [1,+INF[
Parameterized Parameterized — — —
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
Name and description Default value
Default unit Units Value range
Noise bandwidthBandwidth to increase noise bins
1 THz Hz, THz, nm [1e-100, 1e-100]
Noise bins spacingDetermines noise bins spacing
100 GHz Hz, GHz, THz, nm
[1, 1000]
Convert noise binsDetermines if the generated noise bins are incorporated into the signal
Convert noise bins
— — [0, 0]
Name and description Default value
Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
97
CW LASER MEASURED
Technical backgroundThis model is similar to the CW Laser — however, it includes additional effects, such as a side mode and RIN.
If the you enable the parameter Calculate side mode, the side mode will be generated according to:
where P is laser output power, s is the parameter Suppression ratio in linear scale, and is defined by the parameter Separation.
If the parameter Independent side mode is enabled, the average signal power will be greater than P, since it includes the contribution from the side mode. If this parameter is disabled, the output power will be P. This means that the signal will be scaled in order to give the same average power. The signal phase and polarization is calculated in the same way as the CW laser.
If the parameter Include RIN is enabled, the model generates noise bins with bandwidth and spacing that you define. The parameter RIN is the ratio of the mean-square optical intensity noise to the square of the average power [1][2]:
where is the mean-square optical intensity fluctuation at a specific frequency and is the parameter Measured power. This models estimates based on the parameters RIN and Measured power.
The signal phase and polarization is calculated in the same way as the CW laser, where the laser phase noise is modeled using a Gaussian random variable for the phase difference between two successive time instants with zero mean and a variance equal to , where is the laser Linewidth.
The probability density function is:
where is the phase difference between two successive time instants and dt is the time discretization.
The output is multiplied with a complex vector considering the state of polarization:
Eout t( ) P 1 s 2π∆ft( ) s 2π∆ft–( )ejϕcos+cos+[ ]=
∆f
RIN ∆P2⟨ ⟩
Pm2
---------------dB Hz⁄=
∆P2⟨ ⟩ Pm2
∆P2⟨ ⟩
2π ∆f ∆f
f ∆ϕ( ) 12π ∆fdt---------------------- e
∆ϕ2
4π∆fdt------------------–
⋅=
∆ϕ
EX t( )
EY t( ) 1 k–
kejθ P t( )⋅=
98
CW LASER MEASURED
The power splitting k and the phase difference are calculated from the parameters Azimuth and Ellipticity :
θα ε
2α( )tan 2 k 1 k–( ) θ( )cos1 2.k–
-----------------------------------------=
2ε( )sin 2 k 1 k–( ) θ( )sin=
99
CW LASER MEASURED
References:[1] Lau, K. Y. and Yariv, A., "Ultra-High Speed Semiconductor Laser", J. Quant. Elect., 21, 121-136,
(1985).
[2] Agrawal, G.P., Fiber-Optic Communication Systems, Second edition. John Wiley & Sons, Inc., N.Y., (1997).
100
DIRECTLY MODULATED LASER MEASURED
Directly Modulated Laser Measured
Directly modulated laser that allows you to specify the dynamic of the laser based on measured parameters. You can also enter parameters such as linewidth, chirp, side mode, suppression and relative intensity noise (RIN).
Ports
Parameters
Main
Measurements
Name and description Port type Signal type
Modulation Input Electrical
Output Output Optical
Name and description Default value
Default unit Units Value range
FrequencyEmission frequency
193.1 THz Hz,THz, nm [0,+INF[
Power 10 dBm W, mW, dBm ]-INF,+INF[
Extinction ratioSteady state power ratio between marks and spaces
10 dB — [0,+INF[
Linewidth 10 MHz — [0,+INF[
Initial phase 0 deg — ]-INF,+INF[
Name and description Default value
Default unit
Units Value range
OvershootPercentage of overshoot during the transition from 0 to 1 relative to the steady state power
30 % — [0,+INF[
101
DIRECTLY MODULATED LASER MEASURED
Side Mode
UndershootPercentage of undershoot during the transition from 0 to 1 relative to the steady state power
30 % — [0,+INF[
Rise timeDefined as the time from when the rising edges reaches 0% of the amplitude to the time it reaches 100% of the amplitude
1/(Bit rate) * 0.05 s s, ms, ns, ps [0,+INF[
Fall timeDefined as the time from when the falling edges reaches 100% of the amplitude to the time it reaches 0% of the amplitude
1/(Bit rate) * 0.05 s s, ms, ns, ps [0,+INF[
Damping time leading edgeRelaxation time when the signal overshoot reaches 1/e of the max value during the transition from 0 to 1
1/(Bit rate) * 0.5 s s, ms, ns, ps [0,+INF[
Damping time trailing edgeRelaxation time when the signal undershoot reaches 1/e of the min value during the transition from 1 to 0
1/(Bit rate) * 0.5 s s, ms, ns, ps [0,+INF[
Resonant frequency leading edgeFrequency of the oscillations in the transition from 0 to 1
(Bit rate) * 5 Hz Hz, MHz, GHz, THz
[0,+INF[
Resonant frequency trailing edgeFrequency of the oscillations in the transition from 1 to 0
(Bit rate) * 5 Hz Hz, MHz, GHz, THz
[0,+INF[
Name and description Default value
Default unit Units Value range
Calculate side modeDetermines if the signal output will have one side mode
False — — True, False
SeparationMode frequency separation from the laser center frequency
75 GHz Hz, GHz, THz, nm
[0,+INF[
Suppression ratioAttenuation of the side mode relative to the output power
30 dB — [0,+INF[
Name and description Default value
Default unit
Units Value range
102
DIRECTLY MODULATED LASER MEASURED
RIN
Chirp
Polarization
Simulation
Name and description Default value
Default unit Units Value range
RINRelative intensity noise value
–130 dB/Hz — ]-INF,+INF[
Include RINDetermines if the RIN will be added to the output signal
False — — —
Measured powerValue of the power during the measurement of RIN
10 dBm W, mW, dBm ]-INF,+INF[
Name and description Default value
Default unit Value range
Alpha parameter 0 — [-100, 100]
Adiabatic chirpResults from changes in the steady state carrier densities
0 1/(W.s) ]-INF,+INF[
Name and description Default value
Units Value range
Azimuth Azimuth angle of output polarization
0 deg ]-90,90]
EllipticityEllipticity angle of output polarization
0 deg [-45,45]
Polarization filterDetermines the polarization of the filter
None — None, Polarization X, Polarization Y
Name and description Default value
Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
Parameterized Parameterized — [1,+INF[
103
DIRECTLY MODULATED LASER MEASURED
Noise
Random numbers
Technical backgroundThis model is a different from the Laser Measured, where you can enter measured parameters and the model calculates the rate equation parameter by using sophisticated optimization routines. Here you can enter measured parameters that describe the laser dynamics by building the laser output signal.
The range of the amplitude of the signal input is normalized between 0 and 1. This means that this model converts the input signal to a sequence of squared pulses.
The parameter Power is the steady state value of the output power at the 1 level. The steady-state value for the power at the 0 level is calculated from the parameter Extinction ratio:
where P1 is the parameter Power, Er is the parameter Extinction ratio, and P0 is the steady-state power at the 0 level.
Name and description Default value
Default unit Units Value range
Noise bandwidthBandwidth to increase noise bins
1 THz Hz, THz, nm [1e-100, 1e-100]
Noise bins spacingDetermines noise bins spacing
100 GHz Hz, GHz, THz, nm
[1, 1000]
Convert noise binsDetermines if the generated noise bins are incorporated into the signal
Convert noise bins
— — [0, 0]
Name and description Default value
Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
Er 10 P1 P0⁄( )log=
104
DIRECTLY MODULATED LASER MEASURED
The measured parameters will be used to build P(t) (see Figure 1).
Figure 1 Measured parameters used to build P(t)
If you enable the parameter Calculate side mode, the side mode is generated according to:
where P is laser output power, s is the parameter Suppression ratio in linear scale, and is defined by the parameter Separation.
If the parameter Include RIN is enabled, the model will generate noise bins with bandwidth and spacing that you define. The parameter RIN is the ratio of the mean-square optical intensity noise to the square of the average power [1][2]:
where is the mean-square optical intensity fluctuation at a specific frequency and is the parameter Measured power.
This model estimates based on the parameters RIN and Measured power.
Eout t( ) P t( ) 1 s 2π∆ft( ) s 2π∆ft–( )ejϕcos+cos+[ ]=
∆f
RIN ∆P2⟨ ⟩
Pm2
---------------dB Hz⁄=
∆P2⟨ ⟩ Pm2
∆P2⟨ ⟩
105
DIRECTLY MODULATED LASER MEASURED
The chirp is modeled using:
where is the signal phase, is the parameter Alpha parameter or linewidth enhancement factor, and is the parameter Adiabatic chirp.
The signal phase and polarization is calculated in the same way as the CW laser, where the laser phase noise is modeled using a Gaussian random variable for the phase difference between two successive time instants with zero mean and a variance equal to , where is the laser Linewidth. The probability density function is:
where is the phase difference between two successive time instants and dt is the time discretization.
The output is multiplied with a complex vector considering the state of polarization:
The power splitting k and the phase difference is calculated from the parameters Azimuth and Ellipticity :
References:[1] Lau, K. Y. and Yariv, A., "Ultra-High Speed Semiconductor Laser", J. Quant. Elect., 21, 121-136,
(1985).
[2] Agrawal, G.P., Fiber-Optic Communication Systems, Second edition. John Wiley & Sons, Inc., N.Y., (1997).
dϕdt------
αe2
------ ddt-----InP t( ) κP t( )+=
ϕ αeκ
2π ∆f ∆f
f ∆ϕ( ) 12π ∆fdt---------------------- e
∆ϕ2
4π∆fdt------------------–
⋅=
∆ϕ
EX t( )
EY t( ) 1 k–
kejθ P t( )⋅=
θα ε
2α( )tan 2 k 1 k–( ) θ( )cos1 2.k–
-----------------------------------------=
2ε( )sin 2 k 1 k–( ) θ( )sin=
106
WDM TRANSMITTER
WDM Transmitter
This component is a WDM transmitter.
Ports
Parameters
Main
Name and description Port type Signal type
Output 1 Output Optical
Output 2 Output Optical
Output 3 Output Optical
Output 4 Output Optical
Output 5 Output Optical
Output 6 Output Optical
Output 7 Output Optical
Output 8 Output Optical
Name and description Default value Default Unit Value range
Number of output ports 8 — [1, 1000]
FrequencyEmission frequency of the first laser
193.1 THz, Hz, nm [30,+INF[
Frequency spacingFrequency spacing between adjacent lasers
100 GHz, THZ, Hz, nm
]-INF,+INF[
Power 0 dBm W, mW, dBm
Extinction ratio 10 dB [0,1000]
Linewidth 10 MHz [0, 1e+009[
Initial phase 0 deg [-1e+100,1e+100]
107
WDM TRANSMITTER
PRBS
Coding
Enhanced
Name and description Default value Default unit Value range
Bit rate Bit rate Bits/s
MBits/s
GBits/s
[0, 1e+012]
OrderlogOrder of the PRBS generator
(Sequence length)/log(2) — [2,30]
Number of leading zeros 1 — [0,+INF[
Number of trailing zeros 1 — [0,+INF[
Name and description Default value Default unit Value range
Modulation typeDefines the signal modulation type
NRZ Off, NRZ, RZ
Duty cycleOrder of the PRBS generator
—
Rise timeDefined as the time from when the rising edge reaches 10% of the amplitude to the time it reaches 90% of the amplitude
0.05 bit [0,1]
Fall timeDefined as the time from when the falling edge reaches 90% of the amplitude to the time it reaches 10% of the amplitude
0.05 bit [0,1]
Name and description Default value Default unit Value range
Transmitter type EML — EML, DML
OvershootPercentage of overshoot during the transition from 0 to 1 relative to the steady state power
30 % —
UndershootPercentage of undershoot during the transition from 0 to 1 relative to the steady state power
30 % —
108
WDM TRANSMITTER
Side Mode
RIN
Damping time leading edgeRelaxation time when the signal overshoot reaches 1/e of the max value during the transition from 0 to 1
1/(Bit rate) * 0.5 s s, ms, ns, ps
Damping time trailing edgeRelaxation time when the signal undershoot reaches 1/e of the min value during the transition from 1 to 0
1/(Bit rate) * 0.5 s s, ms, ns, ps
Resonant frequency leading edgeFrequency of the oscillations in the transition from 0 to 1
(Bit rate) * 5 Hz Hz, MHz, GHz, THz
Resonant frequency trailing edgeFrequency of the oscillations in the transition from 1 to 0
(Bit rate) * 5 Hz Hz, MHz, GHz, THz
Name and description Default value
Default unit Units Value range
Calculate side modeDetermines if the signal output will have one side mode
False — — True, False
SeparationMode frequency separation from the laser center frequency
75 GHz Hz, GHz, THz, nm
[0,+INF[
Suppression ratioAttenuation of the side mode relative to the output power
30 dB — [0,+INF[
Name and description Default value
Default unit Units Value range
RINRelative intensity noise value
–130 dB/Hz — ]-INF,+INF[
Include RINDetermines if the RIN will be added to the output signal
False — — —
Measured powerValue of the power during the measurement of RIN
10 dBm W, mW, dBm ]-INF,+INF[
Name and description Default value Default unit Value range
109
WDM TRANSMITTER
Chirp
Polarization
Simulation
Name and description Default value
Default unit Value range
Alpha parameter 0 rad/W [-1000, 1000]
Adiabatic chirpResults from changes in the steady state carrier densities
0 1/s [-1000, 1000]
Name and description Default value
Units Value range
Azimuth Azimuth angle of output polarization
0 deg ]-90,90]
EllipticityEllipticity angle of output polarization
0 deg [-45,45]
Polarization filterDetermines the polarization of the filter
None — None, Polarization X, Polarization Y
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
IterationsNumber of times to repeat the calculation
Iterations — — [1,+INF[
Parameterized Parameterized — — —
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
110
WDM TRANSMITTER
Noise
Random numbers
Name and description Default value
Units Value range
Noise bandwidthBandwidth to increase noise bins
Sample rate THz Hz, THz, nm
Noise bins spacingDetermines noise bins spacing
Sample rate GHz Hz, GHz, THz, nm
Convert noise binsDetermines if the generated noise bins are incorporated into the signal
Convert noise bins
— —
Name and description Default value
Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
111
WDM TRANSMITTER
Technical BackgroundWDM systems require multiple transmitters and different parameters for each one of them. In addition, they also require different modulation schemes and formats. By using multiple components, users can customize designs, but it is time consuming. The WDM Transmitter encapsulates different components, allowing users to select different modulation formats and schemes for multiple channels in one single component. It is a transmitter array that allows for different modulation types and schemes.
The block diagram for each WDM channel transmitter is shown below.
The first stage is the PRBS; the same engine used in the Pseudo-Random Bit Sequence Generator component is used in this stage. Parameters Bit rate, Order, Number of leading and trailing zeros are used in the internal Pseudo-Random Bit Sequence Generator. A different seed will be used for each bit sequence for each WDM channel. The operation and parameters of the PRBS component is described in the technical background of the Pseudo-Random Bit Sequence Generator.
The second stage is the Coding/Modulation; the parameter Modulation type has three options: RZ, NRZ and Off. RZ and NRZ coding is generated by the engines of the RZ Pulse Generator and NRZ Pulse Generator respectively. A CW operation of the
112
WDM TRANSMITTER
transmitter is possible by selecting Off as modulation type. The Duty cycle parameter is used when modulation type RZ is selected. The operations and parameters of the electrical pulse generators are described in the technical background of the RZ and NRZ Pulse Generators.
The last stage is the optical source and modulation scheme; by using the parameter Transmitter type the user can select between a external modulated laser scheme (EML) or a directly modulated laser scheme (DML). The laser engine used in this stage is the same used in the Directly Modulated Laser Measured component. The operation and parameters of this component are described in the technical background of the Directly Modulated Laser Measured.
By using 3R regenerators, it is possible to recover the original bit sequence and electrical signals for all the WDM channels:
113
WDM TRANSMITTER
Notes:
114
PSEUDO-RANDOM BIT SEQUENCE GENERATOR
Pseudo-Random Bit Sequence Generator
Generates a Pseudo Random Binary Sequence (PRBS) according to different operation modes. The bit sequence is designed to approximate the characteristics of random data.
Ports
Parameters
Main
Name and description Port type Signal type
Bit sequence Output Binary
Name and description Default value Default unit Value range
Bit rate Bit rate Bits/s
MBits/s
GBits/s
[0, 1e+012]
Operation mode Order — Probability, Order, Alternate, Ones, Zeros
OrderlogOrder of the PRBS generator
(Sequence length)/log(2) — [2,30]
Mark probabilityProbability of ones in the sequence
0.5 — [0,1]
Number of leading zeros (Time window * 3 / 100 ) * Bit rate — [0,+INF[
Number of trailing zeros (Time window * 3 / 100 ) * Bit rate — [0,+INF[
115
PSEUDO-RANDOM BIT SEQUENCE GENERATOR
Simulation
Random numbers
Technical backgroundThis model generates a sequence of N bits:
Tw is the global parameter Time window and Br is the parameter Bit rate.
The number of bits generated is . and are the Number of leading zeros and the Number of trailing zeros.
Operation mode controls the algorithm used to generate the bit sequence:• Probability: Random number generator is used, with parameter Mark probability
specifying the probability of ones in the sequence• Order: PRBS generator[1] with Order k is used to generate a sequence with
period of 2k-1• Alternate: Alternate sequence of ones and zeros is generated• Ones: A sequence of ones is generated• Zeros: A sequence of zeros is generated
References[1] Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T., Numerical Recipes in C.
Cambridge University Press, (1991).
Name and description Default value
Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
IterationsNumber of times to repeat the calculation
Iterations — [1, 1e+009]
Name and description Default value
Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for bit generation
0 — [0,4999]
where N TwBr=
NG N nl– nt–=
NG nl nt
116
USER-DEFINED BIT SEQUENCE GENERATOR
User-Defined Bit Sequence Generator
Generates a bit sequence that is user-defined.
Ports
Parameters
Main
Name and description Port type Signal type
Bit sequence Output Binary
Name and description Default value Units Value range
Bit rate Bit rate Bits/s
MBits/s
GBits/s
[0,+INF[
Load from fileDetermines whether or not the component will load the bit sequence from the file
False — True, False
FilenameFile with the bit sequence
Sequence.dat — Filename
Bit sequenceUser-defined bit sequence
0101101110 — String
Number of leading zeros (Time window * 3 / 100 ) * Bit rate — [0, 1000]
Number of trailing zeros (Time window * 3 / 100 ) * Bit rate — [0, 1000]
117
USER-DEFINED BIT SEQUENCE GENERATOR
Simulation
Technical backgroundYou can enter the string Bit sequence or choose Load from file. In this, case the parameter Filename is enabled.
All bit files are formatted containing one bit per line, e.g. the bit file representing the sequence "01011..." has the following form:
The sequence length is defined by:
N = TwBr
Tw is the global parameter Time window and Br is the parameter Bit rate. If the user-defined sequence is shorter than the N, the sequence will be repeated until the length is equal to N.
Name and description Default value
Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
IterationsNumber of times to repeat the calculation
1 — [1, 1e+009]
0
1
0
1
1
118
MACH-ZEHNDER MODULATOR
Mach-Zehnder Modulator
Simulates a Mach-Zehnder modulator using an analytical model.
Ports
Parameters
Main
Simulation
Technical backgroundThe Mach-Zehnder modulator is an intensity modulator based on an interferometic principle. It consists of two 3 dB couplers which are connected by two waveguides of equal length (see Figure 1). By means of an electro-optic effect, an externally applied voltage can be used to vary the refractive indices in the waveguide branches.
Name and description Port type Signal type
Modulation Input Electrical
Carrier Input Optical
Output Output Optical
Name and description Default value Default unit Value range
Extinction ratio 30 dB [0,+INF[
Negative signal chirp False — True, False
Symmetry factor –1 — [-1,1[
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
119
MACH-ZEHNDER MODULATOR
The different paths can lead to constructive and destructive interference at the output, depending on the applied voltage. Then the output intensity can be modulated according to the voltage.
Figure 1 Mach-Zehnder modulator
The equations that describe the behavior of the MZ modulator are:
where is the phase difference between the two branches and is defined as:
with
and
is the signal phase change defined as:
where the parameter SC is –1 if negative signal chirp is true, or 1 if negative signal chirp is false. extract is the extinction ratio, SF is the symmetry factor, and modulation(t) is the electrical input signal. The electrical input signal is normalized between 0 and 1.
For parameterized and noise bins signals, the average power is calculated according to the above.
Eout t( ) Ein t( ) ∆θ t( )( )cos⋅ j ∆φ t( )⋅( )exp⋅=
∆θ
∆θ t( ) π2--- 0.5 ER Modulation t( ) 0.5–( )⋅–( )⋅=
ER 1 4π--- arc 1
extrat-------------------
tan⋅–=
∆φ
∆φ t( ) SC ∆θ t( ) 1 SF+( ) 1 SF–( )⁄⋅⋅=
120
ELECTROABSORPTION MODULATOR
Electroabsorption Modulator
Simulates an Electro-absorption modulator using an analytical model.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Modulation Input Electrical
Carrier Input Optical
Output Output Optical
Name and description Default value Units Value range
Modulation index 0.95 — [0 ,1[
Chirp factor 0 — ]-INF, +INF[
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
121
ELECTROABSORPTION MODULATOR
Technical backgroundIn this model, the optical carrier is modulated externally by the electrical modulation signal, (see Figure 1).
Figure 1 EA modulator
Assuming that the optical input signal is Ein, the following equation describes the behavior of the model:
where Eout(t) is the output optical signal, is the chirp factor, and Mod(t) is defined as
where MI is the modulation index and modulation(t) is the electrical input signal. The electrical input signal is normalized between 0 and 1.
For parameterized and noise bins signals, the average power is calculated according to the above.
Eout t( ) Ein t( ) Mod t( ) jα2--- Mod t( )( )ln⋅
exp⋅ ⋅=
α
Mod t( ) 1 MI–( ) MI+ modulation t( )⋅=
122
AMPLITUDE MODULATOR
Amplitude Modulator
Simulates an ideal amplitude modulator.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Modulation Input Electrical
Carrier Input Optical
Output Output Optical
Name and description Default value Units Value range
Modulation index 1 — [0,1]
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
Yes — True, False
123
AMPLITUDE MODULATOR
Technical backgroundIn this model, the optical carrier is modulated externally by the electrical modulation signal. Assuming that the optical input signal is Ein, the following equations describe the behavior of the model:
where Eout(t) is the output optical signal and Mod(t) is defined as
where MI is the modulation index and modulation(t) is the electrical input signal. The electrical input signal is normalized between 0 and 1.
For parameterized and noise bins signals, the average power is calculated according to the above.
Eout t( ) Ein t( ) Mod t( )⋅=
Mod t( ) 1 MI–( ) MI modulation t( )⋅+=
124
PHASE MODULATOR
Phase Modulator
Simulates an ideal phase modulator.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Modulation Input Electrical
Carrier Input Optical
Output Output Optical
Name and description Default value Units Value range
Phase deviation 90 deg ]-INF,+INF[
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
125
PHASE MODULATOR
Technical backgroundIn this model, the electrical modulation signal imposes a phase modulation on an optical carrier. Assuming that the optical input signal is Ein, the following equation describes the behavior of the model.
where Eout(t) is the output optical signal, is the phase deviation, and modulation(t) is the electrical input signal. The electrical input signal is normalized between 0 and 1.
The parameterized and noise bins signals are not affected by this modulator.
Eout t( ) Ein t( ) j ∆φ modulation t( )⋅ ⋅( )exp⋅=
∆φ
126
FREQUENCY MODULATOR
Frequency Modulator
Simulates an ideal frequency modulator.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Modulation Input Electrical
Carrier Input Optical
Output Output Optical
Name and description Default value
Default unit Unit Value range
Frequency deviation 10 GHz Hz, GHz, THz [0,+INF[
Name and description Default value
Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
127
FREQUENCY MODULATOR
Technical backgroundIn this model, the electrical modulation signal imposes a frequency modulation on an optical carrier. Assuming that the optical input signal is Ein, the following equation describes the behavior of the model:
where Eout(t) is the output optical signal, is the frequency deviation, and modulation is the electrical input signal. The electrical input signal is normalized between 0 and 1.
The parameterized and noise bins signals are not affected by this modulator.
Eout t( ) Ein t( ) j 2π ∆f modulation τ( ) 0.5–( )⋅ τd⋅0
t
∫⋅
exp⋅=
∆f τ( )
128
DUAL DRIVE MACH-ZEHNDER MODULATOR MEASURED
Dual Drive Mach-Zehnder Modulator Measured
Simulates a Mach-Zehnder modulator with dual-drive modulation using measured parameters.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Modulation Input Electrical
Carrier Input Optical
Output Output Optical
Name and description Default value Default unit Value range
Splitting Ratio 1.3 — [0,10000]
Modulator Type Phase-Shift — Conventional, Phase-Shift
Bias Voltage 1 –2.8 V ]-INF, +INF[
Bias Voltage 2 –1.1 V ]-INF, +INF[
Normalize electrical signal True — True, False
Modulation Voltage12 1.2 V [0 , +INF[
Absorption / Phase FilenameFile with the measured absorption and phase
AbsorptionPhase.dat
— —
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
129
DUAL DRIVE MACH-ZEHNDER MODULATOR MEASURED
Graphs
Technical backgroundIn this model, you can specify the dependence of the measured absorption and phase on applied voltage for a Mach-Zehnder modulator. You can use the default characteristics curves or choose to load from Filename.
For a modulator with the same input and output Y-branch splitting ratios, the output signal is:
where SR = P1/P2 is the Y-branch power splitting ratio
is defined as:
for the normalized case
where is the bias voltage, is the peak-to-peak voltage, and is the normalized modulation waveform with a peak-to-peak amplitude of 1 and an average value of 0. The electrical input signal can be normalized between 0.5 and -0.5.
for the non-normalized case.
The model utilizes a Dual drive (push and pull) modulation ( .
Name and description X Title Y Title
Measured absorption Voltage (V) Absorption (dB)
Measured phase Voltage (V) Phase (radians)
is the attenuation constant
is the phase constant
L is the interaction length of the modulator arm
is 0 radians for a conventional modulator and π radians for phase-shift modulator
V1 and V2 are voltages applied to arms 1 and 2, respectively
I is the intensity of the optical signal
is the phase
E V1 V2,( )E0
1 SR+---------------- SR
∆αa V1( )2
--------------------- j ∆β V1( )⋅+ L–
∆αa V2( )2
--------------------- j ∆β V2( )⋅+ L– j φ0⋅–
exp+exp⋅=
E V1 V2,( ) I V1 V2,( ) j Φ V1 V2,( )⋅( )exp⋅≡
∆αa 2⁄
∆β
φ0
Φ
Vi i 1 2,=( )
Vi t( ) Vbi Vmod12 v t( )⋅+=
Vbi Vmod12 v t( )
Vi t( ) Vbi Vmod± t( )=
∆V1 ∆V2–=
130
DUAL DRIVE MACH-ZEHNDER MODULATOR MEASURED
The model has stored default curves characteristics of a Mach-Zehnder modulator. The dependence of the measured absorption and phase of the optical signal on applied voltage for each arm of a modulator is illustrated in Figure 1.
Figure 1 Default characteristics of absorption and phase in the Dual Mach-Zehnder model
131
DUAL DRIVE MACH-ZEHNDER MODULATOR MEASURED
Reference:[1] Cartledge, J. C., “Combining self-phase modulation and optimum modulation conditions to
improve performance of 10 Gb/s transmission systems using MQW Mach-Zehnder modulators”, J. Light. Techn., 18, 647-654, (2000).
132
ELECTROABSORPTION MODULATOR MEASURED
Electroabsorption Modulator Measured
Simulates an Electro-absorption modulator using measured parameters.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Modulation Input Electrical
Carrier Input Optical
Output Output Optical
Name and description Default value Default unit Value range
Bias voltage –1 V ]-INF, +INF[
Normalize electrical signal True — True, False
Modulation voltage (peak-to-peak) 2 V [0 , +INF[
Absorption / Alpha FilenameFile with the measured absorption and α-parameter αm
AbsorptionAlpha.dat — —
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
133
ELECTROABSORPTION MODULATOR MEASURED
Graphs
Technical backgroundIn this model, you can specify the dependence of the measured absorption and -parameter- on the applied voltage for an EA modulator. You can use the default characteristic curves or choose to load from file. In this case, the parameter Filename is enabled.
In the case of the EA modulator, the output signal response to an applied voltage is:
where IV is the voltage-dependent intensity of the signal.
While Equation 1 is an accurate result, it is not in the most convenient form for simulation purposes when empirical equations for and are obtained from a fitting to measured results. The determination of the argument of the exponential function in Equation 1 requires function evaluation and integration.
The modulator output signal given by Equation 1 can also be written in the convenient form using a voltage-dependent parameter as:
A comparison of the phase terms in Equation and Equation 2 yields
Equation 3 shows how the attenuation constant and α-parameter- jointly combine to determine . Using Equation 2, with determined from measurements of and , the evaluation of the argument of the exponent only requires function evaluation.
Name and description X Title Y Title
Measured absorption Voltage (V) Absorption (dB)
Measured alpha-parameter Voltage (V) Alpha-parameter
Calculated alpha-parameter Voltage (V) Alpha-parameter
(1)
(2)
(3)
ααm
E V( ) I V( ) j12--- αm V( ) I V( )( )lnd∫
exp=
αm V( ) I V( )
I 1 jα+( ) 2⁄ αr V( )
E V( ) I V( )1 jαr V( )+( ) 2⁄
=
αr V( ) 1γ V( )----------- αm V( ) γ V( )d⋅∫=
γ V( ) αm V( )αr V( ) αr V( )
αm V( ) I V( )
134
ELECTROABSORPTION MODULATOR MEASURED
The default characteristics curves stored in the component, the dependence of the measured absorption, and α-parameter- on applied voltage, is illustrated in Figure 1.
Figure 1 Dependence of the absorption and on the applied voltage for an MQW-EAM
For this component, the electrical input signal can be normalized between 0.5 and -0.5. Then, the voltage applied to the modulator is given by:
where Vb is the bias voltage, Vmod is the peak-to-peak voltage, and v(t) is the normlized modulation waveform (electrical input signal ) with a peak-to-peak amplitude of 1 and an average value of 0.
(4)
αm V( )
αm
V t( ) Vb Vmod v t( )⋅+=
135
ELECTROABSORPTION MODULATOR MEASURED
Notes:
136
SINGLE DRIVE MACH-ZEHNDER MODULATOR MEASURED
Single Drive Mach-Zehnder Modulator Measured
Simulates a Mach-Zehnder modulator with single drive modulation using measured parameters.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Modulation Input Electrical
Carrier Input Optical
Output Output Optical
Name and description Default value Default unit Value range
Splitting Ratio 1.3 — [0,10000]
Modulator Type Phase-Shift — Conventional, Phase-Shift
Bias Voltage 1 –2.8 V ]-INF, +INF[
Bias Voltage 2 –1.1 V ]-INF, +INF[
Normalize electrical signal True — True, False
Modulation Voltage 1.5 V [0 , +INF[
Operation mode Change in V2 = 0 — Change in V1 = 0, Change in V2 = 0
Absorption / Phase FilenameFile with the measured absorption and phase
AbsorptionPhase.dat — —
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
137
SINGLE DRIVE MACH-ZEHNDER MODULATOR MEASURED
Graphs
Technical backgroundIn this model, you can specify the dependence of the measured absorption and phase on applied voltage for a Mach-Zehnder modulator. You can use the default characteristics curves or choose to load from Filename.
For a modulator with the same input and output Y-branch splitting ratios, the output signal is:
where SR = P1/P2 is the Y-branch power splitting ratio
Vi(i=1,2) is defined as:
for the normalized case
where Vbi is the bias voltage, Vmodi is the peak-to-peak voltage, v(t) is the normalized modulation waveform with a peak-to-peak amplitude of 1 and an average value of 0. The electrical input signal is normalized between 0.5 and -0.5.
for the non-normalized case
The model utilizes a single drive modulation, i.e., is 0 in one of the arms.
The model has stored default curves characteristics of a Mach-Zehnder modulator. The dependence of the measured absorption and phase of the optical signal on applied voltage for each arm of a modulator is illustrated in Figure 1.
Name and description X Title Y Title
Measured absorption Voltage (V) Absorption (dB)
Measured phase Voltage (V) Phase (radians)
is the attenuation constant
is the phase constant
L is the interaction length of the modulator arm
is 0 radians for a conventional modulator and π radians for phase-shift modulator
V1 and V2 are voltages applied to arms 1 and 2, respectively
I is the intensity of the optical signal
is the phase
E V1 V2,( )E0
1 SR+---------------- SR
∆αa V1( )2
--------------------- j ∆β V1( )⋅+ L–
∆αa V2( )2
--------------------- j ∆β V2( )⋅+ L– j φ0⋅–
exp+exp⋅=
E V1 V2,( ) I V1 V2,( ) j Φ V1 V2,( )⋅( )exp⋅≡
∆αa 2⁄
∆β
φ0
Φ
Vi t( ) Vbi Vmodi v t( )⋅+=
Vi t( ) Vbi Vmod± t( )=
Vmod
138
SINGLE DRIVE MACH-ZEHNDER MODULATOR MEASURED
Figure 1 Default characteristics of absorption and phase in the Single Mach-Zehnder mode
139
SINGLE DRIVE MACH-ZEHNDER MODULATOR MEASURED
Reference:[1] Cartledge, J. C., “Combining self-phase modulation and optimum modulation conditions to
improve performance of 10 Gb/s transmission systens using MQW Mach-Zehnder modulators”, J. Light. Techn., 18, 647-654, (2000).
140
DUAL PORT DUAL DRIVE MACH-ZEHNDER MODULATOR MEASURED
Dual Port Dual Drive Mach-Zehnder Modulator Measured
Simulates a Mach-Zehnder modulator with dual-drive modulation using two ports with measured parameters.
Ports
ParametersMain
Simulation
Name and description Port type Signal type
Modulation 1 Input Electrical
Modulation 1 Input Electrical
Carrier Input Optical
Output Output Optical
Name and description Default value Default unit Value range
Splitting Ratio 1.3 — [0,10000]
Modulator Type Phase-Shift — Conventional, Phase-Shift,
Bias Voltage 1 –2.8 V ]-INF, +INF[
Bias Voltage 2 –1.1 V ]-INF, +INF[
Normalize electrical signal True — True, False
Modulation Voltage12 1.2 V [0 , +INF[
Absorption / Phase FilenameFile with the measured absorption and phase
AbsorptionPhase.dat — —
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
141
DUAL PORT DUAL DRIVE MACH-ZEHNDER MODULATOR MEASURED
Graphs
Technical backgroundIn this model, you can specify the dependence of the measured absorption and phase on applied voltage for a Mach-Zehnder modulator. You can use the default characteristics curves or choose to load from Filename.
For a modulator with the same input and output Y-branch splitting ratios, the output signal is:
where is the Y-branch power splitting ratio
is defined as:
for the normalized case
where is the bias voltage, is the peak-to-peak voltage, and is the normalized modulation waveform with a peak-to-peak amplitude of 1 and an average value of 0. The electrical input signal is normalized between 0.5 and -0.5.
for the non-normalized case.
The model utilizes a Dual drive (push and pull) modulation ( .
Name and description X Title Y Title
Measured absorption Voltage (V) Absorption (dB)
Measured phase Voltage (V) Phase (radians)
is the attenuation constant
is the phase constant
L is the interaction length of the modulator arm
is 0 radians for a conventional modulator and π radians for phase-shift modulator
V1 and V2 are voltages applied to arms 1 and 2, respectively
I is the intensity of the optical signal
is the phase
E V1 V2,( )E0
1 SR+---------------- SR
∆αa V1( )2
--------------------- j ∆β V1( )⋅+ L–
∆αa V2( )2
--------------------- j ∆β V2( )⋅+ L– j φ0⋅–
exp+exp⋅=
E V1 V2,( ) I V1 V2,( ) j Φ V1 V2,( )⋅( )exp⋅≡
SR P1 P2⁄=
∆αa 2⁄
∆β
φ0
Φ
Vi i 1 2,=( )
Vi t( ) Vbi Vmodi± v t( )⋅=
Vbi Vmodi v t( )
Vi t( ) Vbi Vmodi± t( )=
∆V1 ∆V2–=
142
DUAL PORT DUAL DRIVE MACH-ZEHNDER MODULATOR MEASURED
The model has stored default curves characteristics of a Mach-Zehnder modulator. The dependence of the measured absorption and phase of the optical signal on applied voltage for each arm of a modulator is illustrated in Figure 1.
Figure 1 Default characteristics of absorption and phase in the Dual Mach-Zehnder model
143
DUAL PORT DUAL DRIVE MACH-ZEHNDER MODULATOR MEASURED
Reference:[1] Cartledge, J. C., “Combining self-phase modulation and optimum modulation conditions to
improve performance of 10 Gb/s transmission systems using MQW Mach-Zehnder modulators”, J. Light. Techn., 18, 647-654, (2000).
144
LINBO3 MACH-ZEHNDER MODULATOR
LiNbO3 Mach-Zehnder Modulator
This component simulates a Lithium Niobate Mach-Zehnder modulator based on basic parameters.
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Electrical
Input 3 Input Electrical
Output 1 Output Optical
Name and description Default value Default unit Value range
Extinction ratio 20 dB [0,+INF[
Switching bias voltage
DC voltage required to turn the modulator from the OFF state to the ON state, or vice versa
4 V [0,+INF[
Switching RF voltage
RF voltage required to turn the modulator from the OFF state to the ON state, or vice versa
4 V ]-INF,+INF[
Bias voltage1 0 V ]-INF,+INF[
Bias voltage2 4 V ]-INF,+INF[
Insertion loss 5 dB [0,+INF[
Normalize electrical signal True — True, False
Modulation voltage1 0 V ]-INF,+INF[
Modulation voltage2 4 V ]-INF,+INF[
145
LINBO3 MACH-ZEHNDER MODULATOR
Bandwidth Response
Simulation
Technical BackgroundThe Mach-Zehnder structure consists of an input optical branch, which splits the incoming light into two arms, followed by two independent optical arms, which are subsequently recombined by the output optical branch. Application of an electrical signal to one of the optical arms controls the degree of interference at the output optical branch and therefore controls the output intensity.
The optical field at the output of the modulator is given by:
where is the input signal
and are the RF modulating electrical voltage
and are the DC bias voltage applied to arm one and two, respectively
Name and description Default value Units Value range
Load transfer functionDetermines whether you want to load a modulator transfer function or use an ideal one.
False — True, False
File frequency unitDetermines the frequency unit of the file.
Hz — Hz, THz
File formatDetermines the format of the file.
Power — Power; Phase; Power Phase; Real, Imag.
Linear scaleDetermines whether or not the data is in linear scale.
True — True, False
HF filenameFile with the transfer function (S21)
Filter.dat — —
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
EO t( )Ein t( )
10 insertionloss 20⁄( )--------------------------------------------- γ e
j π v2 t( ) VπRF⁄ j π vbias2⋅ ⋅+ VπDC⁄⋅ ⋅( ) ⋅ 1 γ–( ) e
j π v1 t( ) VπRF⁄ j π vbias1⋅ ⋅+ VπDC⁄⋅ ⋅( )⋅+( )⋅=
Ein t( )
v1 t( ) v2 t( )
vbias1 vbias2
146
LINBO3 MACH-ZEHNDER MODULATOR
denotes the power splinting (combining) ration of arm two for the input (output, respectively) Y-branch waveguide, and is given by:
where .
and , the DC bias voltages, are included separately as parameters due to the possibility of the (Switching Bias Voltage) to be different from the Switching RF Voltage.
If the Switching Bias Voltage is equal to the Switching RF Voltage, and the Normalize Electrical Signal parameter is False, the bias voltage can be included in the electrical signal.
The optical power and phase of the modulator output are determined in response to the modulating voltage waveforms. The modulator transfer function relates the effective drive voltage to the applied drive voltage. This component can also load the modulator transfer function data from file or consider an ideal transfer function.
The file is formatted containing two items per line, the frequency and filter measurement. The parameter File frequency unit determines the frequency unit of the first item; it can be Hz or THz.
According to the parameter File format, the second item can be one value (Power or Phase) or two values (Power and Phase or Real and Imag):
Power (Phase is set to zero, assuming frequency units THz)
Power Phase
193.10 0
193.11 0.5
193.12 0.5
193.13 0
193.14 0 0
193.15 0.5 3.14
193.16 0.5 3.14
193.17 0 0
γ
γ 1 1εr
--------–
2⁄=
εr 10ExtRatio 10⁄=
vbias1 vbias2VπDC
147
LINBO3 MACH-ZEHNDER MODULATOR
Real Imag
Phase (Power is set to one)
When the Normalize electrical signal parameter is True, the electrical signals of port1 and port2 are normalized between -0.5 and 0.5. In this case, the amplitude of each RF electrical signal considered in and will be the values in the modulation voltage parameters divided by 2.
References[1] Cartledge, J. C., Rolland, C., Lemerle, S., and Solheim, A., “Theoretical performance of 10 Gb/s
lightwave systems using a III-V semiconductor Mach-Zehnder modulator.”, IEEE Phot. Techn. Letters., 6, 282-284, (1994).
[2] Cartledge, J.C., "Performance of 10 Gb/s lightwave systems based on lithium niobate Mach-Zehnder modulators with asymmetric Y-branch waveguides". IEEE Phot. Techn. Letters., 7, 1090 -1092, (1995).
193.18 0 0
193.19 -0.5 7.9-e-4
193.20 -0.5 7.9-e-4
193.21 0 0
193.22 0
193.23 3.14
193.24 3.14
193.253 0
v1 t( ) v2 t( )
148
Optical Fibers LibraryThis section contains information on the following optical fibers.
• Optical fiber data• Optical fiber• Linear Multimode fiber• Nonlinear Dispersive fiber (obsolete)
149
Notes:
150
OPTICAL FIBER DATA
Optical fiber data
SMF-28The SMF-28 model used in OptiSystem has the following characteristics:
Figure 1 Attenuation
Figure 2 Group Velocity Dispersion
151
OPTICAL FIBER DATA
Figure 3 Effective Area
Figure 4 Group Delay
Attenuation curve shows a minimum of for a wavelength of .
GVD curve reveals a dispersion of at with a dispersion slope of .
Effective area at is .
Group delay is .
This model can be varied in any way because you have the ability to change any particular parameter. Create a new file and then load it into the appropriate section, or just set the parameter to 'Constant' and enter a value. The Nonlinear Fiber model is very flexible, because it has the ability to model practically every manufactured fiber that exists on the market today.
0.185 dBm 1550 nm
16.5 ps/nm/km 1550 nm0.05 ps/nm2 km⁄
1550 nm 76.5 µm2
4897650 ps/km
152
OPTICAL FIBER DATA
+D NZDSF modelThe +D NZDSF model used in OptiSystem has the following characteristics:
Figure 5 Attenuation
Figure 6 Group Velocity Dispersion
153
OPTICAL FIBER DATA
Figure 7 Effective Area
Figure 8 Group Delay
Attenuation curve shows a minimum of for a wavelength of .
GVD curve reveals a dispersion of at with a dispersion slope of .
The effective area at is .
Group delay is .
0.185 dBm 1550 nm
4.5 ps/nm/km 1550 nm0.01 ps/nm2 km⁄
1550 nm 71.5 µm2
4895870 ps/km
154
OPTICAL FIBER DATA
-D NZDSF modelThe -D NZDSF model used in OptiSystem has the following characteristics:
Figure 9 Attentuation
Figure 10 Group Velocity Dispersion
155
OPTICAL FIBER DATA
Figure 11 Effective Area
Figure 12 Group Delay
Attenuation curve shows a minimum of for a wavelength of .
GVD curve reveals a dispersion of at with a dispersion slope of .
Effective area at is .
Group delay is .
0.185 dBm 1550 nm
7.5 ps/nm/km– 1550 nm0.18 ps/nm2 km⁄
1550 nm 92 µm2
4890750 ps/km
156
OPTICAL FIBER DATA
CDF (Standard)The DCF model used in OptiSystem has the following characteristics:
Figure 13 Attenuation
Figure 14 Group Velocity Dispersion
157
OPTICAL FIBER DATA
Figure 15 Effective Area
Figure 16 Group Delay
Attenuation curve shows a minimum of for a wavelength of .
GVD curve reveals a dispersion of at with a dispersion slope of .
Effective area at is .
Group delay is .
0.3 dBm 1600 nm
82 ps/nm/km– 1550 nm4.5 ps/nm2 km⁄
1550 nm 32 µm2
4914000 ps/km
158
OPTICAL FIBER
Optical fiber
The optical fiber component simulates the propagation of an optical field in a single-mode fiber with the dispersive and nonlinear effects taken into account by a direct numerical integration of the modified nonlinear Scrödinger (NLS) equation (when the scalar case is considered) and a system of two, coupled NLS equations when the polarization state of the signal is arbitrary. The optical sampled signals reside in a single frequency band, hence the name total field [1]. The parameterized signals and noise bins are only attenuated.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Symbol Default value Default unit Value range
User defined reference wavelength
If TRUE, frequency value of “Reference wavelength” is used internally as ‘zero’ (or reference) frequency in spectrum of signal envelope. Values of parameters (attenuation, dispersion) are assumed to correspond to this frequency. If parameters are wavelength-dependent (from files), they are evaluated at this frequency. If FALSE, central frequency of simulated band is used.
TRUE — TRUE/FALSE
Reference wavelength
Value of user defined/specified reference wavelength.
1550 nm [100, 2000]
Length
Fiber length
50 km [0, 100,000]
λ0
L
159
OPTICAL FIBER
Dispersion
Attenuation effect
If TRUE, attenuation effect is enabled.
— TRUE — TRUE/FALSE
Attenuation data type
Defines the attenuation as a fixed constant value or as a wavelength dependent curve taken from a file. If ‘constant’, value from “Attenuation” tab in component is used.
— Constant — Constant/ From File
Attenuation
Specified value is used if “Attenuation data type” is set to ‘constant’. If ‘from file’, the value is ignored.
0.2 dB/km [0, 1010]
Attenuation vs. wavelength
Defines the attenuation as a wavelength dependent curve in a file.
— — — —
Name and description Symbol Default value Default unit Value range
Group velocity dispersion
If TRUE, the GVD effect is enabled.
— TRUE — TRUE/FALSE
Third order dispersion
If TRUE, the TOD effect is enabled.
— TRUE — TRUE/FALSE
Frequency domain parameters
Defines domain in which dispersion parameters are specified. If TRUE, frequency domain is used and dispersion effect is specified in terms of and
. Otherwise, wavelength domain is used ( and ).
Dispersion data type
Defines if dispersion parameter valuesare read from component tabs, or taken from a file
Constant — Constant/ From File
Beta 2
Value of the GVD parameter in the frequency domain
-20 ps2/km [-10100, 10100]
Beta 3
Value of the GVD parameter in the frequency domain
-20 ps3/km [-10100, 10100]
Name and description Symbol Default value Default unit Value range
α
β2β3 D
S
β2
β3
160
OPTICAL FIBER
The parameter “Frequency domain parameters” refers to the alternative definitions:
and
of the dispersion parameters, but not to the argument of these functions, which is always assumed to be the wavelength. All the parameters in the component (including and ) are given as functions of wavelength (not frequency). This is also the case when or are specified from a file - the first column of the file contains wavelength values ( ) and the second column - the corresponding values of .
Dispersion
Value of the GVD parameter in the wavelength domain
16.75 — [-10100, 10100]
Dispersion slope
Value of dispersion slope parameter.
— 0.075 [-10100, 10100]
Dispersion file format
Determines contents of dispersion file: group delay or dispersion vs. wavelength. If “Dispersion vs. wavelength” and “Frequency domain parameters” are selected, it is assumed that file contains
. If “Frequency domain parameters” is disabled, component assumes that file contains
. If “Group delay vs wavelength”, the file contains .
— Dispersion vs wavelengtht
— Dispersion vs wavelength/ Group delay vs wavelength
Dispersion file name
Specifies file containing dispersion data
— — — —
Name and description Symbol Default value Default unit Value range
Dps
nm( ) km( )-------------------------
ps
nm( )2 km( )---------------------------
β2 λ( )
D λ( )β1 λ( )
D ∂β1
∂λ-------- S, ∂D
∂λ------- (wavelength domain definition)= =
β2∂β1
∂ω-------- β3
∂β2
∂ω--------= (frequency domain definition),=
β2 β3
β1 β2
λβ1 λ( ) or β2 λ( )
161
OPTICAL FIBER
PMD
Nonlinearities
Name and description Symbol Default value Default unit Value range
Birefringence type
Defines the birefringence. If “Deterministic”, both the strength of birefringence and principal axes are assumed constant, hence random mode coupling is disabled. If “Stochastic”, random mode coupling is enabled.
— Deterministic — Deterministic/ Stochastic
Differential group delay
If Birefringence type is “Deterministic”, this is the value of the differential group delay. If “Stochastic”, parameter is disabled.
0.2 [-10100, 10100]
PMD coefficient
Polarization mode dispersion coefficient. If Birefringence type is “Stochastic”, this is the value of the PMD parameter. If “Deterministic”, parameter is disabled.
0.5 [0,10100]
Mean scattering section length
Averaged value of fiber length at which the polarization state of the signal is randomized by applying the scattering matrix.
500 [0,10100]
Scattering section dispersion
Dispersion of the scattering section length.
100 [0,10100]
Name and description Symbol Default value Default unit Value range
Self-phase modulation
Determines if the self-phase modulation (SPM) effect will be taken into account. If FALSE all the nonlinear effects - self-steepening, SRS - are disabled. In the vector case enabling this effect enables also the cross-phase modulation between the orthogonal polarization components.
— TRUE — TRUE/FALSE
Effective area data type
Defines is effective area parameter value is read from the component tab or from a file. If “Constant”, the value from the component is used.
Constant — Constant/ From File
Effective area
Defines the value of the effective area parameter. This value is used if “Effective area data type” is set to “Constant”. Otherwise, the value is ignored.
80 [0,1010]
ddω------- ∆β( )
pskm-------
Dppskm
-----------
Lscattm
σscatt m
Aeff µm2
162
OPTICAL FIBER
Effective area vs. wavelength
If “Effective area data type” is “From file”, this tab specifies the file containing the effective area data.
— — — —
n2 data typeDetermines if parameter (nonlinear index of refraction) value is read from the component tab or from a file. If “Constant”, value is taken from component.
— Constant — Constant/ From File
n2
The value of the parameter (nonlinear index of refraction). If data type is set to “Constant”, this value is used, otherwise the value is ignored.
2.6 X 10-20 [0,10100]
Self-steepening
Specifies whether self-steepening effect is taken into account. Can be enabled only after enabling the SPM, and is taken into account only in the scalar case (if Model type is set to Scalar), and if Full Raman response parameter is FALSE.
— FALSE — FALSE/TRUE
Full Raman response
Defines the stimulated Raman scattering (SRS) effect representation in the model. If TRUE, SRS is represented through the convolution integrals of the fields with the Raman susceptibilities [6, 18-21]. Intrapulse Raman scatterins is disabled.
— FALSE — FALSE/TRUE
Intrapulse Raman scattering
Defines the stimulated Raman scattering (SRS) for [19-21]. Can be enabled if Full Raman response is FALSE. If both Full Raman response and Intrapulse Raman scattering are FALSE, SRS effect is not taken into account in the simulation.
— FALSE — FALSE/TRUE
Raman self-shift time 1
Value of the Raman self-shift time parameter associated with the parallel SRS effect
t
Units are such that [19-21].
14.2 [0,10100]
Raman self-shift time 2
Units are such that [18, 20, 21].
3 [0,10100]
Name and description Symbol Default value Default unit Value range
n2
n2
n2 m2
W------
τR1 dImχ1111 ω( ) dω⁄( )ω 0==
Re χ1111 ω 0=( )( ) 1=
τR1 fs
τR2 dImχ1122 ω( ) dω⁄( )ω 0==
Re χ1111 ω 0=( )( ) 1=
τR2 fs
163
OPTICAL FIBER
Numerical
Fractional Raman contribution
Fraction of the nonlinear polarization, related to the stimulated Raman scattering effect [2].
0.18 — [0, 1]
Orthogonal Raman factor
Units are such that .
0.75 — [0, 1]
Name and description Symbol Default value Default unit Value range
Model type
Defines model type used for simulation. Depends on polarization state of signal. If “Vector” selected, signal can have arbitrary polarization state and a system of two coupled equations (17) is solved. If “Scalar” selected, the signal preserves its polarization state and a single equation is solved (1). In the following cases, vector simulation is performed regardless of value of model type parameter:• Two polarization components are detected at
fiber input• PMD effect is “Stochastic”.
— Scalar — Scalar/Vector
Propagator type
Method used to apply nonlinear propagator in the split-step Fourier method. “Exponential” corresponds to standard implementation [2], “Runge-Kutta 4th (2nd) order” uses Runge-Kutta 4th (2nd) order (see [3]) to apply nonlinearity operator. Exponential cannot be used when Model type is set to Vector, and SRS effect is enabled. The default selection is Runge-Kutta 2nd order.
Exponential — Exponential Runge-Kutta 4th order
Exponential Runge-Kutta 2nd order
Calculation type
Specifies implementation of split-step Fourier method [2, 4] when Propagator type is “Exponential”.
— Iterative — Iterative/ Noniterative
Number of iterations
Switch On/Off the dispersion slope (the third-order dispersion)
2 — [2, 1010]
Name and description Symbol Default value Default unit Value range
ρ
αf Re χ1122 ω 0=( )( )=
Re χ1111 ω 0=( )( ) 1=
αf
164
OPTICAL FIBER
Step Size
Specifies whether variable or fixed step-size simulation is used. If “Variable”, step size is adaptively changed depending on value of “Max. nonlinear phase shift” parameter, and solution itself. If “Constant”, step size is evaluated once at the beginning of simulation. In some cases, the fixed step size calculation executes faster, due to the smaller number of calculations per step, but the variable step size calculation is more flexible and can be faster if the peak power of the waveform varies considerably in (for example, in the presence of strong attenuation).
— Variable — Variable/ Constant
Max. Nonlinear phase shift
Maximum (over the time window) phase shift induced by the self-phase modulation effect per step.
3.14 [0,10100]
Boundary conditions
Specifies type of boundary conditions used in simulation.
— Periodic — Periodic/ Absorbing
Filter steepness
If “Boundary conditions” option is set to “Absorbing”, the “Filter steepness” parameter determines the absorption/reflection properties of the time window boundaries.
— 0.5 — [0,10100]
Lower/Upper calculation limit
Set the spectral range in which the simulation is performed. Any spectral components outside the range is ignored.
— [1400, 1700] [100, 2000]
Name and description Symbol Default value Default unit Value range
z
ϕmaxNL mrad
nm
165
OPTICAL FIBER
Graphs
Note: The rest of the parameters in the Graphs tab of the component determine which graphs are plotted after the simulation is complete.
Simulation
Name and description Symbol Default value Default unit Value range
Calculate graph
Enables/disables 3D graphs. If disabled, no graphs are plotted and no data are stored.
— FALSE — FALSE/TRUE
Number of distance steps
Number of snapshots used to construct a 3D plot. If this value is increased, the fidelity of the plot is improved only if the value is below the number of actual steps in . The number of snapshots stored cannot be bigger than the number of steps in taken by the simulation to obtain the solution. The latter is determined by the maximum nonlinear phase-shift parameter (numerical tab).
— 200 — [1, 100000000]
Number of wavelength/time steps
Number of stored points per snapshot. If this value is increased, the fidelity of the plot is improved only if the value is below the actual number of points in the time (frequency) domain used by the simulation to obtain the solution. The latter is related to the number of samples, which is a global parameter.
— 200 — [1, 100000000]
Linear scale
Determines axis type (linear or logarithmetic) for the dependent variable. If TRUE, the axis type is linear.
— TRUE — TRUE/FALSE
Name and description Symbol Default value Default unit Value range
Enabled
Determines whether or not the component is enabled. If FALSE, all input signals reach the output port of the component without any changes.
— TRUE — TRUE/FALSE
zz
166
OPTICAL FIBER
Noise
Random numbers
Name and description Symbol Default value Default unit Value range
Convert noise bins
If TRUE, each noise bin within the bandwidth of the signal is converted to a Gaussian white noise, with the correct power spectral density, and the noise is added to the signal.
— FALSE — FALSE/TRUE
Name and description Symbol Default value Default unit Value range
Generate random seed
Determines how random number generator is initialized (seeded). If TRUE, the seed index used for the initialization is the random number itself. Otherwise, a user specified number is used.
— TRUE — TRUE/FALSE
Random seed index
If “Generate random seed” is FALSE, this value specifies the seed index. The generated pseudo-random sequence is the same if the seed index is not changed. The value of the “Random seed index” is ignored if “Generate random seed” is TRUE.
— 0 — [0, 4999]
167
OPTICAL FIBER
Technical Background
Scalar approach
Basic equation
When the optical field is assumed to maintain its polarization along the fiber length, the evolution of a slowly varying electric field envelope can be described by a single nonlinear Schrödinger (NLS) [2] equation (the scalar approach, Model type parameter from the "Numerical" tab is set to "Scalar") of the form:
In Equation 2, is the electric field envelope. A frame moving at the group velocity ( ) is assumed.
The derivatives of the propagation constant of the fiber mode , ( is the mode effective index), with respect to frequency
.
and are the first and the second group velocity dispersion (GVD) parameters, respectively, and is the reference frequency of the signal, related to the parameter "Reference wavelength" ("Main" category of the components tool-box) through with being the light speed in vacuum.
The physical meaning of the terms in Equation 2 is the following. The first term takes into account the slow changes of the electric field along the fiber length. The second term is the (first-order) group velocity dispersion. This is the effect responsible for the pulse broadening. (See "Group velocity dispersion" from the Tutorials). The third term is the second-order GVD, known also as third-order dispersion (TOD). This effect becomes important for a signal with a broad spectrum (e.g. femtosecond pulses or WDM systems with many channels). The pulse shape becomes asymmetric due to the effect of TOD. (See "Third order dispersion" from the Tutorials). The parameters
and are denoted as "frequency domain parameters" in the interface of the component (see the "Dispersion" category in the Parameters table). The following
(1)∂E∂z------ αE iβ2 ω0( )∂2E
∂T 2-------- β3 ω0( )
6----------------∂3E
∂T 3--------–+ + iγ E 2E i
ω0------ ∂
∂T------ E2 E( ) ρτR1E∂ E 2
∂T-----------–+
=
E E z T,( )=T t z vg⁄ t β1 z–≡–=
β ω( ) β ω( )c( ) ω⁄
βn∂nβ ω 0( )
∂ωn------------------- n, 1 2 3, ,= =
β2( ) β3( )ω0
ω02πcλ0
---------= c
β2( ) β3( )
168
OPTICAL FIBER
relations are used internally to convert between them and the commonly used wavelength domain parameters (dispersion) and (dispersion slope).
The parameter is given by:
In Equation 3, is the nonlinear refractive index coefficient and is the fiber effective area. The first term in the right-hand side in Equation 1 accounts for the self-phase modulation effect. It is responsible for the broadening of the pulse spectra and, in the presence of anomalous GVD, for the formation of optical solitons (See "Self-phase modulation" and "Self-phase modulation and group velocity dispersion" from the Tutorials). The second term in the right-hand side of Equation 1 takes into account the self-steepening effect. It leads to an asymmetry in the SPM-broadened spectra of ultrashort (femtosecond) pulses [2] and is responsible for the formation of optical shocks (see "Self-steepening" in the Tutorials). This effect will be taken into account only if the "Full Raman response" parameter is set to False. The last term in Equation 1 accounts for the intra-pulse Raman scattering effect with the parameter
being the parallel Raman self-shift time. The intra-pulse Raman scattering is an approximation to the actual Raman response of the material which is valid provided that signal spectrum is narrow compared to the Raman-gain spectrum. The parameter is related to the slope of the imaginary part of the Raman susceptibility
at zero frequency offset [2]. The parameter is the fractional contribution of the delayed response of the material to the total nonlinearity [2]. The intra-pulse Raman scattering effect is responsible for the self-frequency shift i.e. energy transfer from higher to lower spectral components. It leads to a decay of higher order solitons into its constituents (see "Intrapulse Raman scattering" in the Tutorials). The intrapulse Raman scattering plays the most important role among the higher order nonlinear effects [2].
In a WDM system, the stimulated Raman scattering is responsible for an energy transfer from higher to lower frequency channels (crosstalk). The Raman induced crosstalk can be neglected when the following relation is satisfied [5]:
where is the total effective length, is the fiber loss, is the amplifier spacing, the link length, is the total optical power, and is the total optical bandwidth.
(2)
(3)
(4)
D S
D dβ1
dλ-------- 2πc
λ2---------– β2= =
β3λ
2πc---------
2
λ2S 2λD+( ) S, dDdλ-------= =
γ
γ ω0n2
cAeff-----------=
n2 Aeff
τR1
τR
Im χ1111 ω( )( ) ρ
PTOTBTOTLE 9mWTHzMm ,<
LE z Lampα( )⁄≈ α Lamp
z PTOT BTOT
169
OPTICAL FIBER
Full Raman response
By selecting the option "Full Raman response" from the Numerical tab, the component can simulate the SRS effect even if the signal spectrum is much narrower than the Raman gain spectrum. In this case Equation 1 is replaced by:
Contained within Equation (4a) is which is the (time-domain) Raman response function [2], [20]. It is the Fourier-transform of the of the Raman susceptibility . In this case the self-steeping effect is neglected.
Numerical solution
In dimensionless form, Equation 1 reduces to:
where the coefficients are given by:
The new quantities are introduced according to::
In Equation 7, is the time window size and is the maximum (over the time window) of the electric field intensity .
The symmetrized split-step Fourier method [2, 4] is used to solve Equation 5. The solution is advanced from to ( is the step-size, related to the value of the Max. nonlinear phase shift parameter ) according to:
(4a)
(5)
(6)
(7)
(8)
∂E∂z------ αE iβ2 ω0( )∂2E
2--------------------------- ∂2E
∂T 2-------- β3 ω0( )
6----------------∂3E
∂T 3--------–+ + iγ 1 ρ–( ) E 2E ρE h1111 s( ) E T s–( ) 2 sd
0
∞
∫+
=
h1111 t( )
χ1111 ω( )
i∂U∂ξ------- D2
∂2U∂t2--------- N1 U 2U+ + iD3
∂3U∂t3--------- N2U ∂ U 2
∂t------------ iN3
∂∂t---- U 2U( )– iAU ,–+=
D2sign β2( )
2--------------------- D3,
LDsign β3( )LD'
---------------------------- N1,= LD
L------
NLN2,
LD
L------
NLτR' N3
LD
LNL-------- s .=,= = =
LDT 0
2
β2-------- LNL, 1
γP0-------- LD',= T 0
3
β3-------- s, 1
ω0T0----------- τR',
τR
To----- E, P0U T, T0t z, ξLD .= = = = = = =
T0 P0
E z 0 T,=( ) 2
ξ ξ h+ hϕmax
NL max U 2h( )=
U ξ h t,+( ) h2---D
N ξ'( ) ξ'dξ
ξ h+( )
∫ h
2---D
U ξ t,( ) ,expexpexp=
170
OPTICAL FIBER
where the dispersion and nonlinearity operators are given by:
and
The different options available from the "Numerical" tab specify the details of the implementation of Equation 8 and Equation 10 (see Figure 1). The simplest (and the fastest) implementation corresponds to "Propagator type" set to "Exponential" and "Calculation type" set to "Noniterative". In this case, the following approximation is used:
Figure 1 Component “Numerical" tab
(9)
(10)
(11)
D N
D iD2∂2
∂t2------ D3
∂3
∂t3------ A–+=
N iN1 U 2 iN– 2∂ U 2
∂t------------ N3
∂ U 2
∂t------------ U∗ ∂U
∂t------- +
–=
N ξ'( ) z'dξ
ξ h+
∫ hN h 2⁄( )D[ ]exp U ξ t,( )( ) .≈
171
OPTICAL FIBER
According to Equation 11, the half-step propagated field, with the nonlinear effects ignored, is used in turn to evaluate the nonlinearity operator. The dispersion operator is evaluated in the frequency domain according to:
where means fast Fourier transform. If, in addition the "Step size" option is set to "Constant" ("Propagator type", "Exponential", and "Calculation type" are set to "Noniterative"), the number of operations per step decreases because the first and the last Fourier transform for each step cancels each other out (dispersion operators combine) (see Equation 13).
When the "Propagator Type" is set to "Runge-Kutta 4th order" (or "Runge-Kutta 2nd order") (RK4 or RK2), the exponent with the nonlinearity operator in Equation 8 is replaced by the direct integration of the following system of coupled ordinary differential equations:
by means of the standard RK4 (or RK2) routine (see example in [3]). The application of the dispersion operator is the same.
Note: The Runge-Kutta (2nd or 4th order) implementations in the fiber component enable modeling the stimulated Raman scattering effect with the optical signal having an arbitrary polarization ("Model type" parameter set to "Vector"). However, due to the larger number of operations per step, they are executed slower and are not recommended otherwise (in "scalar" simulations or when the Raman effect is not included in a vector simulation) because the "Exponential" implementation of the nonlinearity provides faster execution.
(12)
(13)
(14)
UD ξ h2---+
FFT 1– h2---D iω( )
FFT U ξ t,( )[ ]exp ,=
FFT
U ξ 2h t,+( ) h2---D
N ξ'( ) ξ'dξ
ξ h+( )
∫ h
2---D
h2---D
exp N ξ'( ) ξ'dξ
ξ h+( )
∫ h
2---D
U ξ t,( ) =expexpexpexpexp=
h2---D
N ξ'( ) ξ'dξ
ξ h+( )
∫
hD( ) N ξ'( ) ξ'dξ
ξ h+( )
∫ h
2---D
U ξ t,( )expexpexpexpexp
∂U∂z-------
NL
NU=
172
OPTICAL FIBER
If the "Propagator type" is set to "Exponential" and "Calculation type" to "Iterative", Equation 11 is replaced by [2], [4]:
The symbol means . Since is unknown at , it is necessary to follow an iterative procedure that is initiated by replacing by
(see [2], [4] for the details). Working with two iterations gives a reasonable combination between accuracy and speed, as recommended in [2].
Figure 2 Evolution of for N=3 soliton over 15 soliton periods with different calculation modes
Note: In the three cases presented, , constant step size.
A comparison between the "Iterative" and "Noniterative" approaches is presented in Figure 2. Evolution of N=3 soliton over 15 soliton periods is presented. The "Step size" is kept "Constant" with the "Max. nonlinear phase shift" parameter is equal to 27.6. mrad. The noniterative approach is the fastest but not accurate enough at this step size. The development of spurious, numerical instability, which breaks the periodicity of the soliton evolution [2], is evident at the end of the run. For the same step size the iterative implementation of the split-step Fourier method suppresses the
(15)N ξ'( ) ξ' h2--- N ξ( ) N ξ h+( )+( )≈d
ξ
ξ h+
∫
N ξ( ) N E ξ( )( ) N ξ h+( ) ξ h 2⁄+N ξ h+( )
N ξ( )
E ξ t, 0=( ) 2
ϕmaxNL 27.6mrad=
173
OPTICAL FIBER
instability, thus improving the quality of the results, however this improvement is at the expense of increased computation time.
The step size in the component is determined through the value of the parameter . In the case of the constant step size calculation, it is
calculated once, using the input signal to obtain the maximum value of the intensity. In the case of variable step size calculation such an evaluation is performed at each step.
Figure 3 Variable step size, value of is
In Figure 3, the calculation presented in Figure 2 is repeated using variable step size. This calculation takes longer in comparison to the "Noniterative" case presented in Figure 2, but less than in the case where two iterations are used. Depending on the behavior of the solution, variable step size calculation can take less time compared to the constant step size, although the fixed step size calculation performs a smaller number of operations per step (see Equation 13). In the presence of considerable attenuation, the importance of nonlinear effects decreases along the fiber length, which would permit the use of a larger step size. In this case, the use of variable step size will reduce the computation time. The variable step size calculation is more flexible, because different tasks can be handled keeping the value of constant. For the case presented in Figure 3, this value is double the size of the one used in Figure 2, but the results are even better (refer to compare with Figure 2, "Noniterative").
The split-step scheme used in the model is locally second order accurate which means that the local error is proportional to the . However, the global error (after N steps) is proportional to [22]. Thus, increasing the fiber length might require decrease of the step size to maintain the same accuracy.
The use of FFT implies periodic boundary conditions. In some cases a part of the pulse energy may spread eventually hitting the time window boundaries. When the energy reaches one of the edges of the time window it automatically reenters from the other edge perturbing the solution. This can be avoided using the absorbing type of
hϕmax
NL γmax E 2( )h=
ϕmaxNL ϕmax
NL 50mrad=
ϕmaxNL
h3
Nh3 Lh2=
174
OPTICAL FIBER
boundary conditions. To achieve this at each step the optical field is multiplied in the time domain [10] by:
where indicates the nearest edge. The effect of periodic and absorbing boundary conditions is shown in Figure 4 where the results presented in Figure 3 from "Birefringence and solitons" (propagation distance is equal to 1262.34km) are redisplayed. However here the time window is reduced to show the effect of the periodic boundary conditions. The oscillatory tail developed by the solution in the case when periodic boundary conditions are used is an unphysical effect, resulting from the interference of the radiation that has reentered the time window and the solution. In the case when absorbing boundary conditions are used the radiation that has separated from the solution is removed. The smaller the value of the filter steepness parameter the better the time window boundaries absorb (and do not reflect), however the larger part of the time window becomes absorbing (see Equation 16.
Figure 4 Periodic (left plot) and absorbing with filter steepness 0.05 (right plot) boundary conditions
(16)Γ t( ) 1 FilterSteepnes t tedge–( )( ) ,sech–=
tedge
175
OPTICAL FIBER
Vector approach
When the polarization state of the incident light is not preserved during its propagation inside an optical fiber the scalar approach is no longer applicable and Equation 1 is replaced by [2], [6] - [10]:
Equation 17, contains the Raman response functions [6], [18]. Their Fourier transformations and Raman susceptibilities , are shown in Figure 4.1. The convolution integrals in Equation 17 are evaluated in the frequency domain, by multiplying the spectra of the electric fields with the Raman susceptibilities and then performing the inverse FFT.
Figure 4.1 Raman susceptibilities for fused quartz [6, 18]
(17)
∂EX
∂z--------- β1X
∂EX
∂t--------- iβ2
2-------∂2EX
∂t2----------- β3
6-----∂3EX
∂t3----------- = iγ 1 ρ–( ) EX
2 23--- EY
2+ EX–+ +
+ iγρEX h1111 s( ) EX t s–( )2 s h1122 s( ) EY t s–( )2 sd0
∞
∫+d0
∞
∫
+ iγρEY h1212 s( )EX t s–( )EY∗ t s–( ) sd0
∞
∫
∂EY
∂z--------- β1X
∂EY
∂t--------- iβ2
2------- ∂2EY
∂t2----------- β3
6-----∂3EY
∂t3----------- = iγ 1 ρ–( ) EY
2 23--- EX
2+ EY–+ +
+ iγρEY h1111 s( ) Eγ t s–( )2 s h1122 s( ) EX t s–( ) 2 sd0
∞
∫+d0
∞
∫
+ iγρEX h1212 s( )Eγt s– E∗X t s–( ) sd0
∞
∫
hijkl t( )χijkl v( )
176
OPTICAL FIBER
The SRS effect is represented by "Intrapulse Raman scattering" (Equation 17) is replaced by [20]:
Note: In the case of Equation 17 or Equation 17a, due to the orthogonal Raman gain terms (the last sections in Equation 17 or Equation 17a), the "Exponential" option for the "Propagator type" is not applicable. The component automatically selects "Runge Kutta 2nd order" when the model type is set to "Vector", and the Raman effect ("Intrapulse Raman scattering" or "Full Raman response" options are selected. Due to the increased number of convolutions performed at each step the fiber component can be slow when solving Equation 17.
In normalized units and when the SRS effect is neglected ( ) Equation 17 reads as:
The quantities and are the inverse group velocities for the and polarization components respectively.
(17a)
(18)
∂EX
∂z--------- β1X
∂EX
∂t--------- iβ2
2-------∂2EX
∂t2----------- β3
6-----∂3EX
∂t3----------- = –+ +
iγ EX2 2
3--- 1 ρ–( ) ρ
1 α f+2
--------------+ + EY
2 ρτR1∂ EX
2
∂t--------------– ρτR2
∂ EY2
∂t--------------– EX
iγρτR1 τR2–
2--------------------∂ EXEY∗( )
∂t-----------------------EY–
∂EY
∂z--------- β1Y
∂EY
∂t--------- iβ2
2------- ∂2EY
∂t2----------- β3
6-----∂3EY
∂t3----------- = –+ +
iγ EY2 2
3--- 1 ρ–( ) σ
1 α f+2
--------------+ EX
2
+ στR1∂ EY
2
∂t-------------- ρ– τR2
∂ EX2
∂t--------------– EY
iγρτR1 τR2–
2--------------------∂ EYEX∗( )
∂t-----------------------EX–
ρ 0=
i ∂u∂ξ------ δ∂u
∂t------+
D2∂2u∂τ2-------- iD3
∂3u∂τ3--------– N1 u 2 2
3--- v 2+
u+ + 0=
i ∂v∂ξ------ δ∂v
∂t-----+
D2∂2v∂τ2------- iD3
∂3v∂τ3-------– N1 v 2 2
3--- u 2+
v+ + 0=
β1X β1Y X Y
177
OPTICAL FIBER
Figure 5 Optical fiber as a concatenation of trunks
Note: The arrows represent the principal axes.
The parameter is given by , where is the value of the differential group delay parameter entered from the "PMD" tab, in the case where "Deterministic" mode is selected for the birefringence effect (see "Birefringence and solitons" from the Tutorials). The effects of four-wave mixing between the orthogonal polarization components are not taken into account due to their negligible contribution for typical values of the birefringence [9], [10]. The normalized time is introduced according to where
. All the other parameters have the same meaning as in the scalar case.
The "coarse-step method" [11] is used to simulate the PMD effects in the "Stochastic" mode. The fiber is represented by a concatenation of trunks and the propagation of light in each trunk is simulated by the split-step Fourier method described in the previous section. The lengths of the trunks are random numbers with a Gaussian distribution [12]. The average and the dispersion of this distribution are the "Scattering section length" and "Scattering section dispersion" parameters:
It is recommended [12] that the dispersion is 20% of the average value. The birefringence of each trunk is given by [11] (see the related PMD examples in the tutorials):
where is the PMD coefficient. The principal axes of the trunks are randomly oriented with respect to each other (see Figure 4). To simulate the random mode coupling at the end of each trunk the following transformation is applied [11], [13]:
(19)
(20)
(21)
δ δ β1X β1Y–( )T0 2 β2( )⁄= β1X β1Y–
τ τ t β1z–( ) T0⁄=β1 β1X β1Y+( ) 2⁄=
Lscatt σscatt
f Lscatti( ) 1
2πσscatt
---------------------- Lscatti Lscatt–( )2–2σscatt
2--------------------------------------exp=
ddω------- ∆β( ) DP
Lscatti
---------------=
DPMD
EX'EY'
α α iϕ( )expsincosα i– ϕ( ) cosαexpsin–
EX
EY
=
178
OPTICAL FIBER
In Equation 20, and are random numbers uniformly distributed in the interval .
Wavelength dependent parameters
The file that specifies the wavelength dependence of the parameters consists of two columns with the left column being the wavelength in nanometers and the right column containing the corresponding values of the parameters (see Table 1 ). The sampling interval is not necessarily be constant. The parameter values must be given in the units specified in the "Units" tab of the table.
Table 1 Wavelength dependence of the attenuation parameter
The values of the parameters in Equation 1 and Equation 17 are evaluated at the reference wavelength.
Note: The reference wavelength must be within the wavelength interval covered by the files for all the wavelength dependent parameters specified.
The reference wavelength can be either user-specified or "automatic". In the last case the wavelength corresponding to the central frequency of the spectrum of the signal is assumed by the component to be the reference wavelength. Linear interpolation is used to calculate the values of the attenuation, effective area and parameters at this wavelength. For the dispersion parameters the following procedure is used. The wavelength dependence specified by the file is fitted internally using the five-term Sellmeier formula [14]. The higher-order dispersion parameters are then obtained by analytically differentiating this expression. If the option frequency domain parameter is unchecked, the file may give either the group delay or dispersion (depending on the choice made in the "Dispersion file format" tab), and if the frequency domain parameters option is selected, either or can be supplied, again determined by the value of the "Dispersion file format" parameter. If the wavelength dependence of the group delay is given by the user, two successive differentiations are applied to its Sellmeier fit. Differentiating the analytical fit instead of using a direct numerical differentiation of the data provides the advantage of being able to produce reasonable results even in the case where the supplied data is noisy (see Appendix 1).
1400 0.31405
1402.5 0.30246
1405 0.29276
1407.5 0.28457
1410 0.27757
1412.5 0.27153
α ϕ0 2π,[ ]
λ nm[ ] α dB km⁄[ ]
n2
β1 λ( ) D λ( )
β1 λ( ) β2 λ( )
179
OPTICAL FIBER
Note: The accuracy of the Sellmeier fit depends on the type of the fiber. This is shown in Figure 6, where the results obtained for dispersion flattened and dispersion shifted fibers are shown.
Figure 6 Comparison between the original dispersion data and their fits for two fiber types
Guidelines for using the component for WDM simulations
Periodic boundary conditions are required for simulating the propagation of long bit sequences at different carrier wavelengths, which is the case when WDM systems are designed.
To avoid the aliasing phenomena (see e.g. [3]), the sample rate is chosen to be at least three times bigger (Figure 7) than the bandwidth occupied by the simulated channels (see e.g. [15]).
Figure 7 WDM channels and their four-wave mixing products
Any frequency component outside the frequency range (Fc-SR/2, Fc+SR/2), where SR is the sample rate and Fc is the reference frequency is falsely translated (aliased) into that range by the very act of discrete sampling [3]. If the sample rate is bigger than
180
OPTICAL FIBER
the bandwidth occupied by the WDM channels (so it can accommodate all the channels) but less than three times that value in the presence of nonlinear effect the four-wave mixing products resulting from the nonlinear interaction between the channels (spurious waves [16]) will be aliased. In [16], to minimize the amount of aliased power the requirement that the value of the power spectrum at the boundary of the available spectral range be -40 dB of its peak value is used.
The longitudinal step size depends on the importance of the nonlinear effects for the particular simulation. If all the nonlinear effects are disabled step size equal to the fiber length will be used. The increase of the impact of nonlinearity will require decrease of the step size (decrease of the value of the max. nonlinear phase shift parameter) to maintain the same accuracy.
Figure 8 Output spectra corresponding to
Note: The propagation distance is 100km. Input configuration is given in "Cross-phase modulation" in the Tutorials.
Values in the order of a few miliradians (one [15] and three [17])) are used with this parameter in a WDM system simulation. The effect of an improperly chosen step size is shown in Figure 8, where the output spectra corresponding to an interaction of two Gaussian pulses with carrier wavelengths one nm spaced are shown (see "Cross-phase modulation" from the Tutorials). While the correct result that the four-wave mixing products (or spurious waves) should disappear when the pulses are no longer over-lapped (in the absence of any loss and gain [16]) is reached when the step-size is small enough, in the opposite case, the spurious frequencies present in the output spectra are still evident. The improperly chosen step size (too big) tends to exaggerate the four wave mixing products (see [22] and references therein).
To increase the accuracy, you can switch from a "Noniterative" to an "Iterative" calculation type, keeping the step size the same (with the same step size, the "Iterative" implementation is more accurate, (see Figure 2), or alternatively, to keep working in the "Noniterative" mode and decrease the step size, or the value of the "Max. nonlinear phase shift" parameter. With respect to saving computational time, the latter strategy is better. It should be noted that computational time will not be saved by simultaneously increasing the number of iterations and the step size.
ϕmaxNL 50mrad and ϕmax
NL 3mrad= =
181
OPTICAL FIBER
Appendix 1
Dispersion fitting according to the Sellmeier formulaWhen the option "Dispersion from file” is selected, the dispersion data are internally fitted according to the five-term Sellmeier formula [14], namely:
where is the group delay (per unit fiber length) or, respectively:
where is the dispersion [ps/nm/km]. The user supplies data either for the dispersion or the group delay that are then fitted according to Equation 2A or Equation 1A, and the slope and/or dispersion are calculated by differentiating Equation 1A and Equation 2A analytically.
The least-square fitting associated with Equation 2A amounts to minimizing:
where is the number of points. Using:
the following linear system is obtained:
(1)A
(2)A
(3)A
(4)A
(5)A
τ c1λ 4– c2λ 2– c3 c4λ2 c5λ4+ + + +=
τ
D dτdλ------ c1'λ
5– c2'λ3– c4'λ c5'λ
3+ + += =
D
Q c1λ i5– c2λ i
3– c4λ i c5λ i3 Di–+ + +( )2
i 1=
N
∑ min= =
N
∂Q∂ci------- 0 i, 1…4 ,= =
λi10–∑ λi
8–∑ λi4–∑ λi
2–∑λi
8–∑ λi6–∑ λi
2–∑ N
λi4–∑ λi
2–∑ λi2∑ λi
4∑λi
2–∑ N λi4∑ λi
6∑
C1
C2
C4
C5
Diλ i5–∑
Diλ i3–∑
Diλ i∑Diλ i
3∑
=
182
OPTICAL FIBER
which is solved by LU-decomposition [3].
In the case when the user supplies a group delay data file, Equation 1A is used and Equation 5A transforms into Equation 6A.
The fitting procedure is useful when/if noisy data is supplied by the user, as the following example shows. Figure 1A shows dispersion-versus-wavelength dependence of SMF-28 and the corresponding "exact" results for dispersion parameters are displayed below the graph.
Figure 1A Lambda = 1550.75nm beta2=-2.08625e-026 s2/m beta3=1.27246e-040 s3/m
D= 1.63411e-005 s/m2 S= 56.9931 s/m3
To assess the influence of noise on the results from the calculation some noise is added to the data presented in Figure 1A with the resulting graph presented in Figure 2A. Supplying the data from Figure 2A to the Nonlinear Dispersive Fiber Total
(6)A
λi8–∑ λi
6–∑ λi4–∑ λi
2–∑ N
λi6–∑ λi
4–∑ λi2–∑ N λi
2∑λi
4–∑ λi2–∑ N λi
2∑ λi4∑
λi2–∑ N λi
2∑ λi4∑ λi
6∑N λi
2∑ λi4∑ λi
6∑ λi8∑
C1
C2
C3
C4
C5
τiλ i4–∑
τiλ i2–∑
τi∑τiλ i
2∑τiλ i
4∑
=
183
OPTICAL FIBER
Field component gives the results for the dispersion parameters presented under Figure 2A.
Figure 2A Lambda = 1550.75nm beta2=-2.10115e-026 s2/m beta3=1.32966e-040 s3/m
D= 1.64578e-005 s/m2 S= 60.3521 s/m3
184
OPTICAL FIBER
References:[1] G. P. Agrawal, "Applications of nonlinear fiber optics", Academic press, 3rd edition, 2001.
[2] G. P. Agrawal, "Nonlinear fiber optics", Academic press, 3rd edition, 2001.
[3] W. H. Press, et al., "Numerical Recipes: The Art of Scientific Computing", 2nd Edition, Cambridge University Press, 1992.
[4] M. Lax, J. H. Batteh and G. P. Agrawal, Journ. Appl. Phys. 52 , 109, (1981).
[5] F. Matera and M. Settembre, Journ. Lightwave Technol. 14, 1 (1996).
[6] R. W. Hellwarth, Prog. Quant. Electr. 5, 1 (1977).
[7] E. A. Golovchenko and A. N. Pilipetskii, JOSA B, 11, 92 (1994).
[8] P. T. Dinda, G. Millot, and S. Wabnitz JOSA B, 15, 1433 (1998).
[9] C. R. Menyuk, Opt. Lett., 12, p. 614 (1987).
[10] C. R. Menyuk, JOSA B, 5, p. 392(1988).
[11] D. Marcuse, C. R. Menyuk and P. K. A. Wai JLT, vol. 15, No. 9, pp. 1735 (1997).
[12] C. H. Prola Jr., J. A. Pereira da Silva, A. O. Dal Forno, R. Passy, J. P. Von der Weid, and N. Gisin IEEE Phot. Technol. Letters, 9, No. 6, 842 (1997).
[13] P. K. A. Wai, C. R. Menyuk, and H. H. Chen , Opt. Lett. 16 1231 (1991).
[14] L. G. Cohen, Journ. Lightwave Technol. 3, 958, (1985).
[15] M. I. Hayee and A. E. Willner, IEEE Phot. Technol. Lett. 11, No. 8, (1999).
[16] D. Marcuse, A. R. Chraplyvy, and R. W. Tkach, Journ. Lightwave Technol, 9, 121 (1991).
[17] R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, Journ. Lightwave Technol, 13, 841 (1995).
[18] P. Tchofo Dinda, G. Millot, and S. Wabnitz, JOSA B, 15, 1433, (1998).
[19] R.H.Stolen, J.P.Gordon, W.J. Tomlinson and H.A. Haus, JOSA B, 6, 1159 (1989).
[20] C.R.Menyuk, M.N.Islam and J.P.Gordon, Optics Letters, 16 566, (1991).
[21] K.J. Blow and D. Wood, IEEE J. Quant. Electr., 25, 2665, (1989).
[22] O. Sinkin, R. Holzlohner, J. Zweck and C. R. Menyuk, Journ Lightwave Technol. 21, 61 (2003).
185
OPTICAL FIBER
Notes:
186
LINEAR MULTIMODE FIBER
Linear Multimode fiber
This component is a multimode fiber that assumes the fiber has sufficient mode mixing due to imperfections or splices; in this case the modal transfer function approaches a Gaussian function. It also includes first- and second-order chromatic dispersion.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value Default unit Value range
Frequency
Reference center frequency
850 nm, Hz, THz [100, 2000]
Length
Fiber length
1 km [0,+INF[
Attenuation
Fiber attenuation
2.61 dB/km [0,+INF[
Modal bandwidth
Fiber modal bandwidth
1324 MHz.km [0,+INF[
Cutback factor
Cutback factor
1 - [0,+INF[
187
LINEAR MULTIMODE FIBER
Chromatic dispersion
Simulation
Name and description Default value Default unit Value range
Include chromatic dispersion
Defines whether the model includes chromatic dispersion effects
False nmHz, THz True, False
Use Sellmeier approximations
Defines whether the user enters data sheet parameters for zero dispersion wavelength or at the reference wavelength
True — True, False
Zero dispersion wavelength
Wavelength at zero dispersion
1354 nm [100, 2000]
Zero dispersion slope
Dispersion slope at zero dispersion
0.097 ps / (nm2.km) ]-INF,+INF[
Dispersion
Dispersion at reference frequency
–100 ps / (nm.km) ]-INF,+INF[
Dispersion slope
Dispersion slope at reference frequency
0.5 ps / (nm2.km) ]-INF,+INF[
Spectral width
Source spectral width
0.4 nm [0, 2000]
Name and description Default value
Default unit Units Value range
Enabled
Determines whether or not the component is enabled
True — — True, False
Resample
Determines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rate
New output signal sample rate
500 GHz Hz, GHz, THz ]0,+INF[
188
LINEAR MULTIMODE FIBER
Noise
Technical backgroundThe optical fiber has three dominant dispersion mechanisms, modal, and first-order chromatic and second-order chromatic. We can assume that modal dispersion and chromatic dispersion mechanisms act independently and can be treated separately[1][2].
Modal dispersionPersonick has shown that if a multimode fiber has sufficient mode mixing due to imperfections or splices, in this case the modal transfer function approaches a Gaussian function [3][4][5]
(1)
where is the angular baseband frequency and is the RMS impulse response width.
In this model, the modal dispersion is characterized by the 6 dB half of the optical power frequency:
(2)
where is defined by the parameter Modal bandwidth and is the fiber parameter Length. is the cutback factor, that takes into account the mode coupling, mixing and concatenation effects.
Rewriting Equation 1 and Equation 2 in terms of frequency and bandwidth:
(3)
Name and description Default value
Units Value range
Noise threshold
Minimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamic
Threshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
HM ω( ) eω2σ2
2-------------–
=
ω σ
B6dB2 1n 2( )⋅2 π σ⋅ ⋅
-------------------------- BM1L---
γ
= =
BM Lγ
HM f( ) e
1n 2( ) f 2⋅
BM1L---
γ ⋅
2---------------------------------- –
=
189
LINEAR MULTIMODE FIBER
Chromatic dispersionSince most of the injection-lasers used in optical fiber communications have a Gaussian line shape [1][2][6][7], we can use the solution for the chromatic transfer function for a perfect Gaussian linewidth case:
(4)
where and are abbreviations for
(5)
where the parameter is defined by Spectral width, S is the parameter Dispersion slope, D is the Dispersion, is the reference center wavelength calculated from the parameter Frequency, and L is the fiber length.
The parameter Use Sellmeier approximations defines whether you will enter D and S directly, or if they will be calculated from the Sellmeier approximations [2]:
(6)
HD ω( ) 11 iω ω2⁄+( )1 2⁄
------------------------------------eω ω1⁄( )2
2 1 iω ω2⁄+( )----------------------------------–
=
ω1 ω2
ω1 σλ D L( ) 1––=
ω1 σλ2 S 2 D λr⁄+( )L[ ] 1–=
σλλr
D S0
4---- λr
λ04
λr3
-----– =
S S0
4---- 1 3λ0
4
λr4
-----+ =
190
LINEAR MULTIMODE FIBER
References
[1] C. Yabre, "Comprehensive Theory of Dispersion in Graded-Index Optical Fibers", Journal of Lightwave Technology, Vol. 18, No. 2, pp. 166-176, February 2000.
[2] G.D. Brown, "Bandwidth and Rise Time Calculations for Digital multimode Fiber-Optical Data Links", Journal of Lightwave Technology, Vol. 10, No. 5, pp. 672-678, May 1992.
[3] S.D.Personick "Baseband Linearity and Equalization in Fiber Optic Digital Communication Systems", The Bell System Technical Journal, pp. 1174-1194, September 1973.
[4] D.G.Duff, "Computer-Aided Design Of Digital Lightwave Systems", IEEE Journal on Selected Areas in Communications, Vol. SAC-2, No. 1, pp. 171-185, January 1984.
[5] D.O.Harris, J.R. Jones "Baud Rate Response: Characterizing Modal Dispersion for Digital Fiber Optic Systems", Journal of Lightwave Technology, Vol. 6, No. 5, pp. 668-677, May 1988.
[6] J.L.Gimlett, N,K,Cheung "Dispersion Penalty Analysis for LED/Single-Mode Fiber Transmission Systems", Journal of Lightwave Technology, Vol. LT-4, No. 9, pp. 1381-1391, September 1986.
[7] T. Pfeiffer, M. Witte, B. Deppisch "High-Speed Transmission of Broad-Band Thermal Light Pulses Over Dispersion Fibers", IEEE Photonic Technology Letters, Vol. 11, No. 3, pp. 385-387, March 1999.
191
LINEAR MULTIMODE FIBER
Notes:
192
NONLINEAR DISPERSIVE FIBER
Nonlinear Dispersive fiber
Fundamental model of a generic nonlinear and dispersive optical fiber. Its power and versatility allow it to represent any type of real fiber by a suitable combination of parameters.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value Default unit Value range
Length
Fiber length
50 km [0, INF]
Attenuation data type
Defines the attenuation as a fixed constant value or as a wavelength dependent curve taken from a file
Constant — Constant, Wavelength Dependent/ From File
Attenuation – constant
Defines the attenuation as a fixed constant value, the same for all channels
0.25 dB/km [0, INF]
Attenuation vs. wavelength
Defines the attenuation as a wavelength dependent curve in a file
AtnVsLambda.dat — [0, INF]
Input coupling loss
Overall input coupling loss resulting from mode mismatch, Fresnel reflections, etc.
-1 dB [-INF,0]
Output coupling loss
Overall output coupling loss resulting from mode mismatch, Fresnel reflections, etc.
-0.022 dB [-INF,0]
193
NONLINEAR DISPERSIVE FIBER
Dispersion
Name and description Default value Default unit Value range
Group delay data type
Defines the group delay as a fixed constant value, or as a wavelength dependent curve taken from a file
Constant — Constant, Wavelength Dependent/ From File
Group delay – constant
Defines the group delay as a fixed constant value, the same for all channels
4.9e+006 ps/km [-INF,INF]
Group delay vs. wavelength
Defines the group delay as a wavelength dependent curve in a file
GroupVs Lambda.dat — [-INF,INF]
GVD data type
Defines the group-velocity dispersion as a fixed constant value, or as a wavelength dependent curve taken from a file
Constant — Constant, Wavelength Dependent/ From File
GVD – constant
Defines the group-velocity dispersion as a fixed constant value, the same for all channels
4.5 ps/nm/km [-INF,INF]
GVD vs. wavelength
Defines the group-velocity dispersion as a wavelength dependent curve in a file
GVDvsLambda.dat — [-INF,INF]
Dispersion slope data type
Defines the dispersion slope as a fixed constant value, or as a wavelength dependent curve taken from a file
Constant — Constant, Wavelength Dependent/ From File
Dispersion slope – constant
Defines the dispersion slope as a fixed constant value, the same for all channels
0.11 ps/nm2/km [-INF,INF]
Dispersion slope vs. wavelength
Defines the dispersion slope as a wavelength dependent curve in a file
DispSlope vs. Lambda.dat
— [-INF,INF]
Effective refractive index vs. wavelength
Defines the effective refractive index as a dispersive curve vs. the wavelength in a file
EffRIVsLambda.dat — [0,INF]
194
NONLINEAR DISPERSIVE FIBER
Birefringence
Name and description Default value Default unit Value range
Birefringence data type
Defines the birefringence (the mismatch between the propagation constants of the two orthogonal polarization modes) as a fixed constant value, or as a wavelength dependent curve taken from a file
Constant — Constant, Wavelength Dependent/ From File
Birefringence – constant
Defines the birefringence as a fixed constant value, the same for all channels
6.2832e-005 rad/m [-1,1]
Birefringence vs. wavelength
Defines the birefringence as a wavelength dependent curve in a file
BirefringenceVs Lambda.dat
— [-1,1]
Coupling length of polarization mixing
Coupling length of polarization scrambling
0.1 km [0,INF]
PMD coefficient
Polarization mode dispersion coefficient
0.07 ps/km1/2 [0,INF]
DGD data type
Defines the differential group delay between the two orthogonal polarization modes as a fixed constant value, or as a wavelength dependent curve taken from a file
Constant — Constant, Wavelength Dependent/ From File
DGD – constant
Defines the differential group delay as a fixed constant value, the same for all channels
3 ps/km [-INF,INF]
DGD vs. wavelength
Defines the differential group delay as a wavelength dependent curve in a file
DGDVsLambda.dat — [-INF,INF]
195
NONLINEAR DISPERSIVE FIBER
Nonlinearities
Name and description Default value Default unit Value range
Effective area data type
Defines the effective area of the fiber as a fixed constant value, or as a wavelength dependent curve taken from a file.
Constant — Constant, Wavelength Dependent/ From File
Effective area – constant
Defines the effective area as a fixed constant value, the same for all channels.
72 µ2 [0,INF]
Effective area vs. wavelength
Defines the effective area as a wavelength dependent curve in a file.
EffAreaVsLambda.dat — [0,INF]
n2 data type
Defines the nonlinear refractive index as a fixed constant value, or as a wavelength dependent curve taken from a file.
Constant — Constant, Wavelength Dependent/ From File
n2 – constant
Define the nonlinear refractive index as a fixed constant value, the same for all channels.
2.6e-020 m2/W [-INF,INF]
n2 vs. wavelength
Defines the nonlinear refractive index as a fixed constant value, or as a wavelength dependent curve taken from a file.
N2VsLambda.dat — [-INF,INF]
Raman-resonant n2 dispersion
Defines the Raman-resonant dispersion of the third-order nonlinear susceptibility as a frequency dependent curve in a file
RamanResN2Vs Freq.dat
— [-INF,INF]
Peak Raman gain coef
The peak Raman gain coefficient at certain pump wavelength
9.9e-014 m/W [0,INF]
Pump Wavelength of Peak Raman gain coef
The pump wavelength corresponding to the above peak Raman gain coefficient
1000 nm [0,INF]
Raman Gain Spectrum
Defines the Raman gain spectrum vs. frequency in a file
RamanGainVsFreq.dat — [0,INF]
Raman self-shift Time
The characteristic Raman self-frequency shifting time
5 fsec [0,INF]
196
NONLINEAR DISPERSIVE FIBER
Effects On/Off; Model Details
Name and description Default value Default unit Value range
Attenuation
Switch On/Off the attenuation
ON — [ON, OFF]
Group velocities mismatch
Switch On/Off the group velocities mismatch
ON — [ON, OFF]
GVD (Group velocity dispersion)
Switch On/Off the group velocity dispersion
ON — [ON, OFF]
GVD Slope (third-order dispersion)
Switch On/Off the dispersion slope (the third-order dispersion)
ON — [ON, OFF]
Polarization evolution
Specify the polarization maintaining capabilities of the fiber and the polarization evolution models to use
Hi-Bi PM fiber, no PMD, fixed DGD
— Hi-Bi PM fiber, no PMD, fixed DGD, Non-PM fiber, PMD, stochastic DGD, Averaged polarizations
Independent pol. mode mixing of WDM channels
In the case of non-PM fiber, determines whether the polarization scrambling follows the same pattern for all the channels or is completely independent
OFF [ON, OFF]
n2 polarization factor 1 dimensionless [0.5, 1]
Raman Gain polarization factor 1 dimensionless [0.5, 1]
Birefringence
Switch On/Off the birefringence
ON — [ON, OFF]
SPM (Self-phase modulation)
Switch On/Off the SPM (Self-phase modulation)
ON — [ON, OFF]
XPM (Cross-phase modulation)
Switch On/Off the XPM (Cross-phase modulation)
ON — [ON, OFF]
XPM of orthogonally polarized modes
Switch On/Off the XPM of orthogonally polarized modes
ON — [ON, OFF]
FWM (four-wave mixing)
Switch On/Off the FWM (four-wave mixing)
OFF — [ON, OFF]
FWM of orthogonally polarized modes
Switch On/Off the XPM of orthogonally polarized modes
OFF — [ON, OFF]
197
NONLINEAR DISPERSIVE FIBER
Simulation details
Maximal phase-mismatch
FWM generated waves with phase-mismatches larger than this value are neglected
100 radian [-1e+100, 1e+100]
SRS (stimulated Raman scattering) ON — [ON, OFF]
SRS with pump wave depletion
Switch On/Off the effect of pump wave depletion in SRS
ON — [ON, OFF]
RSFS (Raman self-frequency shifting)
Switch On/Off the RSFS (Raman self-frequency shifting)
OFF — [ON, OFF]
Name and description Default value Default unit Value range
Enabled
Enable the calculations
ON — [ON, OFF]
Number of steps
Number of longitudinal steps
25 — [0,INF]
Step defined as:
Choose one of the three alternative ways of defining the step size
Fixed = Main Channel Initial Nonlinear length/Number of Steps
— Fixed = Full length/Number of Steps
Fixed = Main Channel Initial Nonlinear length/Number of Steps
Variable = Main Channel Current Nonlinear length/Number of Steps
Time-window boundaries
Choose the type of the time-window boundary conditions
Absorbing — Periodic, Absorbing
Random Phases
Randomize the phase offsets of the channels at input
OFF — [ON,OFF]
Random Phases Seed
The seed of the random phases
1 — [0, 65535]
Name and description Default value Default unit Value range
198
NONLINEAR DISPERSIVE FIBER
3D Graphics selection
Graphs
Name and description Default value Default unit Value range
Power spectrum of channels
Displays the average power spectrum of the channels
OFF — [ON,OFF]
Unit of power spectra
Displays the average power spectrum of channels or the PSD of a selected channel in [mW] or [dBm]
dBm — mW, dBm
Bandwidth spectrum of channels
Displays the rms bandwidths of the channels
OFF — [ON,OFF]
Monitor central sampled channel
Monitors the center most channel if described as a sampled waveform
ON — [ON,OFF]
Wavelength of sampled channel to monitor
Monitors an arbitrary sampled channel, defined by its central wavelength
0 nm [0,INF]
Waveform
Displays the waveform of the selected sampled channel
ON — [ON,OFF]
Chirp
Displays the chirp of the selected sampled channel
OFF — [ON,OFF]
PSD
Displays the PSD of the selected sampled channel
OFF — [ON,OFF]
Spectral Delay
Displays the spectral delay of the selected sampled channel
OFF — [ON,OFF]
Number of 2D snapshots in the 3D graphics
Defines the number of 2D snapshots forming the selected 3D graphics
50 — [2, 1000]
Name and description X Title Y Title
Fiber 3D Graph EmptyX EmptyY
199
NONLINEAR DISPERSIVE FIBER
Parameters—Detailed descriptionsIn the following section, the parameters descriptions are further elaborated. There are descriptions of features pertaining to multiple parameters, and also extended descriptions of individual parameters.
Note: Many parameters pertaining to the NDF can be defined as either constant or wavelength dependent/from file values. The first option is used usually for rapid development of simple designs. If a parameter is wavelength dependent (arb. curve ) you have to prepare a text file with (Wavelength ParameterValue) data pairs, and create the parameter in the appropriate Component properties dialog box. This option is recommended for detailed, quantitatively precise designs. Many parameters of the NDF, such as losses, dispersion, and effective fiber area, can be defined in both ways - as constants or curves loaded from a file. When a parameter is defined as a curve, the format of the text file is as follows:
The units of wavelength are nanometers ( ). The units and the value ranges of the parameter values are the same as those of the respective 'constant' parameters.
For example, when a loss spectrum is loaded from file it might look like:
or:
Wavelength_1 ParameterValue_1
Wavelength_2 ParameterValue_2
Wavelength_3 ParameterValue_3
......
Wavelength_N ParameterValue_N
1500 1.99E-01
1525 1.92E-01
1550 1.89E-01
1575 1.93E-01
1600 2.05E-01
1500 0.199
1525 0.192
1550 0.189
1575 0.193
1600 0.205
nm
200
NONLINEAR DISPERSIVE FIBER
An arbitrary number of points (file lines) are permitted, except 0 (empty file). The column separator can be an arbitrary number (except 0) of either spaces or tabs. The files are opened using the standard Windows "File Open" dialog box.
Technical background
Origin of the nonlinearityAt high optical intensities for intense electromagnetic fields, the dielectric medium behaves as a nonlinear medium. This is also the case for the fiber material. Under the influence of intense electromagnetic fields, the motion of bound electrons becomes anharmonic and, as a result, the induced polarization P from the electric dipoles becomes nonlinear function of the electric field E:
where χ(j) (j =1,2,3, …) denotes the jth order of susceptibility. The lowest order nonlinearity in optical fibers originates from the third order susceptibility χ(3).
Nonlinear effects in optical fibersThe following nonlinear effects in optical fibers are caused by the third-order nonlinear susceptibility and are included in the numerical engine of the component:• Self-phase modulation (SPM)• Cross-phase modulation (XPM)• Cross-phase modulation between the orthogonal modes of a birefringent fiber
(PXPM)• Four-wave mixing (FWM)• Four-wave mixing between the orthogonal modes of a birefringent fiber (PFWM)• Interchannel Stimulated Raman scattering (SRS) and intrachannel Raman self-
shifting (RSS)
OptiSystem currently supports several different models specialized for different signal representations and/or combinations of parameters.
Model IaThis model has been derived for the separated channels signal representation. It also accounts explicitly for the nonlinear interactions and mixing of the orthogonal polarization modes in an SM fiber. It is a system of 2N coupled modified nonlinear Schrödinger equations (NLSE).
This model accounts for:• background loss and linear dispersion up to third order• birefringence and PMD• nonlinearities — SPM, XPM, FWM, SRS, RSS, PXPM, and PFWM
P ε0 x 1( ).E+x 2( ):EE+x 3( ):EEE+...[ ]=
201
NONLINEAR DISPERSIVE FIBER
For Sampled signals, the following effects are accounted for: XPM, XPM of orthogonally polarized modes, Raman, FWM, and SSFS.
Whereas, for Parameterized signals and ASE noise bins, we account for Raman and FWM.
There are 3 types of polarization evolution that could be taken into account:
Hi-Bi PM fiber, no PMD, fixed DGD
In the case of polarization maintaining fiber, we have to specify the birefringence and DGD of the fiber.
Non PM fiber, PMD, stochastic DGD
In this case the correlation length Lcorr and PMD coefficient have to be specified. The component allows the calculation for PMD of any order. To see the effect of PMD, the following effects must also be selected under the Effects tab: Birefringence and Group velocity mismatch
Averaged polarizations
In this case, the effect of the Kerr nonlinearity is averaged over the Poincare sphere, and is taken into account with a coefficient value of 8/9. The effect of nonlinear PMD [2] is not taken into account.
The intrapulse Raman scattering (or Raman Self Shifting) effect, which leads to soliton self frequency shift, has to be considered for very short optical pulses with duration ~ picosecond or smaller.
The model has the following form:
∂Aix
∂z---------- β1ix
∂Aix
∂t---------- i
2---β2i
∂2Aix
∂t2----------- 1
6---β3i
∂3Aix
∂t3-----------– 1
2---αiAix+ +± =
i Mγx µ v ρ, , , δ ωk ωl ωj– ωi–+( )fijkl
fii-------Ajµ∗AkvAlρ i∆βz( ) +exp
j k l, , 1=
j k l i≠, ,
µ x=
v ρ, x y,=
N
∑
i gRj gR
n ωj ωi–( )fij
fii---- Ajx
2Aix igRi gR
n ωi ωj–( )fij
fii---- Ajx
2Aix
j 1=
j 1≠
ωj ωi<
N
∑–j 1=
j 1≠
ωj ωi>
N
∑
13---iγAiy
2Aix∗ 2i∆βxyz–( ) –exp
202
NONLINEAR DISPERSIVE FIBER
(1)
where Aix, Aiy are the slowly varying complex electric field amplitudes of the radiation in the respective x/y polarization mode of the i’th WDM channel,
and are the inverses of the group velocities of the pol. modes,
evaluated at the respective carrier frequency of the channels. is the GVD coefficient, related to the dispersion parameter as:
is the third-order dispersion coefficient, related to the dispersion slope as:
(2)
αi is the loss coefficient for the respective carrier frequency of the channel
is the normalized Raman gain function taken from reference [1], Figure 8.1 on page 300.
γ = ωi n2 / c Aeff is the nonlinear coefficient ( ≈ 1-10 W-1km-1 )
n2 is the nonlinear refractive index equal to 3 χxxxx / 8 neff ( ≈ 3.10-16 cm2/ W )
γ xµνρ = ωi (3 χxµνρ /8 neff )/ (c Aeff ) is the nonlinear coefficient of the four-wave interactions and is proportional to the relevant component of the χ tensor.
iγ Aix2Aix 21γ
fij
fii---- Ajx
2
j 1=
j 1≠
N
∑ Aix+ +
13---iγ Aiy
2Aix23---iγ fij
fii---- Ajy
2
j 1=
j 1≠
N
∑ Aix+ +
iγTR∂ Aix
2
∂t--------------Aix
β1ix1 vg⁄( )ix= β1iy
1 vg⁄( )iy=
β2 i
D 2πcβ2i
λ2----------------–=
β3i
S 2πcλ2
--------- 2
β3i4πcλ3
--------- β2 i+=
gRn
203
NONLINEAR DISPERSIVE FIBER
Aeff is the effective area:
(3)
where F(x,y) is the modal field distribution of the fiber mode.
The overlap integrals fij are defined by:
(4)
M is the multiplicity factor. Its value is 2 if all three waves are different — otherwise, its value is 1.
The overlap integral fijkl is:
(5)
where the angle brackets denote integration over the transverse coordinates x and y.
Aeff =
fii =
fijkl=
F x y,( )( ) 2 xd yd∞–
∞
∫∞–
∞
∫
F x y,( ) 4 xd yd∞–
∞
∫∞–
∞
∫-----------------------------------------------------
Fi x y,( ) 2 Fj x y,( ) 2 xd yd∞–
∞
∫∞–
∞
∫
Fi x y,( ) 2 xd yd∞–
∞
∫∞–
∞
∫ Fj x y,( ) 2 xd yd∞–
∞
∫∞–
∞
∫----------------------------------------------------------------------------------------------
Fi∗Fj∗FkFl⟨ ⟩
Fi2⟨ ⟩ Fj
2⟨ ⟩ Fk2⟨ ⟩ Fl
2⟨ ⟩[ ]1 2⁄--------------------------------------------------------------------------
204
NONLINEAR DISPERSIVE FIBER
Also
(6)
where
(7)
are the propagation constant mismatches of the processes of FWM and (PFWM) and TR ~ 5 fsec is the slope of the Raman gain curve.
Model IbSimilar to Model Ia, but disregards the polarization evolution of the signal and uses the average power of the two polarization modes. It consists of a system of only N coupled modified nonlinear Schrödinger equations (NLSE) with correspondingly adjusted nonlinear coefficients.
Model IDerived for the case of the total field signal representation. All sampled signals are in a single frequency band. This is the basic method used for modeling WDM systems.
It also accounts explicitly for the mixing of the orthogonal polarization modes in an SM fiber. It is a system of two coupled modified nonlinear Schrödinger equations (NLSE).
This model accounts for:• background loss and linear dispersion up to third order• birefringence and PMD• nonlinearities - SPM, XPM, FWM, SRS, RSS, PXPM
It works with all types of signals: Sampled, Parameterized and ASE noise bins. For parameterized and ASE noise bins, only linear losses are taken into account.
'Total field approach' automatically accounts the XPM and FWM effects. There is no possibility to switch off these effects.
'Total field approach for both polarizations' will additionally account for PXPM of orthogonally polarized signals' and PFWM of orthogonally polarized signals'.
The model for the case of one polarization has the following form:
(8)
All the parameters in the above equation have been explained, along with the Model Ia.
∆β ωknk ωlnl ωjnj– ωini–+( ) c⁄=
∆βxy βy βx–=
∂A∂z------ β1
∂A∂t------ i
2---β2
∂2A∂t2-------- 1
6---β3
∂3A∂t3--------– 1
2---αAx+ +± iγ A 2A iγTR
∂ A 2
∂t-----------A–=
205
NONLINEAR DISPERSIVE FIBER
Numerical Methods
The three models (Model la, Model lb, and Model l) are solved by a scalar or vectorial version of the split-step Fourier transform method:
(9)
with symmetrized step size [1].
In addition, the step size can be controlled along the propagation.
Step size selection rulesThe user can choose one of the following three ways to calculate the step size:• Fixed• Initial Nonlinear Length / Number of Steps• Current Nonlinear Length / Number of Steps
FixedIn this case the step size is simply , where is the length of the fiber and is the user defined number of steps.
Initial Nonlinear Length / Number of StepsOne of the well known strategies for guaranteeing accurate split-step calculations is to limit the value of the accumulated nonlinear phase-shift per step.
This is equivalent to set
where is the nonlinear length at the input of the fiber (a measure of the distance needed for considerable nonlinear distortions to occur), and
is the user specified number of steps per .
Another limitation imposed is that the maximum temporal displacement of the channels due to group-velocity mismatch per step is less than 1% of the bit period.
Current Nonlinear Length / Number of StepsIn this case, the nonlinear length is periodically recalculated along the fiber:
.
In this way, the possible changes in due to loss or gain are taken into account.
The term indicates the channel used in the calculations above. When the separate channels signal representation is used, it is either the channel with the highest power or the central channel. If we use only one continuous spectral band, as in the total field signal representation, there can be only one main channel.
∂A∂z------ D N+[ ]A=
∆z L N⁄= LN
∆z LNL NLNL⁄=
LNL 1 γP 0( )⁄=
NLNL LNL
LNL z( ) 1 γP⁄ z( )=
LNL z( )
206
NONLINEAR DISPERSIVE FIBER
References[1] Agrawal, G.P., “Nonlinear Fiber Optics, 3rd Edition”, Academic Press, 2001.
[2] Marcuse, D., Menyuk, C.R., and Wai, P.K.H., "Application of the Manakov - PMD Equation to Studies of Signal Propagation in Optical Fibers with Randomly Varying Birefringence", Journ. Light. Technol.,15, 1735-1746 (1997).
[3] Tchofo Dinda, P., Milot, G., and Wabnitz, S. "Polarization Switching and Suppression of Stimulated Raman Scattering in Birefringent Optical Fibers", JOSA B, 15, 1433-1441 (1998).
207
NONLINEAR DISPERSIVE FIBER
Notes:
208
Receivers Library
This section contains information on the following receivers.
Regenerators
Electrical
• Clock Recovery• Data Recovery• 3R Regenerator
Optical
Demodulators
• Ideal Frequency Demodulator• Ideal Phase Demodulator
Photodetectors
• Photodetector PIN• Photodetector APD
209
Notes:
210
CLOCK RECOVERY
Clock RecoveryCompensates the time delay between the original signal at the reference port and the signal that is received at the input port.
Ports
Parameters
Simulation
Results
Technical background
The time delay is calculated from cross-correlation of the reference signal and the received signal. The signal is then shifted in time.
Name and description Port type Signal type
Reference Input Electrical
Input Input Electrical
Output Output Electrical
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
Name and description Units
Signal delay s
Signal delay samples
211
DATA RECOVERY
Data RecoveryThis component recovers the binary data from the electrical signal. It can be used in 3R generators for the data recovery stage.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Electrical
Bit sequence Output Binary
Name and description Default value Default unit Units Value range
Reference bit rateReference bit rate to use for the decision instant calculation
Bit rate Bits/s Bits/sMBits/sGBits/s
[0,+INF[
User defined delayDefines whether the user can define the delay compensation or not
False — — True, false
Delay compensationDelay to apply to the signal input
0 s s, ms, ns ]-INF,+INF[
User defined decisionDefines whether the component will automatically calculate the decision instant or it will be defined by the user
False — — True, false
Decision instantValue for the decision instant to use when recovering the bit sequence
0.5 Bit — [0,1]
User defined thresholdDefines whether the component will be automatically calculated or willbe user-defined
False — — True, false
Absolute thresholdValue for the threshold to use when recovering the bit sequence
0.5 a.u. — ]-INF,+INF[
212
DATA RECOVERY
Random numbers
Technical Background
This component allows the user to recover a bit sequence from an electrical signal. In order to recover the bit sequence, the user should provide the signal bit rate, given by the parameter Reference bit rate. The decision instant and the threshold level can be defined by the user or automatically calculated by this component. If the parameter User defined decision is disabled, the model automatically estimates the decision instant by generating internally an eye diagram and searching for the maximum opening for the eye amplitude. The time instant with the maximum opening is the decision instant, this method is valid for RZ and NRZ modulation types. The user can disable the searching and enter directly the value of the decision instant by disabling User defined decision and entering the instant using the parameter Decision instant.
If the parameter User defined threshold is disabled, the threshold is calculated at the decision instant, by searching for the maximum eye opening. The threshold value will be at the center of the maximum eye opening. The user can disable the searching and enter directly the value of the threshold by disabling User defined threshold and entering the threshold using the parameter Absolute threshold.
The parameter Delay compensation allows the user to compensate the propagation delays of the input signal by enabling the parameter User defined delay. If the parameter User defined delay is disable, the delay will be estimated by comparing the input signal with a signal generated by the internal clock.
Name and description Default value Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
213
3R REGENERATOR
3R RegeneratorThis component regenerates an electrical signal.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Electrical
Bit sequence Output Binary
Reference signal Output Electrical
Output Output Electrical
Name and description Default value Default unit Units Value range
Reference bit rateReference bit rate to use for the decision instant calculation
Bit rate Bits/s Bits/sMBits/sGBits/s
[0,+INF[
User defined delayDefines whetherthe u;ser can define the delay compensation or not
False — — True, false
Delay compensationDelay to apply to the signal input
0 s s, ms, ns ]-INF,+INF[
User defined decisionDefines whether thecomponent will automatically calculate the decision instant or it will be defined by the user
False — — True, false
Decision instantValue for the decision instant to use when recovering thebit sequence
0.5 Bit — [0,1]
User defined thresholdDefines whether the component will be automatically calculated or willbe user-defined
False — — True, false
214
3R REGENERATOR
Technical Background
This component regenerates an electrical signal. It generates the original bit sequence, and a modulated electrical signal to be used for BER analysis. It is a subsystem based on the Data Recovery component and a NRZ Pulse Generator.
This first output port is the bit sequence, the second one is a modulated NRZ signal and the last output is a copy of the input signal. These three signals can be connected directly to the BER Analyzer, avoiding additional connections between transmitter and the receiver stage.
The following system shows a conventional connection between the BER Analyzer in the receiver stage with the transmitter stage, 2 additional connections are required between the transmitter and the BER Analyzer.
Absolute thresholdValue for the threshold to use when recovering the bit sequence
0.5 a.u. — ]-INF,+INF[
Name and description Default value Default unit Units Value range
215
3R REGENERATOR
By using the 3R Regenerator, there is no need for connections between the transmitter and the BER Analyzer. This is especially important for WDM systems, where you have with multiple transmitters, receivers and BER Analyzers. For more information, see “WDM Transmitter” on page 107.
216
IDEAL FREQUENCY DEMODULATOR
Ideal Frequency DemodulatorConverts the received optical signal phase into electrical signal amplitude.
Ports
Parameters
Main
Downsampling
Name and description Port type Signal type
Input Input Optical
Output Output Electrical
Name and description Default value Units Value range
Min. amplitudeMinimum electrical signal amplitude at the output port
0 a.u. ]-INF,+INF[
Max. amplitudeMaximum electrical signal amplitude at the output port
1 a.u. ]-INF,+INF[
Name and description Default value Default unit Units Value range
Centered at max powerDetermines whether the internal filter will be centered at the maximum amplitude of the signal or if it will be user-defined
True — — True, False
Center frequencyUser-defined center frequency for the internal filter
193.1 THz Hz, THz, nm [30, 3e5]
Sample rateInternal filter bandwidth
5*(Sample rate) Hz Hz, GHz, THz, nm
[0,+INF[
217
IDEAL FREQUENCY DEMODULATOR
Polarization
Random numbers
Technical background
The incoming optical signal and noise bins are filtered by an ideal rectangle filter to reduce the number of samples in the electrical signal. The new sample rate is defined by the parameter Sample rate. You can define the center frequency, or it can be calculated automatically by centering the filter at the optical channels with maximum power.
Optical noise bins are converted to gaussian noise inside the signal bandwidth. You must supply the polarization for the frequency extraction. The signal frequency is then normalized in the range between the parameters Min. and Max. amplitude.
Figure 1 Filtered signal
The converter resamples the signal and converts the noise bins. They are added in time domain.
Name and description Default value Units Value range
PolarizationDetermines if the frequency from the polarization X or Y of the optical signal will be converted to amplitude
X — X, Y
Name and description Default value Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
218
IDEAL PHASE DEMODULATOR
Ideal Phase DemodulatorConverts the received optical signal phase into electrical signal amplitude.
Ports
Parameters
Main
Downsampling
Name and description Port type Signal type
Input Input Optical
Output Output Electrical
Name and description Default value Units Value range
Min. amplitudeMinimum electrical signal amplitude at the output port
0 a.u. [-1e+100, -1e+100]
Max. amplitudeMaximum electrical signal amplitude at the output port
1 a.u. [-1e+100, -1e+100]
Name and description Default value Default unit Units Value range
Centered at max powerDetermines whether the internal filter will be centered at the maximum amplitude of the signal or if it will be user-defined
True — — True, False
Center frequencyUser-defined center frequency for the internal filter
193.1 THz Hz, THz, nm [30, 3e5]
Sample rateInternal filter bandwith
5*(Sample rate) Hz Hz, GHz, THz, nm
[0,+INF[
219
IDEAL PHASE DEMODULATOR
Polarization
Random numbers
Technical background
The incoming optical signal and noise bins are filtered by an ideal rectangle filter to reduce the number of samples in the electrical signal. The new sample rate is defined by the parameter Sample rate. You can define the center frequency, or it can be calculated automatically by centering the filter at the optical channels with maximum power.
Optical noise bins are converted to gaussian noise inside the signal bandwidth. You must supply the polarization for the phase extraction. The signal phase is then normalized in the range between the parameters Min. and Max. amplitude.
Figure 1 Converted noise bins enabled
The converter resamples the signal and converts the noise bins. They are added in time domain.
Name and description Default value Units Value range
PolarizationDetermines if the frequency from the polarization X or Y of the optical signal will be converted to amplitude
X — X, Y
Name and description Default value Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
220
PHOTODETECTOR PIN
Photodetector PINPIN photodiode.
Ports
Parameters
Main
Downsampling
Name and description Port type Signal type
Input Input Optical
Output Output Electrical
Name and description Default value Units Value range
Responsivity 1 A/W [0,100]
Dark current 10 nA [0,+INF[
Name and description Default value Default unit Units Value range
Centered at max powerDetermines whether the internal filter will be centered at the maximum amplitude of the signal or if it will be user-defined
True — — True, False
Center frequencyUser-defined center frequency for the internal filter
193.1 THz Hz, THz, nm [30,3e5]
Sample rate 5*(Sample rate) Hz Hz, GHz, THz, nm
[1e-3,+INF[
221
PHOTODETECTOR PIN
Noise
Random numbers
Name and description Default value Default unit Units Value range
Noise calculation type Numerical — — Analytical, Numerical, Numerical - Convert noise bins
Add signal-ASE noise True — — True, False
Add ASE-ASE noise True — — True, False
Add thermal noise True — — True, False
Thermal noise 0 W/Hz — [0,+INF[
Add shot noiseDetermines if shot noise is added to the signal
True — — True, False
Shot noise distributionDetermines the distribution used to generate the shot noise
Gaussian — — Poisson, Gaussian
Name and description Default value Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
222
PHOTODETECTOR PIN
Technical backgroundThe incoming optical signal and noise bins are filtered by an ideal rectangle filter to reduce the number of samples in the electrical signal. The new sample rate is defined by the parameter Sample rate. You can define the center frequency, or it can be calculated automatically by centering the filter at the optical channel with maximum power.
If the noise calculation type in Numerical:
Optical noise bins are converted to Gaussian noise inside of the signal bandwidth. The combined optical field is then converted to optical power. If the option Numerical — Convert Noise Bins is selected, the output noise and signal are combined. This means that you cannot see the the separate contributions of the noise. However, if you select Numerical only, the signal and noise are separated and you can select the different contributions of the noise.
Figure 1 Convert noise bins enabled
The PIN resamples the signal and converts the noise bins when Convert Noise Bins is enabled.
Gaussian shot noise distribution
If the parameter Add shot noise is enabled and the Shot noise distribution parameter is Gaussian, the optical power is converted to electrical current by:
where is(t) is the optical signal calculated from the responsivity r:
where ith(t) is the thermal noise current calculated from the power spectral density defined by the parameter Thermal noise, and id is the dark current.
(1)
(2)
i t( ) is t( ) ith t( ) id ish t( )+ + +=
is t( ) rPs t( )=
223
PHOTODETECTOR PIN
The shot noise current ish(t) is calculated according to the power spectral density [1]:
Poisson shot noise distribution
If the parameter Add shot noise is enabled and Shot noise distribution parameter is Poisson, the electrical current is calculated according to [2]:
where ne denotes the number of electrons generated in the time instant ∆t. The average number of generated electrons (equal to the average number of detected photons) within the time interval is given by:
The number of generated electrons is the Poisson random variable with mean and variance equal .
If the noise calculation type is Analytical:
In this case, the signal and the noise components are calculated independently. The noise components are the variance and the noise PSD.
(3)
(4)
(5)
Nsh q is id+( )=
i t( ) qne
∆t-------- ith t( )+=
ne⟨ ⟩ ∆t
ne⟨ ⟩is t( )
q----------∆t id
q---∆t .+=
nene⟨ ⟩
224
PHOTODETECTOR PIN
Figure 2 Convert noise bins disabled
In Figure 2, the PIN resamples the signal and does not convert the noise bins if Convert Noise Bins is disabled.
225
PHOTODETECTOR PIN
)
)
)
The output electrical signal is:
Note: This signal does not include the noise components. The noise components are calculated by the noise variance and by the power spectral density.
For the noise variances:
where is the signal shot noise:
where is the electrical bandwidth.
and is the signal ASE beating:
For the noise PSD components:
where PTH(f) is the thermal noise and PASE-ASE(f) is the beating of ASE-ASE:
and the ASE shot noise is:
Defining sensitivity
The sensitivity of a receiver can be defined by optimizing the receiver parameters.
A typical way of doing this is to optimize the thermal noise in your receiver, to obtain a specific BER .
(6)
(7)
(8)
(9)
(10
(11
(12
i t( ) rP t( ) id+=
σ2 t( ) σsh2 t( ) σs ASE–
2 t( )+=
σsh2 t( )
σsh2 t( ) qis t( )Be=
Be
σs ASE–2 t( )
σs ASE–2 t( ) 4r2PASE t( )Ps t( )=
P f( ) PTH f( ) PASE ASE– f( ) PASEsh f( )+ +=
PASE ASE– f( ) r2 PASE f( )∗PASE f( )( )=
PASEsh f( ) qrPASE f( )Be=
1 10 9–×( )
226
PHOTODETECTOR PIN
References:[1] Agrawal, G.P., Fiber-Optic Communication Systems. John Wiley & Sons, New York, (1997).
[2] Jeruchim, M.C., Balaban, P., Shanmugan, K., Simulation of Communication Systems: Modeling, Methodology, and Techniques. Plenum Press, New York, (1997).
227
PHOTODETECTOR APD
Photodetector APDFilter with a square cosine roll off frequency transfer function.
Ports
Parameters
Main
Downsampling
Name and description Port type Signal type
Input Input Optical
Output Output Electrical
Name and description Default value Default unit Units Value range
GainAvalanche multiplication factor
3 — — [0,+INF[
Responsivity 1 A/W — [0,100]
Ionization ratioIonization factor
0.9 — — ]0,1]
Dark currentDark current amplified by the avalanche effect
10 nA — [0,+INF[
Name and description Default value Default unit Units Value range
Centered at max powerDetermines whether the internal filter will be centered at the maximum amplitude of the signal or if it will be user-defined
True — — True, False
Center frequencyUser-defined center frequency for the internal filter
193.1 THz Hz, THz, nm [30,3e5]
Sample rate 5*(Sample rate) Hz Hz, GHz, THz, nm
[1e-3,+INF[
228
PHOTODETECTOR APD
Noise
Random numbers
Technical background
The incoming optical signal and noise bins are filtered by an ideal rectangle filter to reduce the number of samples in the electrical signal. The new sample rate is defined by the parameter Sample rate. You can define the center frequency, or it can be calculated automatically by centering the filter at the optical channel with maximum power.
If the noise calculation type in Numerical:
Optical noise bins are converted to Gaussian noise inside of the signal bandwidth. The combined optical field is then converted to optical power. If the option Numerical — Convert Noise Bins is selected, the output noise and signal are combined. This means that you cannot see the the separate contributions of the noise. However, if you select Numerical only, the signal and noise are separated and you can select the different contributions of the noise.
Name and description Default value Default unit Units Value range
Noise calculation type Numerical — — Analytical, Numerical, Numerical - Convert noise bins
Add signal-ASE noise True — — True, False
Add ASE-ASE noise True — — True, False
Add thermal noise True — — True, False
Thermal noise 0 W/Hz — [0,+INF[
Add shot noiseDetermines if shot noise is added to the signal
True — — True, False
Shot noise distributionDetermines the distribution used to generate the shot noise
Gaussian — — [WMC, Gaussian]
Name and description Default value Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
229
PHOTODETECTOR APD
Figure 1 Convert noise bins enabled
The APD resamples the signal and converts the noise bins when Convert Noise Bins is enabled.
If the parameter Add shot noise is enabled and Shot noise distribution parameter is Gaussian, the optical power is converted to electrical current:
where is(t) is the optical signal calculated from the responsivity r and the gain M as:
and ith(t) is the thermal noise current calculated from the power spectral density defined by the parameter Thermal noise and id is the additive dark current.
The shot noise current ish(t) is calculated according to the power spectral density:
where idm is the dark current and F depends on M:
where k is the Ionization ratio.
(1)
(2)
(3)
(4)
i t( ) is t( ) ith t( ) id ish t( )+ + +=
is t( ) MrPs t( )=
Nsh t( ) qM2F rPs t( ) idm+( )=
F M( ) kM 2 1 M⁄–( ) 1 k–( )+=
230
PHOTODETECTOR APD
If the noise calculation type is Analytical:
In this case, the signal and the noise components are calculated independently. The noise components are the variance in time and the noise PSD.
Figure 2 Convert noise bins disabled
The PIN resamples the signal and does not convert the noise bins if Convert Noise Bins is disabled.
The output electrical signal is:
The noise variances are:
where is the signal shot noise:
where is the electrical bandwidth.
and is the signal ASE beating:
(5)
(6)
(7)
(8)
i t( ) rP t( ) id+=
σ2 t( ) σsh2 t( ) σs ASE–
2 t( )+=
σsh2 t( )
σsh2 t( ) qM2Fis t( )Be=
Be
σs ASE–2 t( )
σs ASE–2 t( ) 4r2M2PASE t( )Ps t( )=
231
PHOTODETECTOR APD
)
)
The noise PSD components are:
where PTH(f) is the thermal noise and PASE-ASE(f) is the beating of ASE-ASE:
and the ASE shot noise is:
Reference:
[1] Agrawal, G.P., Fiber-Optic Communication Systems. John Wiley & Sons, New York, (1997).
(9)
(10
(11
P f( ) PTH f( ) PASE ASE– f( ) PASEsh f( )+ +=
PASE ASE– f( ) r2M2 PASE f( )∗PASE f( )( )=
PASEsh f( ) qM2FrPASE f( )Be=
232
Amplifiers Library
This section contains information on the following amplifiers.
Optical
Raman
• Raman Amplifier• Raman Amplifier—Average power model• Raman Amplifier—Dynamic model
EDFA
• EDFA Black Box• EDF Dynamic — Full model• EDF Dynamic — Analytical model• EDFA• EDFA Ideal• EDFA Measured• Erbium doped fiber• Er-Yb codoped fiber• Er-Yb codoped waveguide amplifier
SOA
• Semiconductor Optical Amplifier
233
AMPLIFIERS LIBRARY
Electrical
• Limiting Amplifier• Electrical Amplifier• Transimpedance Amplifier• AGC Amplifier
234
RAMAN AMPLIFIER
Raman Amplifier
Fundamental model of a generic fiber Raman Amplifier. Its power and versatility allow it to represent virtually any type of Raman amplifier — employing any type of fiber, with arbitrary pump configuration and multiple sections — with a suitable combination of parameters.
Ports
Parameters
Fiber
Name and description Port type Signal type
Input 1 Input Optical
Output 1 Output Optical
Input 2 Input Optical
Output 2 Output Optical
Name and description Default value Default unit Value range
Fiber length 10 km [0, INF]
Attenuation data type Constant — Constant, Wavelength Dependent /From File
Attenuation – constant 0.25 dB/km [0, INF]
Attenuation vs. wavelength AtnVsLambda.dat — [0, INF]
Forward Input Coupling Loss 1 dB [0, 106]
Forward Output Coupling Loss 0.022 dB [0, 106]
Backward Input Coupling Loss 1 dB [0, 106]
Backward Output Coupling Loss
0.022 dB [0, 106]
Effective area data type Constant — Constant, Wavelength Dependent/From File
Effective area – constant 72 µm2 [0, INF]
Effective area vs. wavelength EffAreaVsLambda.dat — [0, INF]
235
RAMAN AMPLIFIER
Raman effect
Rayleigh effect
Reflections
Name and description Default value Default unit Value range
Peak Raman gain coef 9.9e-14 m/W [0, INF]
Pump wavelength of peak Raman gain coef
1000 nm [0, INF]
Raman gain spectrum vs. freq. RamanGainVsFreq.dat — —
Raman gain polarization factor 0.5 — [0, INF]
Temperature 300 K [0, INF]
Name and description Default value Unit Value range
Rayleigh coef. data type Constant — Constant, Wavelength Dependent/From File
Rayleigh coef. — constant 5e-005 1/km [0, INF]
Rayleigh coef. vs. wavelength RayleighGainvsLambda.dat — [0, INF]
Name and description Default value Unit Value range
Left end reflection data type Constant — Constant, Wavelength Dependent/From File
Left end reflection — constant –30 dB [-INF, 0]
Left end reflection vs. wavelength
NearEndReflVsLambda.dat — [-INF, 0]
Right end reflection data type Constant — Constant, Wavelength Dependent/From File
Right end reflection — constant
–30 dB [-INF, 0]
Right end reflection vs. wavelength
FarEndReflVsLambda. dat — [-INF, 0]
236
RAMAN AMPLIFIER
Other nonlinearities
Effects on/off
Name and description Default value Unit Value range
Brillouin gain coef 5e-011 m/W [0, INF]
Brillouin bandwidth data type Constant — Constant, Wavelength Dependent/From File
Brillouin bandwidth — constant
40 MHz [0, INF]
Brillouin bandwidth vs. wavelength
FarEndReflVsLambda.dat — [0, INF]
Brillouin Stokes shift 11 GHz [0, INF]
Nonlinear refr. index data type Constant — Constant, Wavelength Dependent/From File
Nonlinear refr. index — constant
3e-020 m2/W [0, INF]
Nonlinear refr. index vs. wavelength
N2VsLambda.dat — [0, INF]
Raman-resonant n2 dispersion RealHiRezVsLambda.dat — [–INF, INF]
Eff. refr. index vs. wavelength EffRIVsLambda.dat — [0, INF]
Group velocity dispersion 5 ps/nm/km [0, INF]
Dispersion slope 0.1 ps/nm2/km [0, INF]
Name and description Value range Dependence
Attenuation ON [ON, OFF]
Rayleigh backscattering gain ON [ON, OFF]
SRS gain(Stimulated Raman scattering gain)
ON [ON, OFF]
SpRS gainSpontaneous Raman scattering gain)
OFF [ON, OFF]
Pump depletion in SRS ON [ON, OFF]
Double Rayleigh scattering OFF [ON, OFF]
Left end reflection OFF [ON, OFF]
Right end reflection OFF [ON, OFF]
Polarisation maintaining fiber OFF [ON, OFF]
237
RAMAN AMPLIFIER
Simulation details
Noises
SBS gain(Stimulated Brillouin scattering gain)
OFF [OFF]
Pump depletion in SBS OFF [OFF]
FWM(four-wave mixing)
OFF [OFF]
Nonlinear contribution to the phase-mismatch OFF [OFF]
Note: The last four effects will be implemented soon — they are currently disabled.
Name and description Default value Unit Value range
Enable ON — [ON, OFF]
Parameter set Default — Default, Auto, User
Upper Pump wavelength 1450 nm [0, INF]
Power accuracy 0.001 — [0, INF]
Max. number of iterations 100 — [1, 10000]
Number of power iterations 4 — [1, 10000]
ODE integration method 5th-order Runge-Kutta with step size control
— 5th-order Runge-Kutta with step size control, Gear's stiff eq. solver with step size control
ODE integrator accuracy 1e-006 — [0, 1]
Max. number of steps per iteration
100000 — [1, 10000]
Number of longitudinal points 256 — [10, 100000]
Background noise PSD level 1e-100 W/Hz [0, 10000]
Inphase noise ratio 0 — [0, 1]
Calculate 3D graphics ON — [ON,OFF]
3D graphics resolution 10 — [1, 100]
Name and description Default value Default unit Unit Value range
Noise center frequency 193.1 THz Hz, THz, nm [30, 3e+006]
Noise bandwidth 30 THz Hz, THz, nm [0, INF]
Name and description Value range Dependence
238
RAMAN AMPLIFIER
Random numbers
Results
Graphs
Noise bins spacing 1000 GHz Hz, GHz, THz, nm [0, INF]
Noise threshold –100 dB — [-INF,+INF]
Noise dynamic 3 dB — [0, INF]
Convert noise bins Convert noise bins — — [ON, OFF]
Name and description Default value
Unit Value range
Generate random seedDetermines if the seed is automatically defined and unique
ON — [ON,OFF]
Random seed indexUser-defined seed index for noise generation
0 — [0, 4999]
Name and description Default value
Unit Value range
Lower limit of Region of Interest 1550 nm [0, INF]
Upper limit of Region of Interest 1600 nm [0, INF]
Name and description X Title Y Title
Forward Output Power Spectrum [dBm] Wavelength [nm] Power [dBm]
Forward Output Gain [dB] Wavelength [nm] Gain [dB]
Forward Output OSNR [dB] Wavelength [nm] OSNR [dB]
Forward Output Multiple Rayleigh Scattering Spectrum [dBm]
Wavelength [nm] Power [dBm]
Backward Output Power Spectrum [dBm] Wavelength [nm] Power [dBm]
Backward Output Gain [dB] Wavelength [nm] Gain [dB]
Backward Output OSNR [dB] Wavelength [nm] OSNR [dB]
Backward Output Multiple Rayleigh Scattering Spectrum [dBm]
Wavelength [nm] Power [dBm]
Forward Power Spectrum [dBm] Wavelength [nm] Fiber Length [km]
Forward Gain [dB] Wavelength [nm] Fiber Length [km]
Name and description Default value Default unit Unit Value range
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RAMAN AMPLIFIER
When a parameter is defined as a curve loaded from a file, the format of the file is:
The unit of the wavelengths is always [nm]. The units of the parameter values are given in the table above, and are the same as the units of the respective Constant parameter. Arbitrary number of points (file lines) are allowed, except 0 (empty file).
ResultsThe component produces the following results:
Maximum Forward Gain [dB]
Maximum Forward On/Off Gain [dB]
Forward Gain Flatness [dB]
Maximum Forward Power [dB]
Wavelength of Maximum Forward Power [dB]
Minimum Forward Effective Noise Figure [dB]
Forward Effective Noise Figure Flatness [dB]
Maximum Backward Gain [dB]
Maximum Backward On/Off Gain [dB]
Backward Gain Flatness [dB]
Forward Gain Coefficient [dB/km] Wavelength [nm] Fiber Length [km]
Forward OSNR [dB] Wavelength [nm] Fiber Length [km]
Forward Double Rayleigh Scatt. Spectrum [dBm] Wavelength [nm] Fiber Length [km]
Backward Power Spectrum [dBm] Wavelength [nm] Fiber Length [km]
Backward Gain [dB] Wavelength [nm] Fiber Length [km]
Backward Gain Coefficient [dB/km] Wavelength [nm] Fiber Length [km]
Backward OSNR [dB] Wavelength [nm] Fiber Length [km]
Backward Double Rayleigh Scatt. Spectrum [dBm] Wavelength [nm] Fiber Length [km]
Wavelength_1 ParameterValue_1
Wavelength_2 ParameterValue_2
Wavelength_3 ParameterValue_3
......
Wavelength_N ParameterValue_N
Name and description X Title Y Title
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RAMAN AMPLIFIER
Maximum Backward Power [dB]
Wavelength of Maximum Backward Power [dB]
Minimum Backward Effective Noise Figure [dB]
Backward Effective Noise Figure Flatness [dB]
These results are calculated for the wavelength range defined in the Results tab of the Component Properties dialog box.
Forward and Backward are names used to distinguish the characteristics pertaining to the left and right ends of the fiber respectively. They have nothing to do with the frequently used terms forward / (backward) Raman amplification, meaning amplifier configuration having co-propagating / (counter-propagating) pump and signals.
GraphicsThe Raman Amplifier presents the results of the calculations in a variety of both 2D and 3D graphics.
2D graphicsThe following 2D graphs are available:• Forward Output Power Spectrum [dBm]• Forward Output Gain [dB]• Forward Output On/Off Gain [dB]• Forward Output OSNR [dB]• Forward Double Rayleigh Scattering Spectrum [dBm]• Forward Eff. Noise Figure Spectrum [dB]• Backward Output Power Spectrum [dBm]• Backward Output Gain [dB]• Backward Output On/Off Gain [dB]• Backward Output OSNR [dB]• Backward Double Rayleigh Scattering Spectrum [dBm]• Backward Eff. Noise Figure Spectrum [dB]
3D graphicsThe following 3D graphs are available:• Forward Power Spectrum [dBm]• Forward Gain [dB]• Forward Gain Coefficient [dB/km]• Forward OSNR [dB]• Forward Double Rayleigh Scattering Spectrum [dBm]• Backward Power Spectrum [dBm]
241
RAMAN AMPLIFIER
• Backward Gain [dB]• Backward Gain Coefficient [dB/km]• Backward OSNR [dB]• Backward Double Rayleigh Scattering Spectrum [dBm]
2D/3D graphicsThe following 2D/3D graphics are available:• Forward Power Spectrum [dBm]• Forward On/Off Gain [dB]• Forward Gain [dB]• Forward Gain Coefficient [dB/km]• Forward OSNR [dB]• Forward Double Rayleigh Scattering Spectrum Power [dBm]• Forward Eff. Noise Figure [dB]• Backward Power Spectrum [dBm]• Backward On/Off Gain [dB]• Backward Gain [dB]• Backward Gain Coefficient [dB/km]• Backward OSNR [dB]• Backward Double Rayleigh Scattering Spectrum Power [dBm]• Backward Eff. Noise Figure [dB]
Forward and Backward are names used to distinguish the characteristics pertaining to the overall optical spectra propagating from the left end to the right end of the fiber respectively, and vice-versa. They have nothing to do with the frequently used terms forward / (backward) Raman amplification, meaning amplifier configuration having co-propagating / (counter-propagating) pump and signals.
242
RAMAN AMPLIFIER
Technical background
IntroductionThe most promising technology to support almost unlimited bandwidth employs the nonlinear effect of stimulated Raman scattering (SRS) in hybrid EDFA + Raman fiber amplifiers (HRA) or purely Raman fiber amplifiers (RFA) [1,2]. The most important advantage of this effect is that the pump wavelength λp does not need to be tied to a particular energy level/absorption band, as it is in EDFAs. Raman amplification is readily obtainable in any spectral region and in any type of fiber, provided a practical pump source with wavelength 80-100 nm shorter than that of the signal and with sufficiently high power is available. Given the progress in the manufacturing of high-power pump lasers in the infrared [3] along with the seemingly limitless demand for amplification bandwidth, Raman amplification will play an increasingly important role in WDM networks.
SRS is among the best-understood third-order nonlinear processes, observed experimentally for the first time in 1962 in bulk media [4] and in 1972 in optical fibers [5]. It manifests itself as an exponential growth of a signal (Stokes) wave in the field of a shorter wavelength-intensive pump. As mentioned above, SRS is a non-resonant effect with respect to pump wavelength, which may lie anywhere in the transparency windows of the medium. On the other hand, the frequency difference ωp-ωs between the pump and signal waves should be resonant with one of the vibrational modes ωR of the host. SRS does not require phase-matching, and for CW pumps, it allows both forward (pump and signal co-propagating) and backward (counter-propagating) pumping configurations. The most important characteristics of SRS in telecom-grade fibers are [6 (and references)]:• The SRS gain spectrum peaks at 13.2 THz (≈ 100 nm at λp =1.55 µm), but
extends up to 30 THz.• The 3dB bandwidth of the gain spectrum is 6-7 THz (≈ 50 nm at λp =1.55 µm).• The peak gain gR
peak (λ) coefficient is 6.4x10-13 m/W for λp = 1.55 [µm], and is inversely proportional to λp.
• Both the shape of the spectrum and the value of gRpeak (λ) depend on the
concentration of the dopants; the peak gain coefficient of pure GeO2 is 8 times larger than that of fused silica. Figure 1 shows the zero temperature Raman gain coefficient spectra of pure fused silica, pure fused GeO2, and silica doped with 25 mol.% GeO2. The spectra are scaled to the peak gain coefficient of silica.
• The SRS effect is in principle highly polarization-dependent. Raman gain is negligible for orthogonal polarizations of the pump and signal. However, in non-polarization maintaining fibers, the gain becomes polarization independent due to mode-scrambling. In this case gR
peak(λ) is reduced by a factor of 2.
243
RAMAN AMPLIFIER
Figure 1 Zero temperature Raman coefficient spectra
The arbitrary choice of pump(s) wavelength(s) allows for a key new feature in all types of hybrid and Raman fiber amplifiers: the possibility to arrange several pumps in a finite pump band and to amplify the WDM signals in their extended aggregate gain spectrum. Gain-equalization is achieved by a proper choice of the wavelengths and powers of the individual pumps.
On the device level, the HRA and FRA come in a variety of configurations: backward-, forward- and bidirectionally pumped, discrete or distributed, single- or multi-stage. The ubiquitous nature of the Raman effect allows numerous types of fibers to be used as the SRS–active media — from standard transmission fibers in distributed FRA to short (5-8 km) DCFs or highly nonlinear heavily-doped fibers with small effective areas [9]. Typically, several hundred milliwatts of pump power are required.
The challenges in modeling and optimizing FRAs are related mainly to the nonlinear, inefficient nature of SRS, requiring high pump powers and long fibers, and to the different pump mechanism.• All participating optical waves interact with each other. The shorter wavelengths
transfer power to the longer wavelengths (all long wavelengths deplete all short wavelengths), resulting in a complex longitudinal distribution of gain coefficients and noise powers.
• Other third-order nonlinear processes among the pumps take place — SPM and XPM, FWM, and stimulated Brillouin scattering (SBS).
• Considerable noise powers and crosstalk are generated by multi-path Rayleigh scattering.
An additional challenge is the requirement to build a model that is both quantitatively and qualitatively precise. While the general features of any of the effects above are well known [6], it is the complex interplay of the details that matters if such a model is
244
RAMAN AMPLIFIER
to be used as a versatile design tool by the photonics industry. As a result, some of the simplifications (usually found in the literature) should be rejected:• The Raman spectrum of pure fused silica must be used with care. For discrete
FRAs, the magnitude and the spectrum of the Raman gain coefficient must always be defined in dependence on the concentration of the dopants [14]. The dispersion of the real part of the Raman-resonant nonlinear susceptibility must also be accounted for [15].
• The assumption that the fiber parameters, such as effective areas/overlap integrals, losses, and Brillouin gain bandwidth, are constants. In the wavelength region of 1.4-1.65 [µm], the effective areas of SMF-28TM and a typical DSF vary by 25% and 50% respectively.
The comprehensive model described here uses the unified spectral signal representation illustrated in Figure 2. It features arbitrary number and location of pumps, signals and ASE bands, and complete forward / backward symmetry. Each forward propagating wave has a backward counterpart at the same wavelength and vice-versa.
Figure 2 Unified spectral signal representation
245
RAMAN AMPLIFIER
Formulation of the modelAs an example, the power and the phase change of any type of wave (pump, signal, or ASE) with central carrier frequency ωk as PF,B(z, ωk) and θF,B (z, ωk) respectively, where the subscripts F and B discriminate against the forward and backward propagating waves at the same wavelength. The system of coupled differential equations describing the operation of a FRA or the Raman sub-unit of a HRA has the form:
(1)
dPF z ωk,( )dz
------------------------- α ωk( )PF z ωk,( )–=
ρ ωk( )PB z ωk,( )+
+ gR ωk ω1,( ) PF z ω1,( ) PB z ω1,( )+[ ] PF z ωk,( ) Psp ω1 ωk T Bk,,,( )+[ ]l k 1+=
N
∑
gR ωl ωk,( ) PF z ωl,( ) PB z ωl,( )+[ ]PF z ωk,( )l 1=
k 1–
∑–
2Ftotalsp ωk T,( )PF z ωk,( )–
+ BBr
BBr Bk+( )-------------------------gBrPB z ωk ∆ωBr+,( ) PF z ωk,( ) Psp ωk ∆ωBr ωk T Bk,,,+( )+[ ]
BBr
BBr Bk+( )-------------------------gBr PB z ωk ∆ωBr–,( ) Psp ωk ωk ∆ωBr T Bk,,–,( )+[ ]PF z ωk,( )–
gR ωk ωl ωm ωn,,,( ) Ψ z( )[ ] 4γ ωk ωl ωm ωn,,,( ) Ψ z( )[ ]sin–cos{ }n 1=
N
∑m 1=
N
∑l 1=
N
∑+
ωk ωl ωm ωn–+=
x PF z ωk,( )PF z ωl,( )( )PF z ωm,( )PF z ωn,( )
246
RAMAN AMPLIFIER
z( )]
(2)
The equations describing the evolution of and are obtained by alternative interchanging of subscripts F and B.
The notations are explained in Table 1.
Table 1 Description of notations
Notation Description
N Number or pumps+signals+ASE bands in each direction
2N Total number of interacting waves
Total losses
Rayleigh scattering coefficient
Raman gain coefficient
Peak Raman gain coefficient, depending on the frequency of the current pump wave. In fused silica, it is downshifted by
= 13.2 THz from the respective pump.
Normalized Raman gain spectrum of the fiber, as dependent on the type and concentration of the dopant.
Mode overlap integrals; for definitions see, for example [6] (chap. 7 and 10)
dθF z ωk,( )dz
------------------------- γ ωk ω, l ω, k ωl,( ) 2 δkl–( )PF z ωl,( ) 2PB z ωl,( )+[ ]l 1=
N
∑=
+ 2γ ωk ωl ωm ωn,,,( ) Ψ z( )[ ]gR ωk ωl ωm ωn,,,( )
2------------------------------------------ Ψ[sin+cos
n 1=
N
∑m 1=
N
∑l 1=
N
∑
ωk ωl ωm ωn–+=
XPF z ωl,( )PF z ωm,( )PF z ωn,( )
PF z ωk,( )--------------------------------------------------------------------
PB z ωk,( ) θB z ωk,( )
α ωk( )
ρ ωk( )
gR ωk ω1,( ) f ωk ω1,( )gpeakR ω1( )gnorm
R ω1 ωk–( )=
gpeakR ω1( )
∆ω ωR=
gnormR ∆ω( )
f ωl ωk,( ) f ωk ωl ωm ωn,,,( );
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RAMAN AMPLIFIER
Power generated by spontaneous Raman and Brillouin scattering of the wave with carrier frequency into the bandwidth of the wave with carrier . Although the forms of these terms are identical, their values are different:
for SpRS, while for SpBS.
A factor (with dimension of length) determining the integrated total power lost by the current wave via spontaneous Raman scattering into all possible lower frequencies, as depending on the Raman spectrum and the temperature.
B Bandwidth of the respective wave.
h, K, T Planck bar constant, Boltzmann constant, Temperature.
gBr, BBr, Br Brillouin gain coefficient, line width, and Stokes shift.
.z Total phase difference between the nonlinearly mixed waves
Input phase mismatch
Kroneker delta
Notation Description
Psp ωl ωk T B,,,( ) =
2hωkB 1 1 e
h ω1 ωk–( )
KT---------------------------
1–⁄+
=
ω1ωk
Psp ω1 ωk T B,,,( ) 2hωkB≈Psp ω1 ωk T B,,,( ) 2hωkB»
Ftotalsp ωk T,( ) =
2πhωk gR ω ωk,( ) 1 1 e
h ωk ω–( )KT
-------------------------⁄ 1–+
ωd0
ωk
∫
∆ω
Ψ z( ) θ1 z( ) θm z( ) θn z( )– θk z( )– ∆k–+=
∆k
δlm
248
RAMAN AMPLIFIER
References[1] H. Masuda, S. Kawai, IEEE Photonics Technology Letters, Vol. 11, p. 647, 1999.
[2] T. Nielsen, P. Hansen, A. Stentz, M. Aquaro, J. Pedrazzani, A. Abramov, and R. Espindola, IEEE Photonics Technology Letters, Vol. 10, p. 1492, 1998.
[3] Laser Focus World, January 2000; SDL Press Release, http://www.sdli.com/investor/releases/19990630_BROADENS.html
[4] E. Woodbury and W. Ng, Proc. IRE, Vol. 50, p. 2347, 1962.
[5] R. Stolen, E. Ippen, and A. Tynes, Applied Physics Letters, Vol. 20, p. 62, 1972.
[6] G. Agrawal, “Nonlinear Fiber Optics,” 2nd Edition, Academic Press Inc., San Diego, California, 1995.
[7] F.L. Galeener, J.C. Mikkelsen Jr., R.H. Geils, and W.J. Mosby, Applied Physics Letters, Vol. 32, p. 34, 1978.
[8] Y. Emori, K. Tanaka, and S. Namiki, Electronics Letters, Vol. 35, p. 1355, 1999.
[9] T. Hosaka, S. Sudo, H. Itoh, and K. Okamoto, Electronics Letters, Vol. 24, p. 770, 1988.
[10] H. Kidorf, K. Rottwitt, M. Nissov, M. Ma, and E. Rabarijaona, IEEE Photonics Technology Letters, Vol. 11, p. 530, 1999.
[11] M. Nissov, K. Rottwitt, H. Kidorf, and M. Ma, Electronics Letters, Vol. 35, p. 997, 1999.
[12] Y. Chen, Journal of the Optical Society of America, Vol. B7, p. 43, 1990.
[13] B. Foley, M. Dakss, R. Davies, and P. Melman, Journal of Lightwave Technology, Vol. 7, p. 2024, 1989.
[14] S. Davey, D. Williams, B. Ainslie, W. Rothwell, and B. Wakefield, IEE Proceedings, Vol. 136, p. 301, 1989.
[15] R. Hellwarth, Progress of Quantum Electronics, Vol.5 , p. 1, 1977.
[16] Y. Shen, “The Principles of Nonlinear optics,” J. Wiley & Sons Inc., 1984.
[17] A. Uchida, M. Takeoka, T. Nakata, and F. Kannari, Journal of Lightwave Technology, Vol. 16, p. 92, 1998.
[18] S. Evangelides, L. Mollenauer, J. Gordon, and N. Bergano, Journal of Lightwave Technology, Vol. 10, p. 28, 1992.
249
RAMAN AMPLIFIER
Notes:
250
RAMAN AMPLIFIER—AVERAGE POWER MODEL
Raman Amplifier—Average power model
This component simulates a Raman amplifier based on the average power approach [1], [2].
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 Input Optical
Output 1 Output Optical
Input 2 Input Optical
Output 2 Output Optical
Name and description Symbol
Default value Default unit Value range
LengthAmplifier length.
L 10 km ]0; 1,000,000[
Attenuation data typeDefines if attenuation is entered as scalar, used for all wavelengths, or if it is wavelength dependent / downloaded from a file.
Constant — Constant, From File
AttenuationConstant attenuation value
0.2 dB/km [0,+INF[
Attenuation fileAttenuation value dependent on wavelength.
- FiberLoss.dat nm - dB/km -
Effective area data typeDefines if effective area is entered as scalar, used for all wavelengths, or if it is wavelength dependent/ downloaded from a file.
- Constant — Constant, From File
α
251
RAMAN AMPLIFIER—AVERAGE POWER MODEL
Enhanced
Effective interaction areaConstant effective area.
72 µm2 [0, INF[
Effective interaction area fileEffective area dependent on wavelength.
- EffectiveArea.dat nm - µm2 -
Raman gain typeDefines type of Raman gain. If Raman gain efficiency is selected, effective area is disabled, and value is
. Otherwise, it is normalized multiplied by Raman gain peak
(see below).
- Raman gain - Raman gain, Raman gain efficiency
Raman gain peakNormalized Raman gain is multiplied by Raman gain peak. Formula is detailed later in this section.
- 1e-013 - [0,+INF[
Raman gain reference pumpValue used for Raman gain calculation. Formula is detailed later in this section.
- 1000 nm [0,+INF[
Gain X frequencyFile that defines Raman gain or the Raman gain efficiency.
RG.dat THZ - normalized Raman gain
-
Name and description Symbol
Default value Default unit Value range
TemperatureAbsolute temperature at which fiber is operating. Used for noise consideration.
T 300 K [0,500]
Polarization factorActual value depends on relative polarization of fields of channels i and j. Equals 1 if fields of both channels are polarization-aligned, and 2 for totally scrambled polarization [4].
2 - [1,2]
Name and description Symbol
Default value Default unit Value range
Aeff
gr / Aeffgr
gr
Keff
252
RAMAN AMPLIFIER—AVERAGE POWER MODEL
Numerical
Rayleigh back scattering data typeDefines whether Rayleigh back scattering coefficient is entered as scalar, used for all wavelengths, or wavelength dependent/downloaded from a file.
- Constant - Constant, From File
Rayleigh back scattering
Constant Rayleigh back scattering.
- 5.0e-005 1/km [0, INF[
Rayleigh back scattering file
Rayleigh back scattering dependent on wavelength.
- Rayleigh.dat nm - 1/km -
Upper pump reference
Used for convergence test. All wavelengths below this value are considered pump, and are not taken into account for the convergence test.
- 1450 nm [0,3000]
Enable dispersion
Enables the linear chromatic dispersion application for the signals.
- False - True, False
Dispersion
Value of the GVD (Group Velocity Dispersion) parameter in wavelength domain.
- 16.75 ps/nm/km ]-INF,+INF[
Dispersion slope
Value of the dispersion slope parameter.
- 0.075 ps/nm2/km ]-INF,+INF[
Reference wavelength
Used internally as “zero” (or reference) frequency in spectrum of signal envelope. Attenuation value is assumed to correspond to this frequency.
- 1550 nm [100,2000]
Name and description Default value Unit Value range
ToleranceUsed to check convergence of the model. Based on gain of the signals.
0.01 - ]0,+INF[
Name and description Symbol
Default value Default unit Value range
γ
253
RAMAN AMPLIFIER—AVERAGE POWER MODEL
Graphs
Simulation
Number of divisionsNumber of divisions (in space) of the fiber.
50 - [1;50,000]
Number of iterationsMaximum number of iterations executed. If convergence is not reached in this number of iterations, model returns the calculated values anyway.
50 - [1;50,000]
Check convergence using:Defines if convergence is checked using “All signals” or “First signal”.
All signals - All signals, First signal
Name and description Default value
Unit Value range
Calculate graphsDefines if graphs are calculated or not. If False, component graphs are not represented.
False - True, False
Number of distance steps
Number of distance steps considered for graph generation.
20 - [1,1e8]
Number of wavelength steps
Number of wavelength steps considered for graph generation.
20 - [1,1e8]
Linear scale
Defines if a linear scale (Watt) or logarithmic one (dBm) is used.
True - True, False
Minimum value
If a logarithmic scale is used, this parameter defines the minimum value for the power that is displayed on the graph.
-50 dBm ]-INF,+INF[
Name and description Default value Unit Value range
EnabledDefines whether the component is enabled or not.
True - True, False
Name and description Default value Unit Value range
254
RAMAN AMPLIFIER—AVERAGE POWER MODEL
Noise
Random numbers
Technical BackgroundIn recent years, Raman amplifiers have become one of the most promising technologies for the next generation of fiber amplifiers, mostly due to their flexibility in bandwidth design.
Nevertheless, the simulation techniques that are commonly used for RA's have demanded exhaustive computational time, mainly due to the use of direct integration of the coupled differential equations that describe the RA behavior [3].
The coupled differential equations have the shape observed in Equation 1. A similar set of equations, describing the backward propagation, is solved at the same time we solve the forward equations written below.
Name and description Default value Default unit Unit Value range
Noise center frequencyDetermines noise center frequency.
193.4 THz Hz, THz, nm [30, 30e5]
Noise bandwidthBandwidth to create noise bins.
13 THz Hz, THz, nm ]0,+INF[
Noise bins spacingSpecifies the noise bins spacing.
125 GHz Hz, GHz, THz, nm [1,1000[
Noise thresholdMinimum value for adaption of noise bins.
-100 dB — ]-INF,0[
Noise dynamicThreshold ratio for adaption of noise bins.
3 dB — [0,+INF[
Convert noise binsDetermines if generated noise bins are incorporated into the signal.
Convert noise bins — — True, False
Name and description Default value
Unit Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0, 4999]
255
RAMAN AMPLIFIER—AVERAGE POWER MODEL
where
In the equations, the following physical effects were taken into account:• pump-to-pump, signal-to-signal, and pump-to-signal Raman interactions• spontaneous Raman emission and its temperature dependency
(1)
Symbol Definition
frequencies (Hz)
fiber attenuation [N/m]
Rayleigh back scattering coefficient [N/m]
Raman gain coefficient for frequency difference ( ) [m/W]
backward propagating power [W]
effective core area [m2]
polarization factor
frequency interval
Plank’s constant
Boltzman’s constant
temperature [K]
dPf z υ,( )dz
---------------------- α υ( )Pf z υ,( ) γ υ( )Pb z υ,( ) ++=
Pf z υ,( )gr υ ζ–( )KeffAeff
---------------------- Pf z ζ,( ) Pb z ζ,( )+[ ] +v ζ<∑
h∆υgr υ ζ–( )
Aeff---------------------- Pf Pb+[ ] 1 h ζ υ–( ) kT⁄[ ] 1–( ) 1–exp+[ ] –
v ζ<∑
Pf z υ,( )gr υ ζ–( )KeffAeff
----------------------υζ--- Pf z ζ,( ) Pb z ζ,( )+[ ] –
v ζ>∑
2hυ∆υPf z υ,( )gr υ ζ–( )
Aeff---------------------- 1 h υ ζ–( ) kT⁄[ ] 1–( ) 1–exp(+[ ]
v ζ>∑
υ ζ,α υ( )γ υ( )
gr υ ζ–( )υ ζ–( )
Pb z υ,( )
AeffKeffδυhkT
256
RAMAN AMPLIFIER—AVERAGE POWER MODEL
• stimulated Raman scattering• pump depletions due to Raman energy transfer• high-order Stokes generation• multiple Rayleigh back scattering• fiber loss• spontaneous emission noise
A very interesting approach that considerably reduces the computational time for simulating RA is the one used for this component. The idea behind this technique is first to split the amplifier into a concatenation of small segments, and then to use the small-signal-traveling wave solution in each section (see Equation 3). In order to eliminate the dependence in a small segment length, average powers in each section are introduced (see Equation 4). So, basically, we rearrange some terms of the original Equation 1 and reduce the propagation equations to a simpler form.
This new form, suitable for the purpose of average power analyses, can be written as [2]:
if we substitute , , in (2a), (2b) in each lump by average powers in the lump,coefficients , are independent of (within the lump, , and the solution of Equation 2 can be written as:
where is the length of the lumps. Within each lump, powers , must be replaced by average powers
(2)
(2a)
(2b)
(3)
(4)
z
dPf z v,( )dz
--------------------- A z v,( )Pf z v,( ) B z v,( )+=
where
A z v,( ) α– υ( )gr υ ζ–( )KeffAeff
---------------------- Pf z ζ,( ) Pb z ζ,( )+[ ] υζ---
gr υ ζ–( )KeffAeff
---------------------- P[ f z ζ,( ) Pb z ζ,( ) ] +v ζ>∑–
v ζ<∑+=
2– hυ∆υgr υ ζ–( )
Aeff---------------------- 1 1
h υ ζ–( ) kT⁄[ ] 1– 1–exp-----------------------------------------------------------+
v ζ>∑
B z υ,( ) γ υ( )Pb= z υ,( ) hυ∆υgr υ ζ–( )
Aeff---------------------- Pf z ζ,( )[ Pb z ζ,( ) ] 1 1
h υ ζ–( ) kT⁄[ ] 1– 1–exp-----------------------------------------------------------++
v ζ<∑+
Pf z ζ,( ) Pb z ζ,( )
A z v,( ) B z v,( ) z A υ( ) B υ( )
Pf z0 H υ,+( ) Pf z0 υ,( ) A υ( )H( ) B υ( )A υ( )------------ A υ( )H( ) 1–( )exp[ ]+exp=
H Pf z ζ,( ) Pb z ζ,( )
Pf b, v( )⟨ ⟩ Pf b,in G 1–
1nG------------- B v( )
A v( )----------- G 1–
1nG------------- 1–+=
257
RAMAN AMPLIFIER—AVERAGE POWER MODEL
where are forward and backward propagating input powers to the lump, .
The user is responsible to guarantee that the term does not become zero. For example, it is impossible to simulate the chromatic dispersion of just one signal if the attenuation is not considered, once the term will become zero.
Numerical approachThe relaxation method is used in order to satisfy the boundary conditions of the two-point boundary problem with given accuracy.
There are two different iteration procedures, for both forward and backward directions. Forward direction is from Input port 1 to Output port 1, and backward is from Input port 2 to Output port 2.
The first procedure, the innermost one, is intended to evaluate the self-consistent convergence for the average powers used in Equation 4 for every amplified segment. When a certain tolerance is reached (10-12), the average powers are considered good enough to be used as an approximation of the desired functions.
In the outermost one, or second procedure, the convergence is checked after the integration in forward direction is performed. If the variance in the gain is less than the tolerance desired (see “Numerical” on page 253) , the simulation is considered finished. Otherwise, the component runs for the maximum number of iterations set by the user.
The reason for the reduction in computational time is that direct numerical integration of Equation 1 is replaced by algebraic operations.
The user can choose the signals that will be used in the convergence checking. There are two available choices: All signals and First signal. When the First signal option is chosen, just the signal with the smallest wavelength is used in checking the convergence by the given tolerance. Otherwise, if the All signals option is chosen, all signals are used in the checking. In the case where there a signal has not been transmitted, the convergence test is performed based on the pumps.
FilesSome data necessary for this model may be downloaded from a file. In general, these files are in the ASCII format and follow Optiwave's standard format. For clarity, the units of each column in the files are listed in the following table.
Field First column Second column
Attenuation Wavelength (nm) Attenuation (dB/km)
Effective area Wavelength (nm) Effective area (µm2)
Pf b,in
G A υ( )H( )exp=A v( )
A v( )
258
RAMAN AMPLIFIER—AVERAGE POWER MODEL
When a file with the normalized Raman gain is used, it must be provided values for the Raman gain peak and Raman gain reference pump to use in the calculation of the Raman gain used in the simulation. The following formula is used:
where is the Raman gain, is the Raman gain peak, is the gain reference pump and is the normalized Raman Gain.
The unit of Raman gain is given in .
ComparisonAs stressed in the beginning of the technical description, the average power model is intended to decrease the computational time required to solve the Raman Amplifier differential equations by simplifying the way the equations are written.
In fact, the model shows a reduction in computation time of over two orders of magnitude [2] compared to the model using direct integration approach (fourth-order Runge-Kutta). However, in some cases, it is known that the model fails in converging (for example, when the total pump becomes very high).
Therefore, based on the characteristics presented, this model is very useful in getting a first approximation for a network under certain limits. Once the rough estimation is reached, the system could be generalized using the full steady state model.
A validation example for this model is presented in Lesson: "Raman amplifier - Average power model" in the tutorials section.
Raman gain X frequency Frequency shift (THz) Normalized Raman gain
Raman gain efficiency X frequency
Frequency shift (THz) Raman gain efficiency
Rayleigh back scattering Wavelength (nm) Back scattering (1/km)
Field First column Second column
m2
W------
1W m⋅-------------
gRPRλp------ gN=
gR PR λpgN
mW-----
259
RAMAN AMPLIFIER—AVERAGE POWER MODEL
References:[1] M. Karasek, M. Menif, "Protection of surviving channels in pump-controlled gain-locked Raman
fibre amplifier", Optics Communications 210 (2002) 57-65.
[2] B. Min, W. J. Lee, N. Park, "Efficient Formulation of Raman Amplifier Propagation Equations with Average Power Analysis", IEEE Photonics Technology Letters, Vol. 12, No. 11, November 2000.
[3] E. Desurvire, "Erbium-doped fiber amplifiers: principles and applications", Wiley-Interscience, 1994.
[4] S. Tariq, J.C. Palais, "A Computer Model of Non-Dispersion-Limited Stimulated Raman Scattering in Optical Fiber Multiple-Channel Communications", IEEE Journal of Lightwave Technology, Vol. 11, No. 12, December 1993.
260
RAMAN AMPLIFIER—DYNAMIC MODEL
Raman Amplifier—Dynamic model
This component simulates a Raman amplifier using a dynamic model based on direct integration of the differential equations that describe it.
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 Input Optical
Output 1 Output Optical
Input 2 Input Optical
Output 2 Output Optical
Name and description Symbol
Default value Default unit Value range
LengthAmplifier length.
L 10 km ]0; 1,000,000[
Attenuation data typeDefines if attenuation is entered as scalar, used for all wavelengths, or if it is wavelength dependent / downloaded from a file.
— Constant — Constant, From file
AttenuationConstant attenuation value
0.2 dB/km [0,+INF[
Attenuation fileAttenuation value dependent on wavelength.
— FiberLoss.dat nm - dB/km —
α
261
RAMAN AMPLIFIER—DYNAMIC MODEL
Enhanced
Effective area data typeDefines if effective area is entered as scalar, used for all wavelengths, or if it wavelength dependent/downloaded from a file.
— Constant — Constant, From file
Effective interaction areaConstant effective area.
72 µm2 ]0, +INF[
Effective interaction area fileEffective area dependent on wavelength.
— EffectiveArea.dat nm - µm2 —
Raman gain typeDefines type of Raman gain. If Raman gain efficiency is selected, effective area is disabled, and value is
. Otherwise, is is normalized multiplied by Raman gain peak
(see below).
— Raman gain — Raman gain, Raman gain efficiency
Raman gain peakNormalized Raman gain is multiplied by Raman gain peak. Formula is detailed later in this section.
— 1e-013 — [0,+INF[
Raman gain reference pumpValue used for Raman gain calculation. Formula is detailed later in this section.
— 1000 nm [0,+INF[
Gain X frequencyFile that defines Raman gain or the Raman gain efficiency.
RG.dat THZ - normalized Raman gain
—
Name and description Symbol
Default value Default unit Value range
TemperatureAbsolute temperature at which fiber is operating. Used for noise consideration.
T 300 K [0,500]
Name and description Symbol
Default value Default unit Value range
Aeff
gr / Aeffgr
gr
262
RAMAN AMPLIFIER—DYNAMIC MODEL
Polarization factorActual value depends on relative polarization of fields of channels i and j. Equals 1 if fields of both channels are polarization-aligned, and 2 for totally scrambled polarization [4].
2 — [1,2]
Rayleigh back scattering data typeDefines whether Rayleigh back scattering coefficient is entered as scalar, used for all wavelengths, or wavelength dependent/downloaded from a file.
— Constant — Constant, From file
Rayleigh back scattering
Constant Rayleigh back scattering.
- 5.0e-005 1/km [0, +INF[
Rayleigh back scattering file
Rayleigh back scattering dependent on wavelength.
— Rayleigh.dat nm - 1/km —
Upper pump reference
Used for convergence test. All wavelengths below this value are considered pump, and are not taken into account for the convergence test.
— 1450 nm [0,3000]
Enable dispersion
Enables the linear chromatic dispersion application for the signals.
— False — True, False
Dispersion
The value of the GVD (Group Velocity Disperion) parameter in the wavelength domain.
— 16.75 ps/nm/km ]-INF, +INF[
Dispersion slope
The value of the dispersion slope parameter.
— 0.075 ps/nm2/km -INF, +INF[
Reference wavelength
This value is used internally as a “zero” or reference frequency in the spectrum of the signal envelope. The attenuation value is assumed to correspond to this frequency.
— 1550 nm [100, 2000]
Name and description Symbol
Default value Default unit Value range
Keff
γ
263
RAMAN AMPLIFIER—DYNAMIC MODEL
Numerical
Graphs
Group delay data type
Defines if the group delay is entered as a scalar used for all wavelengths, or if it wavelength dependent/entered from a file.
— Constant — Constant, From file
Group delay
Constant group delay
1/Vg(v) 4900000 ps/km [0, 1010]
Group delay file — GroupDelay.dat ns—ps/km —
Name and description Default value Unit Value range
ToleranceUsed to check convergence of the model. Based on gain of the signals.
0.01 — ]0,+INF[
Number of divisionsNumber of divisions (in space) of the fiber.
50 — [1;50,000]
Number of iterationsMaximum number of iterations to be executed. If convergence is not reached in this number of iterations, model returns the calculated values regardless.
50 — [1;50,000]
Check convergence using:Defines if convergence is checked using “All signals” or “First signal”.
All signals - All signals, First signal
Name and description Default value
Unit Value range
Calculate graphsDefines if graphs are calculated or not. If False, component graphs are not represented.
False - True, False
Number of distance steps
Number of distance steps considered for graph generation.
20 - [1,1e8]
Number of wavelength steps
Number of wavelength steps considered for graph generation.
20 - [1,1e8]
Name and description Symbol
Default value Default unit Value range
264
RAMAN AMPLIFIER—DYNAMIC MODEL
Simulation
Noise
Random numbers
Linear scale
Defines if a linear scale (Watt) or logarithmic one (dBm) is used.
True - True, False
Minimum value
If a logarithmic scale is used, this parameter defines the minimum value for the power that is displayed on the graph.
-50 dBm ]-INF,+INF[
Name and description Default value Unit Value range
EnabledDefines whether the component is enabled or not.
True - True, False
Name and description Default value Default unit Unit Value range
Noise center frequencyDetermines noise center frequency.
193.4 THz Hz, THz, nm [30, 30e5]
Noise bandwidthBandwidth to create noise bins.
13 THz Hz, THz, nm ]0,+INF[
Noise bins spacingSpecifies the noise bins spacing.
125 GHz Hz, GHz, THz, nm [1,1000[
Noise thresholdMinimum value for adaption of noise bins.
-100 dB — ]-INF,0[
Noise dynamicThreshold ratio for adaption of noise bins.
3 dB — [0,+INF[
Convert noise binsDetermines if generated noise bins are incorporated into the signal.
Convert noise bins — — True, False
Name and description Default value
Unit Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Name and description Default value
Unit Value range
265
RAMAN AMPLIFIER—DYNAMIC MODEL
Technical backgroundIt is widely believed that Raman Amplifier (RA) will play an increasing role in future optical fiber communication (OFC) systems [1]. They have already been widely utilized due to their fundamental advantages [1]:• there is amplification at any wavelength, provided the appropriate pump sources
are available.• a fiber itself can be used as an active medium.• a pump spectrum determines a gain spectrum.
The equations that describe a Raman amplifier are [2]:
where
Random seed indexUser-defined seed index for noise generation
0 — [0, 4999]
(1)
Symbol Definition
frequencies (Hz)
fiber attenuation [N/m]
Rayleigh back scattering coefficient [N/m]
Name and description Default value
Unit Value range
dPf z υ,( )dz
---------------------- α υ( )Pf z υ,( ) γ υ( )Pb z υ,( ) ++=
Pf z υ,( )gr υ ζ–( )KeffAeff
---------------------- Pf z ζ,( )[ ] Pb z ζ,( ) ++v ζ<∑
h∆υgr υ ζ–( )
Aeff---------------------- Pf z ζ,( )[ ] 1 h ζ υ–( ) kT⁄[ ] 1–( ) 1–exp+[ ] –
v ζ<∑
Pf z υ,( )gr υ ζ–( )KeffAeff
----------------------υζ--- Pf z ζ,( )[ ] Pb z ζ,( ) –+
v ζ>∑
2hυ∆υPf z υ,( )gr υ ζ–( )
Aeff---------------------- 1 h υ ζ–( ) kT⁄[ ] 1–( ) 1–exp(+[ ]
v ζ>∑
υ ζ,α υ( )γ υ( )
266
RAMAN AMPLIFIER—DYNAMIC MODEL
In these equations, the following physical effects were taken into account:• pump-to-pump, signal-to-signal and pump-to-signal Raman interactions;• spontaneous Raman emission and its temperature dependency;• stimulated Raman scattering;• pump depletions due to Raman energy transfer;• high-order stokes generation;• multiple Rayleigh backscattering;• fiber loss;• spontaneous emission noise.
In this component, the equations in Equation 1 (forward and backward) are solved spatially through direct integration using a standard classical fourth-order Runge-Kutta formula without adaptive step size [3].
Numerical approachThe convergence of the model is checked in two directions: forward and backward. An iterative forward and backward integration of propagation equations must be applied because backward propagating ASE powers and a counter-directional pumping scheme may be defined, and the possibility of counter directional signal propagation [2]. The forward direction is from Input Port 1 to Output Port 1 and backward is from Input Port 2 to Output Port 2.
The iterative scheme is started with a forward integration of forward signals, propagating ASE spectral components, and pumps. The backward pumps and backward ASE powers are set to zero. At each backward integration, the final results
of the previous forward integration, together with the boundary conditions for the backward pump, backward ASE powers, and backward signals, are used as starting conditions.
Raman gain coefficient for frequency difference ( ) [m/W]
backward propagating power [W]
effective core area [m2]
polarization factor
frequency interval
Plank’s constant
Boltzman’s constant
temperature [K]
gr υ ζ–( )υ ζ–( )
Pb z υ,( )
AeffKeffδυhkT
P+ z( L υ ),=
267
RAMAN AMPLIFIER—DYNAMIC MODEL
Similarly, the results of the previous backward integration together with the boundary conditions for forward signal channels, pumps, and forward ASE, are used as starting conditions for each forward integration [2].
The convergence checking is done after integration in the forward direction is complete. If the variance in the gain is less than the tolerance desired (see “Numerical” on page 264) , the simulation is considered complete. Otherwise, the component runs for the maximum number of iterations set by the user.
The user can choose the signals that will be used in the convergence checking. There are two available choices: All signals and First signal. When the First signal option is chosen, just the signal with the smallest wavelength is used in checking the convergence by the given tolerance. Otherwise, if the All signals option is chosen, all signals are used in the checking. In the case where there a signal has not been transmitted, the convergence test is performed based on the pumps.
After the spatial integration is complete, the time evolution of pumps, signals, and amplified spontaneous emission waves is performed by direct integration with Equation 1, starting with the steady-state solution for longitudinal distribution of individual powers along the Raman fiber. To avoid possible oscillations of the solution in time domain, care must be taken in the selection of bin widths used in space ( ), and time ( ) discretization schemes. Stable solutions has been obtained when the time bin ( ) is equal to or less than the propagation time through a space bin .
In order to determine the rise/fall times of the surviving channel power transients with sufficient resolution, the ratio of time and space bins should be independently kept for the Raman fiber length, as in the examples.
Some data necessary for this model may be downloaded from a file. In general, these files are in the ASCII format and follow Optiwave's standard format.
For clarity, the units of each column in the files are listed in the following table.
Field First column Second column
Attenuation Wavelength (nm) Attenuation (dB/km)
Effective area Wavelength (nm) Effective area (µm2)
Raman gain X frequency Frequency shift (THz) Normalized Raman gain
Raman gain efficiency X frequency
Frequency shift (THz) Raman gain efficiency
P_ z( 0 υ ),=
∆z∆t
∆t∆t ∆z Vg⁄≤
∆t ∆z⁄ 4 10 9–× s m⁄[ ]=
m2
W------
1W m⋅-------------
268
RAMAN AMPLIFIER—DYNAMIC MODEL
When a file with the normalized Raman gain is used, it must be provided values for the Raman gain peak and Raman gain reference pump to use in the calculation of the Raman gain used in the simulation. The following formula is used.
where is the Raman gain, is the Raman gain peak, is the gain reference pump and is the normalized Raman Gain.
The unit of Raman gain is given in .
Rayleigh back scattering Wavelength (nm) Back scattering (1/km)
Field First column Second column
gRPRλp------ gN=
gR PR λpgN
mW-----
269
RAMAN AMPLIFIER—DYNAMIC MODEL
References:[1] E. M. Dianov, "Advances in Raman Fibers", Journal of Lightwave Technology, Vol. 20, No. 8,
August 2002.
[2] M. Karasek, M. Menif, "Protection of surviving channels in pump-controlled gain-locked Raman fibre amplifier", Optics Communications 210 (2002) 57-65.
[3] W. H. Press, et al., "Numerical Recipes: The Art of Scientific Computing", 2nd Edition, Cambridge University Press, 1992.
[4] S. Tariq, J.C. Palais, "A Computer Model of Non-Dispersion-Limited Stimulated Raman Scattering in Optical Fiber Multiple-Channel Communications", IEEE Journal of Lightwave Technology, Vol. 11, No. 12, December 1993.
270
EDFA BLACK BOX
EDFA Black Box
Designs erbium doped fiber amplifiers (EDFAs) pumped by 980 nm or 1480 nm. Requires just the experimental characterization of a practical device such as the gain spectrum and noise figure under non-saturated and saturated conditions. Details about erbium-doped fiber specifications and elements in the layout are not required to perform the simulations.
The amplifier is specified to operate under conditions required by wavelength division multiplex (WDM) systems.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value
Default unit Units Value range
Operation modeAmplifier operation mode
Saturation — — Gain control, Power control, Saturation
GainDetermines the signal gain
20 dB — [0,100]
PowerDetermines the signal output power
5 dBm W, mW, dBm [-100,100]
271
EDFA BLACK BOX
Measurements
Numerical
Polarization
Name and description Default value
Units Value range
File wavelength unitDetermines the wavelength unit
m — nm, m, Hz, THz
First gain spectrum file nameFilename with the gain spectra measurements
Gain1.dat — —
Second gain spectrum file nameFilename with the gain spectra measurements
Gain2.dat — —
OSA bandwidthSet the bandwidth of the Optical Spectrum Analyzer
0.1 nm [0.0001,10]
Noise typeSelect the noise type
Power dBm Power, Spectral density, Noise figure
Noise spectrum file nameFilename concerning the noise spectra
Noise.dat — —
Saturation wavelengthDetermines the saturation wavelength
1540 nm [800,1700]
Saturation file nameFilename concerning the saturation spectra
Saturation.dat — —
Name and description Default value
Units Value range
Relative errorDetermines the relative error acceptable in each calculation
0.1 dB ]0,100]
Interpolation algorithmDetermines the interpolation algorithm for the measured data
Cubic — Linear, Cubic
Name and description Default value
Units Value range
Polarization filterDetermines the polarization of the filter
None — None, Polarization X, Polarization Y
272
EDFA BLACK BOX
Simulation
Noise
Random numbers
Name and description Default value
Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
Name and description Default value
Default unit Units Value range
Noise bins spacingSpecifies the noise bins spacing
125 GHz Hz, GHz, THz, nm
[1,1000]
Noise thresholdMinimum value for adaptation of noise bins
–100 dB — ]-INF,0[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB — [0,+INF]
Convert noise binsDetermines if the generated noise bins are incorporated into the signal
Convert noise bins
— — True, False
Name and description Default value
Units Value range
Generate random seed
Determines if the seed is automatically defined and unique
True — True, False
Random seed index
User-defined seed index for noise generation
0 — [0,4999]
273
EDFA BLACK BOX
Graphs
Technical backgroundUsing input parameters as the characterization of the gain spectrum and noise figure under non-saturated and saturated conditions measured to a practical device is sufficient for designing the amplifier performance using this black box model. Additional information concerning fiber specifications, such as absorption and emission cross-sections, erbium doping, core radius, or details related to the amplifier layout, is not required in this case. Curves containing the amplifier characterization are available internally as a default in the software, which makes it possible for you to perform simulations.
Three different control modes are available that allow you to perform the amplifier analysis under distinct points of view. Each mode control – gain, power control, and saturation – defines a different amplifier operating condition.
The black box model enables passive components, such as optical isolators, equalizer filters, and several types of couplers, to be included in the amplifier design while considering an additional loss variation along the amplifier due to the active and passive components. The gain and the noise characterization measured to distinct states of operation are provided as input files that enable the complete modelling of the amplifier performance.
Operation Mode descriptionFiber amplifiers used in WDM systems usually make use of control systems as power or gain. It is useful to include the option in the EDFA Black Box to select one of three operation modes:• Gain mode: Based on a control of the amplifier gain (Gain Control) relating the
input and output signals (with or without the generated amplified spontaneous emission (ASE).
• Power Control mode: Considers the value of the output power to control the amplifier performance (Power Control).
• Saturation mode: Considers the amplifier operating in a saturated condition (Saturation).
Name and description X Title Y Title
First gain spectrum Wavelength (m) Gain (dB)
Second gain spectrum Wavelength (m) Gain (dB)
Noise spectrum Wavelength (m) Power (dBm)
Saturation Input power (dBm) Gain (dB)
274
EDFA BLACK BOX
Gain Control modeIn this mode, you set the gain amplifier (Gain in dB units). The gain calculation is performed using Equation 1, where the total input (Pin) and the output (Pout) power spectra are considered. The specified amplifier gain (Gspeci) is given by the ratio of the total output power and input total power, with or without the generated ASE.
SASE(f) represents the spectral density of the amplified spontaneous emission integrated on the optical frequency f.
Note: You can include the noise by selecting the noise type as power, spectral density, or noise figure in the EDFA Black Box Properties dialog box.
Power Control modeThe value that you define in the power control mode is the desired amplifier output power (Power in dBm units). The specified amplifier output power (Pspeci) that includes the spectral ASE is:
where is the amplifier gain.
The option to select the noise type that will be included in the simulations is also available in this control mode.
Saturation modeIn the saturation mode, the gain is the specified parameter. The noise type can be selected in this mode, and two experimental gain curves are inserted as input files considering two different saturation conditions. The gain curve in a saturated condition is provided in a file format containing two columns. The first column refers to the signal output power given in [dBm] units. The second column gives the gain in [dB] units.
(1)
(2)
Gspeci
Pout λ( ) SASE f( ) fd∞–
+ ∞
∫+λ∑
Pin λ( )λ∑
---------------------------------------------------------------=
Pspeci G Pin λ( ) SASE f( )
∞–
+ ∞
∫–λ∑× df=
G
275
EDFA BLACK BOX
An example of the saturated gain input file is:
where the signal output power is given in [dBm] units and the gain is in [dB] units. There is no limit of rows or power spacing previously defined.
Basic equationsThe black box model considers a two-level Er3+ system assumption that is usually adopted to model erbium-doped fiber amplifiers [1]. The propagating equation written as a function of the absorption and emission coefficients, α(λ) and γ(λ) respectively, is [2]:
I(z) represents the fraction of active ions in the excited state, P(λ,z) describes the propagating power at a specific wavelength and fiber position, and PASE
eq is the term that includes the amplified spontaneous emission (ASE) as an equivalent ASE power.
The solution to Equation is:
where L is the total Er-doped fiber length and P(λ,0) represents the power at the wavelength λ and at the fiber input. Considering the scope of this approximation, PASE
eq(λ) works as an independent source of amplified spontaneous emission.
The total gain along the erbium-doped fiber is:
where is the updated term that represents the detailed evolution of the population inversion along the erbium-doped fiber.
The black box model takes into account a multiple-stage amplifier, where all amplifier stages use the same type of erbium-doped fiber (the same absorption and emission coefficients are considered). Figure 1 shows a sketch of an amplifier set up in two sections, containing passive elements such as optical isolators, couplers, taps and
Signal output power (dBm) Gain (dB)
–40 28.82
–30 28.83
–20 28.82
–10 28.81
0 28.72
...
(3)
(4)
(5)
dP λ z,( )dz
------------------- α λ( ) γ λ( )+[ ]I z( ) α λ( )–{ }P λ z,( ) γI z( )PASEeq λ( )+=
P λ L,( ) G λ( ) P λ 0,( ) PASEeq λ( )+[ ]=
Gz λ( ) α λ( ) γ λ( )+{ }Iz α λ( )– z×{ }exp=
Iz
276
EDFA BLACK BOX
one filter. The total Er-doped fiber length and the total gain are L and G respectively.
Figure 1 Erbium doped amplifier set up in multiple stages, where the black box parameters G , IL , ILin are indicated
If the insertion loss is included in the analysis, the gain G is written as:
G = [GA + GB ]/ IL .
Amplifier GainIn order to model the gain of the amplifier, two different states of operation are considered where each state has a characteristic population inversion. The amplifier gain expression is given as a function of a reference gain value, (for example, [2]):
where and specifies the wavelength and the gain at a reference amplifier operating point.
The term is named tilt function and is obtained by the ratio of the gain curves measured in the two states of operation. One acts as a reference curve (for example,
).
The tilt function is given by the analytical expression:
where and are the gain measured to the state1 and state2 respectively of the amplifier operation. The experimental gain, measured at these two states of operation, is provided as input file in the black box model.
It is convenient to introduce this concept of tilt function in the model, since it considers the interdependence between the ratio of the characteristic gain and the absorption
(6)
(7)
λ( )
λ( ) λ( )λ( )
λ( )
λ( ) λ( ) λ( ) λ( )
G λ( )log Tλrefλ( ) G λref( ) Gref λref( )log–log[ ] Gref λ( )log+=
λref Gref λref( )
Tλrefλ( )
Gref λ( )
T λ( )G1 λ( ) G2 λ( )log–log
G1 λref( ) G2 λref( )log–log----------------------------------------------------------------=
G1 λ( ) G2 λ( )
277
EDFA BLACK BOX
and emission coefficients. On the other side, as the internal losses IL(λ) caused by passive elements modify both G1(λ) and G2(λ) in the same manner, the tilt function isn’t affected by optical circuitry variations.
By choosing G2(λ) equal to G(λ), the expression for the amplifier at the operation point is:
where specifies the gain difference between or . The term is a free parameter and may be altered to adjust
the gain.
Gain measurementThe gain curves are critical to the black box model operation. The best way to obtain these values used as input files in the model is by measuring them in a practical amplifier. It is important to note that the precision of these measurements defines the accuracy of the simulated results. However, the model alternatively accepts curves generated by a simulated amplifier that supplies gain and ASE curves as the output files.
Obtaining Gain Curve G1The first gain profile is acquired with the amplifier operating in a constant saturated regime that assures a specific population inversion. This condition can be obtained by coupling a large signal input power to the amplifier, typically −10 dBm, at the wavelength λref (e.g., 1540 nm), which is maintained constantly.
A small signal with power equal to −30 dBm (for instance) is added to the amplifier input as a probe signal. Its frequency (probe signal) is scanned through the range defined by the two-limit frequencies, which is written in terms of signal wavelength and usually varies from 1530 nm to 1570 nm. This scan over the probe signal allows you to obtain the spectral gain for one specific saturated condition.
This method was checked by analyzing a series of gain curves measured at the same saturated conditions, and a nominally identical population inversion was recorded [2].
Obtaining Gain Curve G2Analogous measurement procedure is repeated to obtain the second gain profile. However, in this case, the probe signal input is enlarged to –20 dBm, and the reference signal at a selected wavelength (1540 nm) can be varied. This new signal input combination results in a different population inversion condition, which characterizes the gain .
(8)
(9)
G λ( )log G1 λ( ) Tλrefλ( ) G1 λref( ) Gref λref( )log–log[ ]×–log=
G λ( )log G2 λ( ) Tλrefλ( ) ∆Glog×+log=
∆Glog Gref λref( ) G2 λref( )log–logG1 λref( ) G2 λref( )log–log ∆Glog
G2 λ( )
278
EDFA BLACK BOX
The difference is that the added signal test presents larger potency, typically −20 dBm, which causes a change in the gain curve profile by saturating the amplifier. With the value obtained for the gain in each wavelength, the gain curve profile is obtained. The high signal power, with the same λref, can also be altered, since the total sum of the power is larger than the sum of the power to generate the curve G1.
The experimental gain curves must be provided in files containing two columns. The first column refers to the wavelength specified in [nm], [m], [Hz] or [THz] units. The second column gives the gain in [dB] units.
As an example of the gain input file is:
where the wavelength is given in [nm] units and the gain is in [dB] units. There is no limit of rows or wavelength spacing previously defined.
Amplifier Noise FigureThe noise figure is the figure of merit that usually describes the amplifier noise performance. In order to evaluate the noise figure, three different options are available. You can select the input format of noise that will be considered to perform the calculations.
The first option is to select the noise input in terms of ASE power. In this case, the ASE noise spectral density is written as:
where P(λ) is the ASE power measured at each wavelength range and ∆f is the bandwidth considered in the ASE spectrum acquisition.
Another option to evaluate the amplifier noise performance is to select the ASE spectral density. In this case, the spectral density S(λ) is required as input file and is written as:
where h is the Planck constant, f is the optical frequency, and the exponent NF(λ) is the noise figure as a function of the signal wavelength.
Wavelength [nm] G [dB]
1535.58 38.17
1538.95 34.09
1542.11 33.35
1545.26 33.17
...
(10)
(11)
Spower λ( ) P λ( )∆f
------------=
S λ( ) hf 10NF λ ) 10⁄( G λ( ) 1–×[ ]=
279
EDFA BLACK BOX
The model will internally calculate the noise figure considering the noise curve provided as input file. Rewriting Equation 11 in terms of noise figure produces [3]:
The third option is to select the noise figure value given as a function of the signal wavelength. In this case, the ASE spectrum is modeled considering the provided noise figure value.
It is also possible to evaluate the noise figure considering different amplifier state operation that means to consider distinct gain values. In this case, the spectral density given by Equation 11 is rewritten including the gain variation (∆G in linear units or log∆G in dB units).
The new spectral noise density is dependent on the amplifier gain and is:
where can be calculated from Equation 8 and Equation 9.
Equivalent ASE Noise Measurement The experimental ASE noise curves complement the measured parameters required by the black box model.
Obtaining Equivalent ASE NoiseThe third input to obtain (experimental) is the amplified spontaneous emission. In the ASE acquisition curve, only the saturating signal must be maintained turned-on and operating with a constant power at a specified signal wavelength (1540 nm as suggested in the previous measurement descriptions). This is sufficient to produce population inversion along the Er-doped fiber.
The spectrum obtained at the fiber output registers the amplified spontaneous emission observed along the whole wavelength range considered (1530 nm to 1570 nm, typically).
The experimental gain curves must be provided in files containing two columns. The first column refers to the wavelength specified in [nm], [m], [Hz] or [THz] units. The second column gives the ASE noise curve in [dBm] units.
An example of input file:
(12)
(13)
Wavelength [nm] ASE [dBm]
1543 –25.13
1544 –25.20
1546 –25.42
NF λ( ) 10 S λ( ) hf+hf G λ( )×------------------------log=
S λ ∆Glog,( ) hf 10NF λ ) 10⁄( G λ ∆Glog,( ) 1–×=
∆Glog
280
EDFA BLACK BOX
where the wavelength is in [nm] units and the gain is in [dB] units. There is no limit of rows or wavelength spacing previously defined.
1551 –26.43
Wavelength [nm] ASE [dBm]
281
EDFA BLACK BOX
References[1] E. Desurvire, “Erbium-Doped Fiber Amplifiers – Principles and Applications”, John Wiley &
Sons, Inc., USA, 1994.
[2] J. Burgmeier, A. Cords, R. März, C. Schäffer, B. Stummer “A black box model of EDFA’s operating in WDM systems”, J. Lightwave Technol., Vol. 16, N. 7, pp. 1271-1275, 1998.
[3] S. P. Bastien, H. R. D. Sunak, B. Sridhar, V. E. Kalomiris “Temporal, spatial and spectral modeling of erbium doped fiber amplifiers”, SPIE – Physic and Simulations of Optoelectronic Devices, pp. 2-11, 1992.
282
EDF DYNAMIC — FULL MODEL
EDF Dynamic — Full model
Incorporates time-varying input signal and pump powers that enable simulating dynamic effects presented by erbium-doped amplifiers inserted in a fiber link. This powerful tool solves the full rate and propagation equations in the time and spatial domain. The powers and population densities are calculated as a function of the time variation at each point of the z fiber. This model is specifically designed to simulate cascaded amplifiers in a long fiber link, considering multiple signal input.
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Output 1 Output Optical
Output 2 Output Optical
Name and description Default value
Default unit Units Value range
Core radiusDetermines the Er-doped fiber core radius
2.2 µm — [0.1,10]
Er doping radiusSpecifies the Er-doped radius
2.2 µm — [0.1,10]
Er metastable lifetimeDetermines the Er metastable lifetime
10 ms — [0.01,100]
Numerical apertureSpecifies the numerical aperture of the Er-doped fiber
0.24 — — [0.1,1]
Er ion densitySpecifies the Er doping in the Er-doped fiber
1e+025 m–3 m–3~ppm-wt ~wt%
[1,+INF[
283
EDF DYNAMIC — FULL MODEL
Cross-sections
Numerical
Loss at 1550 nmDetermines the fiber loss at 1550 nm
0.1 dB/cm — [0,100]
Loss at 980 nmDetermines the fiber loss at 980 nm
0.15 dB/cm — [0,100]
LengthDetermines the Er-doped fiber length
5 m — [0,10000]
Reference timeDetermines the instant of time used to take the powers to use as input powers in the fiber to solve the steady-state regime that will determine the initial values for the population levels.
Name and description Default value
Units Value range
OptiAmplifier formatDetermines the format of the OptiAmplifier file
False — True, False
File frequency unitDetermines the frequency unit of the file with the measurements
nm — nm, m, Hz, THz
cross-section file nameDetermines the cross-section file
Erbium.dat — —
Name and description Default value
Units Value range
Relative errorDetermines the relative error acceptable in each calculation for the steady-state solution used as initial condition for the dynamic behavior
0.0001 — ]0,1]
Max. number of iterationsSpecifies the maximum number of times to repeat the longitudinal integrations for the powers when solving the steady-state equations used as initial condition for the dynamic behavior
50 — [10,10000]
Longitudinal stepsDetermines the number of longitudinal steps in the calculation
100 — [10,10000]
Name and description Default value
Default unit Units Value range
284
EDF DYNAMIC — FULL MODEL
Simulation
Noise
Random numbers
Graphs
Name and description Default value
Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
Name and description Default value
Default unit Units Value range
Noise center frequencyDetermines the noise center frequency
193.4 THz Hz, THz, nm [30,30e5]
Noise bandwidthBandwidth to create noise bins
13 THz Hz, THz, nm ]0,+INF[
Noise bins spacingSpecifies the noise bins spacing
125 GHz Hz, GHz, THz, nm
[1,1000]
Noise thresholdMinimum value for adaptation of noise bins
–100 dB — ]-INF,0[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB — [0,+INF[
Convert noise binsDetermines if the generated noise bins are incorporated into the signal
Convert noise bins
— — True, False
Name and description Default value
Units Value range
Generate random seed
Determines if the seed is automatically defined and unique
True — True, False
Random seed index
User-defined seed index for noise generation
0 — [0,4999]
Name and description X Title Y Title
Absorption parameters Wavelength (m) Cross-section (m2)
Emission parameters Wavelength (m) Cross-section (m2)
285
EDF DYNAMIC — FULL MODEL
Technical backgroundDifferent solutions to the problem of transient fluctuations due to gain cross-saturation observed in EDFAs inserted in multi-wavelength networks have been suggested. Gain cross-saturation in fiber amplifiers induces transients in the surviving channels remaining as a consequence of the process of adding or removing channels in the network reconfiguration. Although this perturbation will be small in a single amplifier, it becomes considerable along cascaded amplifiers. As a result, a tool that enables analyzing the effects of addition and/or dropping wavelength channels in a multi-wavelength optical network containing EDFAs is important.
In opposition to the steady-state model (EDF module), the EDF Dynamic enables you to calculate the variation of signals and pumps power with the time when sampled channels are present in the layout. The dynamic behavior of cascaded EDFAs can be simulated as well. The results will help you design cascaded amplifier systems with suppression of both transient and steady state signal power fluctuations due to channel addition/removal.
The numerical EDF Dynamic uses a two-level system approximation and is based on the solution of the propagation and rate equations for transitions between the upper and lower levels. These equations are given by Equation 1, Equation 2, and Equation 3, which are also in the technical background for the Erbium doped fiber [1]:
(1)
(2)
(3)
where the optical powers are expressed in units of number of photons per unit time, is the metastable spontaneous emission lifetime, N is the number of channels taken into account in the simulation (including signals, pumps, and ASE bins), is the number density of the active erbium ions, is the attenuation coefficient (which takes into account the background loss of the fiber), is the frequency step used in the simulation to resolve the ASE spectrum, and Aeff is the effective doped area given by , where is the Er doping radius (it is considered a uniform distribution of erbium ions in the area given by the Er doping radius region).
∂N2 z t,( )∂t
--------------------N2 z t,( )
τ-----------------– 1
Aeff------- Γn σn
e σna+( )N2 z t,( ) σn
a–[ ]{ } Pn+ z t,( ) Pn
– z t,( )+[ ]n 1=
N
∑–=
N2 N1+ 1=
∂Pn± z t,( )∂z
----------------------- un ρΓn σne σn
a+( )N2 z t,( ) σna– α–[ ]{ }Pn
± z t,( ) 2ρ∆νN2Γnσne+=
τ
ρα
∆νπ b2× b
286
EDF DYNAMIC — FULL MODEL
The nth channel of wavelength has optical power Pn(z,t) at location z and time t, with emission and absorption cross-section and respectively, and confinement factor . The superscript symbols + and – are used to indicate channels traveling in forward (from 0 to L) and backward (from L to 0) directions, respectively. For beams traveling in the forward direction and for beams in the opposite direction . The overlap integrals between the LP01 mode intensity (which is used in this program) distribution doped region area are given by:
(4)
where E(r, ) gives the electric field intensity.
This model assumes that the signal and pump powers change slowly compared to the optical transit time in the fiber. This assumption is valid since the typical time that the light takes to pass by one 100 m fiber (one EDFA does not use fibers larger than that) is 500 ns. The time scales we deal with are always on the order of microseconds or longer.
Numerical solutionThe solution of the time-dependent rate equations and the propagation equations is based on the assumption that the atomic populations remain constant during a time step , typically microseconds. This assumption is acceptable since the metastable lifetime is relatively long (around 10 ms) and the transit time of photons through the Er3+-doped fiber is short.
Initial values for the population of the upper level in each point of the fiber of the program first solves the steady-state case. The parameter reference time determines the instant of time used to take the powers that will be used as input powers in the fiber to solve the steady-state regime that will determine the initial values for the population levels. When the calculation of the dynamic behavior for the sampled signal and pump channels starts at t=0, the program assumes that the population inversion is already different from zero, and the value of the population of the upper level at each point of the fiber (N2(z)) is given as t=0 by the powers at the reference time.
Generally speaking, you will be interested in the behavior of the amplifier in scales of times that go from a few microseconds to some tens of milliseconds. It is important to set the bit rate and the sequence length of the simulations in such a way that the time windows obey this requirement. If the time windows in your simulation are too short (for example, by a few nanoseconds), the gain of the EDF Dynamic amplifier will be given at almost all instants by the gain that one amplifier operating in the steady-state regime with the input powers given by the reference time would have, because the time response scales in EDFA are always on the order of microseconds or longer.
λn
σne σn
a
Γn
un 1=un 1–= Γn
Γn ν( )
E r ν,( ) 2r rd0
b
∫
E r ν,( ) 2r rd0
∞
∫
---------------------------------=
ν
δt
287
EDF DYNAMIC — FULL MODEL
The parameterized channels and noise bins input powers are considered constant in time. The output powers for these channels are average in time. This means that during the calculation, the program saves the output powers that each one of these channels would have at each sample point, and then gives as output power the sum of the power at each sample divided by the total number of samples.
References
[1] C.R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” Journal of Lightwave Technology, Vol. 9, N. 2, pp. 271-283, 1991.
288
EDF DYNAMIC — ANALYTICAL MODEL
EDF Dynamic — Analytical model
Enables you to simulate the dynamic response of an EDF for input powers that vary in time. In opposition to the EDF Dynamic — Full model component, it doesn't solve the full rate and propagation equation. Neglecting ASE these equations can be solved analytically, which is described in this module. An additional approximation which considers the population of the upper level constant for the propagation equations is used to include the ASE effects on the behavior of the amplifier. The results using analytical solutions are achieved faster than using the EDF Dynamic — Full model, but the results are less accurate. The model which you use depends on the trade off between time and accuracy.
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Output 1 Output Optical
Output 2 Output Optical
Name and description Default value
Default unit Units Value range
Core radiusDetermines the Er-doped fiber core radius
2.2 µm — [0.1,10]
Er doping radiusSpecifies the Er-doped radius
2.2 µm — [0.1,10]
Er metastable lifetimeDetermines the Er metastable lifetime
10 ms — [0.01,100]
Numerical apertureSpecifies the numerical aperture of the Er-doped fiber
0.24 — — [0.1,1]
289
EDF DYNAMIC — ANALYTICAL MODEL
Cross-sections
Numerical
Er ion densitySpecifies the Er doping in the Er-doped fiber
1e+025 m–3 m–3~ppm-wt ~wt%
[1,+INF[
Loss at 1550 nmDetermines the fiber loss at 1550 nm
0.1 dB/cm — [0,100]
Loss at 980 nmDetermines the fiber loss at 980 nm
0.15 dB/cm — [0,100]
LengthDetermines the Er-doped fiber length
5 m — [0,10000]
Reference timeDetermines the instant of time used to take the powers to use as input powers in the fiber to solve the steady-state regime that will determine the initial values for the population levels.
Name and description Default value
Units Value range
OptiAmplifier formatDetermines the format of the OptiAmplifier file
False — True, False
File frequency unitDetermines the frequency unit of the file with the measurements
nm — nm, m, Hz, THz
Cross-section file nameDetermines the cross-section file
Erbium.dat — —
Name and description Default value
Units Value range
Relative errorDetermines the relative error acceptable in each calculation for the steady-state solution used as initial condition for the dynamic behavior
0.0001 — ]0,1]
Max. number of iterationsSpecifies the maximum number of times to repeat the longitudinal integrations for the powers when solving the steady-state equations used as initial condition for the dynamic behavior
50 — [10,10000]
Name and description Default value
Default unit Units Value range
290
EDF DYNAMIC — ANALYTICAL MODEL
Simulation
Noise
Random numbers
Longitudinal stepsDetermines the number of longitudinal steps in the calculation
100 — [10,10000]
Name and description Default value
Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
Name and description Default value
Default unit Units Value range
Noise center frequencyDetermines the noise center frequency
193.4 THz Hz, THz, nm [30,30e5]
Noise bandwidthBandwidth to create noise bins
13 THz Hz, THz, nm ]0,+INF[
Noise bins spacingSpecifies the noise bins spacing
125 GHz Hz, GHz, THz, nm
[1,1000]
Noise thresholdMinimum value for adaptation of noise bins
–100 dB — ]-INF,0[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB — [0,+INF[
Convert noise binsDetermines if the generated noise bins are incorporated into the signal
Convert noise bins
— — True, False
Name and description Default value
Units Value range
Generate random seed
Determines if the seed is automatically defined and unique
True — True, False
Random seed index
User-defined seed index for noise generation
0 — [0,4999]
Name and description Default value
Units Value range
291
EDF DYNAMIC — ANALYTICAL MODEL
Graphs
Technical backgroundThis model uses analytical solutions for the same rate and propagation as [1], Equation 2, and Equation 3 described in Erbium doped fiber. These equations consider a two-level system interacting with light. As with the EDF Dynamic — Full model, it's assumed in this analytical model that the signal and pump powers change slowly compared to the optical transit time along the fiber.
Neglecting the ASE and the background loss in Equation 1, Equation 2, and Equation 3 for the Erbium doped fiber [1]:
(1)
and
(2)
where all the parameters were defined in Erbium doped fiber. Integrating Equation 1 and Equation 2 over z from 0 to L and defining as the total number of erbium ions in the upper state:
(3)
Name and description X Title Y Title
Absorption parameters Wavelength (m) Cross-section (m2)
Emission parameters Wavelength (m) Cross-section (m2)
∂N2 z t,( )∂t
--------------------N2 z t,( )
τ-----------------– 1
ρAeff----------- uj
∂Pn± z t,( )∂z
-----------------------n 1=
N
∑–=
∂Pn z t,( )∂z
-------------------- un ρΓn σne σn
a+( )N2 z t,( ) σna–[ ]{ }Pn z t,( )=
N2
N2 t( ) ρAeff N2 z t,( ) zd0
L
∫=
292
EDF DYNAMIC — ANALYTICAL MODEL
we have
(4)
and
(5)
where
(6)
A further approximation enables us to estimate the ASE effects on this model. Considering N2(z) constant at each instant of time (which is a good approximation for strongly inverted EDFA), the propagation equations have an analytical solution which gives [2]:
(7)
where
(8)
is called the spontaneous emission factor. Substituting Equation 8 for Equation 4, we finally obtain:
(9)
This module uses Equation 5 and Equation 9 to simulate the dynamic behavior of the amplifier. Once given an initial value for the total number of excited ions, that is,
dN2 t( )dt
---------------- N2 t( )–τ
---------------- Pnout± t( ) Pn
in± t( )–n 1=
N
∑–=
Pnout± t( ) Pn
in± Gn 1–( )–
Gn Γn σne σn
a+( )N2 z t,( ) ρσna–[ ]L{ }exp=
Pnout± t( ) Pn
in± t( )– Pnin± t( ) Gn t( ) 1–[ ] 2nn
sp Gn t( ) 1–[ ]∆νASE+=
nnsp N2 t( )σn
e
σne σn
a+( )N2 σnaρ–
----------------------------------------------=
dN2 t( )dt
---------------- N2 t( )–τ
---------------- Pnin± t( ) Gn t( ) 1–[ ] 4nn
sp Gn t( ) 1–[ ]∆νASE
n
N
∑+n 1=
N
∑–=
N2
293
EDF DYNAMIC — ANALYTICAL MODEL
(t=0), and the input powers at each time, these coupled equations can be solved with an interactive loop between them.
Numerical solutionAs initial values for the total population of the upper level, the program solves the steady-state case. The parameter reference time determines the instant of time used to take the powers that will be used as input powers in the fiber in order to solve the equations in the steady-state regime. The obtained results will determine the initial value for the total number of excited erbium ions at t=0 ( (t=0)). In this way, when the calculation of the dynamic behavior to the sampled signal and pump channels starts at t=0, the program assumes that the population inversion is already different from zero, and the value of the upper level population is given at t=0 by the powers at the reference time.
Generally speaking, it is interesting to determine the behavior of the amplifier in scales of time that go from a few microseconds to tens of milliseconds. It is important to set the bit rate and the sequence length of the simulations in such a way that the time windows obey this requirement. If the time windows in your simulations are too short (for example, by a few nanoseconds), the gain of the EDF Dynamic amplifier will be given at almost all instants by the gain that one amplifier operating in the steady-state regime with the inputs powers given by the reference time would have, because the time response scales in EDFA are always in the order of microseconds or longer.
The parameterized channels and noise bins input powers are considered constant in time. The output powers for these channels are calculated averaging in time . This means that during the calculation, the program saves the values of at each instant of time and then calculates the medium value . Equation 4 and are then used to calculate the output powers of the parameterized and noise channels.
References[1] Y. Sun, J.L. Zyskind, and A.K. Srivastava, "Average Inversion Level, Modeling, and Physics of
Erbium-Doped Fiber Amplifiers," Journal of Selected Topics in Quantum Electronics, Vol. 3, N. 4, pp. 991-1006, 1997.
[2] T. Georges and E. Delevaque, "Analytical Modeling of High-Gain Erbium-Doped Fiber Amplifiers," Optics Letters, Vol. 17, N. 16, pp. 1113-1115, 1992.
N2
N2N2
N2⟨ ⟩ N2⟨ ⟩
294
EDFA
EDFA
Designs Er-doped fiber amplifiers by considering numerical solutions of the rate and the propagation equations under stationary conditions. The model includes amplified spontaneous emission (ASE) as observed in the amplifier Erbium Doped Fiber. However, this module allows you to select forward and/or backward pump, as well as the pump power values.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value
Default unit
Units Value range
Core radiusDetermines the Er-doped fiber core radius
2.2 µm — [0.1,10]
Er doping radiusSpecifies the Er-doped radius
2.2 µm — [0.1,10]
Er metastable lifetimeDetermines the Er metastable lifetime
10 ms — [0.01,100]
Numerical apertureSpecifies the numerical aperture of the Er-doped fiber
0.24 — — [0.1,1]
Er ion densitySpecifies the Er doping in the Er-doped fiber
1e+025 m–3 m–3~ppm-wt~wt%
[1,+INF[
Loss at 1550 nmDetermines the fiber loss at 1550 nm
0.1 dB/cm — [0,100]
Loss at 980 nmDetermines the fiber loss at 980 nm
0.15 dB/cm — [0,100]
295
EDFA
Pumping
Cross-sections
Numerical
LengthDetermines the Er-doped fiber length
5 m — [0,10000]
Name and description Default value
Default unit Units Value range
Forward pump powerDetermines the co-propagating pump power
100 mW W, mW, dBm [0,+INF[
Backward pump powerDetermines the counter-propagating pump power
0 mW W, mW, dBm [0,+INF[
Forward pump wavelength Determines the co-propagating pump wavelength
980 nm — [700,1600]
Backward pump wavelengthDetermines the counter-propagating pump wavelength
980 nm — [700,1600]
Name and description Default value
Units Value range
File frequency unitDetermines the frequency unit of the file with the measurements
nm — nm, m, Hz, THz
OptiAmplifier formatDetermines the format of the OptiAmplifier file
False — True, False
cross-section file nameDetermines the cross-section file
Erbium.dat — —
Name and description Default value
Units Value range
Relative errorDetermines the relative error acceptable in each calculation
0.0001 — ]0,1]
Max. number of iterationsSpecifies the maximum number of times to repeat the calculation
50 — [10,10000]
Name and description Default value
Default unit
Units Value range
296
EDFA
Polarization
Simulation
Noise
Longitudinal stepsDetermines the number of longitudinal steps in the calculation
100 — [10,10000]
Name and description Default value
Units Value range
Polarization filterDetermines the polarization of the filter
None — None, Polarization X, Polarization Y
Name and description Default value
Units Value range
EnabledDetermines whether or not the component is enabled
Yes — [0, 0]
Name and description Default value
Default unit Units Value range
Noise center frequencyDetermines the noise center frequency
193.4 THz Hz, THz, nm [30, 30]
Noise bandwidthBandwidth to increase noise bins
13 THz Hz, Thz, nm [1e-100, 1e-100]
Noise bins spacingDetermines noise bins spacing
125 GHz Hz, GHz, THz, nm
[1,1]
Noise thresholdMinimum value for adaptation of noise bins
–100 dB — [-1e+100, -1e+100]
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB — [0, 0]
Convert noise binsDetermines if the generated noise bins are incorporated into the signal
Convert noise bins
— — [0, 0]
Name and description Default value
Units Value range
297
EDFA
Random numbers
Graphs
Technical backgroundThe routines in EDFA numerically solve the rate equations coupled with propagating equations under stationary conditions. It is assumed a two-level Er system approximation and the rate equations are based on the energy level diagram. The same expressions described in the module Erbium doped fiber are adopted by this model.
The main difference is related to the amplifier pump scheme selection. You can choose co-propagating, counter-propagating, or bi-directional pump schemes with the option to set wavelength and pump power. Geometrical Er-doped fiber parameters and cross-section curves are required as input files. As output files, you can access gain, output power values, and noise figure determined in the ASE bandwidth set as noise input data.
Er Doped Fiber Rate and Propagation EquationsThe lifetime transition from level 4I11/2 is of the order of microseconds for silicate hosts. Therefore, it is reasonable to neglect the population density N3 in the rate equations description. A two-level system approximation is used in this case. Under the assumption of the normalized population densities N1 and N2 at the ground and metastable energy level, 4I15/2 and 4I13/2 populations are calculated by numerically solving the rate and propagation equations[1]:
(1)
Name and description Default value
Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
Yes — [0, 0]
Random seed indexUser-defined seed index for noise generation
0 — [0, 0]
Name and description X Title Y Title
Absorption parameters Wavelength (m) Cross-section (m2)
Emission parameters Wavelength (m) Cross-section (m2)
∂N2 z t,( )∂t
--------------------N2 z t,( )
τ-----------------– 1
Aeff------- Γn σn
e σna+( )N2 z t,( ) σn
a–[ ]{ } Pn+ z t,( ) Pn
– z t,( )+[ ]n 1=
N
∑–=
298
EDFA
(2)
(3)
where the optical powers are expressed in units of number of photons per unit time, is the metastable spontaneous emission lifetime, N is the number of channels taken into account in the simulation (including signals, pumps, and ASE bins), is the number density of the active erbium ions, is the attenuation coefficient (which takes into account the background loss of the fiber), is the frequency step used in the simulation to resolve the ASE spectrum, and Aeff is the effective doped area given by , where is the Er doping radius (it is considered a uniform distribution of erbium ions in the area given by the Er doping radius region).
The nth channel of wavelength has optical power Pn(z,t) at location z and time t, with emission and absorption cross-section and respectively, and confinement factor . The superscript symbols + and – are used to indicate channels traveling in forward (from 0 to L) and backward (from L to 0) directions, respectively. For beams traveling in the forward direction and for beams in the opposite direction . The overlap integrals between the LP01 mode intensity (which is used in this program) distribution doped region area are given by:
(4)
where E(r, ) gives the electric density field.
Solving Equation 1, Equation 2, and Equation 3 under stationary conditions allows you to determine the amplifier performance features. The fiber parameters such as core and Er doping radius, Er metastable lifetime, numerical aperture, Er ion density, loss at 980 nm and 1550 nm, and the fiber length are required as input values. The absorption and emission cross-section are also required as input files.
Absorption and Emission cross-sectionsThere are two options available to you to prepare the cross-section file, which is specified in an ASCII file. The first option is to provide the cross-section input file in three columns. The first column refers to the wavelength in [m], [nm], [Hz] or [THz] units. The second column gives the absorption cross- section in [m2] units. The third
N2 N1+ 1=
∂Pn± z t,( )∂z
----------------------- un ρΓn σne σn
a+( )N2 z t,( ) σna– α–[ ]{ }Pn
± z t,( ) 2ρ∆νN2Γnσne+=
τ
ρα
∆νπ b2× b
λn
σne σn
a
Γn
un 1=un 1–= Γn
Γn ν( )
E r ν,( ) 2r rd0
∫
E r ν,( ) 2r rd0
∞
∫
---------------------------------=
ν
299
EDFA
column gives the emission cross-section in [m2] units. In this case, the cross-section file format is:
The second option is to consider the absorption and emission coefficients (or Giles parameters) as input parameters that are converted to cross-section by internal routines in the software. This is especially interesting when only Giles parameters are measured to the Er-doped fiber. The file format in this case contains three columns. The first column refers to the wavelength in [m], [nm], [Hz] or [THz] units. The second column gives the absorption coefficient in [dB/m] units. The third column gives the emission coefficient in [dB/m] units. An example of this input file is:
(nm)
929.982 9.28e-27 0
930.172 7.05e-27 0
.
.
.
1029.972 2.85e-27 0
1030.072 3.59e-27 0
1450.6 2.086e-26 1.726e-27
1450.8 2.186e-26 1.823e-27
.
.
.
1649.8 1.540e-26 8.228e-26
1650.0 1.540e-26 8.280e-26
(nm) (dB/m) g* (dB/m)
929.982 0.39168 0
930.172 0.2856 0
.
.
.
1029.972 –0.05508 0
1030.072 –0.14484 0
1450.6 1.8075 0.35599973
1450.8 1.815 0.360619883
λ σa m2[ ] σe m2[ ]
λ α
300
EDFA
where the wavelength is given in [nm] units, absorption and emission coefficients are in [dB/m].
.
.
.
1649.8 0.005 0.484116259
1650.0 –0.0175 0.477803876
(nm) (dB/m) g* (dB/m)λ α
301
EDFA
Reference:
[1] C.R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” Journal of Lightwave Technology, Vol. 9, N. 2, pp. 271-283, 1991.
302
EDFA IDEAL
EDFA Ideal
Enables designing EDFAs considering pre-defined operation conditions that means to specify previously the expected gain, the noise figure and the amplifier output power. The EDFA Ideal presents the same facilities as a black box model, which enables you to select the operation mode with gain control, power control, or performing simulations under saturated condition, as well as to define the expected amplifier performance. It is specially indicated for the prompt performance analysis of one or cascaded amplifiers present in a long-haul system.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value
Default unit Units Value range
Operation modeAmplifier operation mode
Gain control — — Gain control, Power control, Saturation
GainDetermines the signal gain
20 dB — [0,100]
PowerDetermines the signal output power
10 dBm W, mW, dBm [-100,100]
Saturation powerSpecifies the optical power at the gain compressed by 3 dB
10 dBm — [-100,100]
Saturation portDetermines the amplifier saturation port
Output — — Input, Output
Include noise YES — — —
303
EDFA IDEAL
Polarization
Simulation
Noise
Random numbers
Noise figureDetermines the amplifier noise figure
4 dB — [3,100]
Name and description Default value
Units Value range
Polarization filterDetermines the polarization of the filter
None — None, Polarization X, Polarization Y
Name and description Default value
Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
Name and description Default value
Default unit Units Value range
Noise center frequency 193.4 THz Hz, THz, nm [30, 3e+006]
Noise bandwidth 13 THz Hz, THz, nm [1e-100, 1e+100]
Noise bins spacingSpecifies the noise bins spacing
125 GHz Hz, GHz, THz, nm
[1,1000]
Convert noise binsDetermines if the generated noise bins are incorporated into the signal
Convert noise bins
— — True, False
Name and description Default value
Units Value range
Generate random seed
Determines if the seed is automatically defined and unique
True — True, False
Random seed index
User-defined seed index for noise generation
0 — [0,4999]
Name and description Default value
Default unit Units Value range
304
EDFA IDEAL
Technical backgroundThe simulation of the ideal amplifier is performed in the opposite way than that used by the previous described models. In this case, the desired amplifier performance given by the gain, the output power, the saturated output power, and the noise figure values are used as input parameters to design the amplifier.
The input data are related by the propagation equation written in terms of the parameter required in each mode selected. There are three different mode controls — Gain control, Power Control, and Saturation. Large and small input signal can be considered in this amplifier model. The concept of the ideal amplifier enabling you to define the device performance makes this model flexible to design amplifiers considering different applications in a system such as booster, in-line, and pre-amplifier.
The amplified spontaneous emission is included in the model of the EDFA Ideal and it is built from the noise figure input value.
Mode Controls Description The EDFA Ideal subsystem enables three operation modes, which you can select in the EDFA Ideal Properties dialog box by clicking on Main/Operation Mode/Value. The first option is the Gain Control that maintains the gain constant and allows you to include (or not include) the amplified spontaneous emission in the calculations. In the second operation mode option, Power Control, the value of the output power is maintained constantly. The third operation mode, Saturation, considers the amplifier operating in a saturated condition — operating in an output signal power correspondent to a gain 3 dB lower than the saturated gain.
Gain Control ModeIn this mode, you set the desired amplifier gain (in dB units), which is given by the ratio of the total output power (Pout) and total input power (Psin), including (or not including) the generated ASE (PASE), as given by Equation 1. There are no additional iterations or complicated equation solutions in this mode. The set amplifier input parameters as gain and noise figure give the performance of this sub-system to be inserted in the global system.
(1)
Power Control ModeThe value that you define in the power control mode is the desired amplifier output power (in dBm units), which is maintained constantly. Analogous with the gain-controlled mode, there is no additional calculation involved in the designed amplifier. The output power set as input parameter defines the amplifier performance to be considered in the system where this amplifier is inserted. The ASE, which basically computes the noise introduced by the amplifier into the system, can be included (or
GPout PASE–( )
Psin---------------------------------=
305
EDFA IDEAL
not included) in the amplifier performance. Note that the specified output power is not degraded by the ASE noise included in the amplifier subsystems — however, this noise source is computed in the global system analysis.
Saturation ModeIn the saturation mode, it is assumed that the pump power is constant, causing the amplifier to operate in a saturated regime. The saturation power, gain, and noise figure are the parameters required by this mode. The saturation power is the input parameter maintained constant in this mode selection, and in an ASE-free model can be related with the gain (G), output power (Pout), and intrinsic saturation power (Psat
int) by the expression:
(2)
where G0 is the small-signal gain or unsaturated gain.
The intrinsic saturation power is written as:
(3)
where A is the mode-field area, h is the Planck’s constant, ν is the frequency at the propagating signal, σa is the absorption cross-section, and τ is the Er metastable lifetime in silica.
These fiber specifications are not required in this Ideal Amplifier module, since the intrinsic saturation power will be related to the amplifier saturation power under the gain compression condition.
Under the 3 dB gain compression, the output power is proportional to the intrinsic saturation power. This relation is:
(4)
ASE CalculationThe ASE noise spectrum is built in this model from the noise figure provided as input parameter, considering the expression that relates spectral ASE noise with noise figure. The noise figure (NF) evaluated at a specific signal wavelength is:
(5)
The term 1/G corresponds to the shot noise, Sout is the output ASE spectral density at the signal wavelength, and hν is the photon energy. In practical cases, there is ASE
G G0G 1–
G-------------
Pout
Psatint
----------–exp=
Psatint Ahv
σaτ----------=
Pout Compressed3dB In 2( )Psat
int=
NF 1G----
SoutGhv----------+=
306
EDFA IDEAL
present at the input of the doped fiber so that the amplified input ASE must be added to the output ASE spectral density. The output ASE can be written as:
(6)
where Samp is the spectral density ASE generated by the doped fiber.
Correcting for the input ASE gives the signal-spontaneous beat noise limited noise figure as a function of the signal gain, and input and output ASE spectral densities:
(7)
In the signal-spontaneous beat noise limited regime, with high gain and negligible input coupling, the noise figure of the optical preamplifier approaches a theoretical limit of [1]:
(8)
where the spontaneous emission factor, nsp, is defined as:
(9)
where
(10)
Since nsp ≥ 1, an EDFA at high gain has a minimum noise figure of 3 dB. This is derived by assuming that the input signal is shot noise limited and the output noise is signal-spontaneous beat noise limited. In practical situations, the noise figure is degraded by the amplifier input coupling loss.
Noise figureThis lists the signal-spontaneous beat noise limited noise figure. For each signal wavelength, the noise figure is:
(11)
where is the output ASE spectral density (W/Hz) at the signal wavelength, and is the input ASE spectral density at the signal wavelength.
Sout Samp Sin G×+=
NF 1G----
SoutGhv----------
Sinhv------–+=
NFoptσsig sp–
2
σsig sh–2 in( )G2
----------------------------------- 2nsp= =
nsp v z,( )N2 z( )
N2 z( ) N1 z( )ε v( )–--------------------------------------------=
ε v( )σa v( )σe v( )-------------=
NoiseFigure dB( ) 10 101G----
Sout λs( )Ghv
-------------------Sin λs( )
hv-----------------–+log×=
Sout λs( ) Sin λs( )
307
EDFA IDEAL
Rewriting the ASE spectral density as a function of noise figure value, the noise spectrum can be generated considering the noise figure input parameter. Therefore, the ASE spectrum is obtained from the expression:
(12)
References
[1] T. Okoshi, "Exact Noise-Figure Formulas for Optical Amplifiers and Amplifier-Fiber Cascaded Chains," IEEE/OSA Topical Meeting on Optical Amplifiers and their Applications, Monterrey, PDP11, 1990.
Sout λs( ) G hv 10NoiseFigure dB( )
10------------------------------------- 1
G----–
Sin λs( )hv
-----------------–×=
308
EDFA MEASURED
EDFA Measured
Enables you to design EDFAs considering pre-defined operation conditions that mean to specify previously the measured gain, noise figure, and amplifier output power. It is specially indicated for the prompt performance analysis of one or cascaded amplifiers present in a long-haul system. It can be also used for flat gain amplifiers.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value
Default unit Units Value range
Measured gain and noise figureWavelength, gain, and NF table with the measured data
(nm dB dB) — — —
Gain and noise figure file nameFilename with the measured data
GainAndNF.dat — — —
Max. output powerDetermines the total signal output power
25 dBm W, mW, dBm [-100,+100]
Include noiseDetermines if the component add noise to the output signal
True — — True, False
309
EDFA MEASURED
Polarization
Simulation
Noise
Random numbers
Name and description Default value
Units Value range
Polarization filterDetermines the polarization of the filter
None — None, Polarization X, Polarization Y
Name and description Default value
Units Value range
EnabledDetermines whether or not the component is enabled
Yes — [0, 0]
Name and description Default value
Default unit Units Value range
Noise center frequencyDetermines the noise center frequency
193.4 THz Hz, THz, nm [30, 30]
Noise bandwidthBandwidth to increase noise bins
13 THz Hz, Thz, nm [1e-100, 1e-100]
Noise bins spacingDetermines noise bins spacing
125 GHz Hz, GHz, THz, nm
[1, 1]
Noise thresholdMinimum value for adaptation of noise bins
–100 dB — [-1e+100, -1e+100]
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB — [0, 0]
Convert noise binsDetermines if the generated noise bins are incorporated into the signal
Convert noise bins
— — [0, 0]
Name and description Default value
Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
Yes — [0, 0]
310
EDFA MEASURED
Technical backgroundThe simulation of the ideal amplifier is performed in similar way to the EDFA Ideal. In this case, the desired amplifier performance given by the measured gain, noise figure, and maximum output power. Large and small input signals can be considered in this amplifier model. The concept of the measured amplifier enabling you to define the device performance makes this model flexible to design amplifiers for different applications in a system such as booster, in-line, pre-amplifier, gain flat, and noise flat. It can also load measurements from other software tools such as Optiwave's OptiAmplifier.
This maximum output power can be limited when the total output power is greater then the parameter Max. output power. The calculation engine reduces the amplifier gain in order to have the total output power equal to the parameter Max. output power.
ASE CalculationThe ASE noise spectrum is built in this model from the noise figure provided as input parameter, considering the expression that relates spectral ASE noise with noise figure. The noise figure (NF) evaluated at a specific signal wavelength is:
(1)
The term 1/G corresponds to the shot noise, Sout is the output ASE spectral density at the signal wavelength, and hν is the photon energy.
In practical cases, there is ASE present at the input of the doped fiber so that the amplified input ASE must be added to the output ASE spectral density. Therefore, the output ASE can be written as:
(2)
where Samp is the spectral density ASE generated by the doped fiber.
Correcting for the input ASE gives the signal-spontaneous beat noise limited noise figure as a function of the signal gain, and input and output ASE spectral densities:
Random seed indexUser-defined seed index for noise generation
0 — [0, 4999]
Name and description Default value
Units Value range
NF 1G----
SoutGhv----------+=
Sout Samp Sin G×+=
NF 1G----
SoutGhv----------
Sinhv------–+=
311
EDFA MEASURED
(3)
In the signal-spontaneous beat noise limited regime, with high gain and negligible input coupling, the noise figure of the optical preamplifier approaches a theoretical limit of [1]:
(4)
where the spontaneous emission factor, nsp, is defined as:
(5)
where
(6)
Since nsp ≥ 1, an EDFA at high gain has a minimum noise figure of 3 dB. This is derived by assuming that the input signal is shot noise limited and the output noise is signal-spontaneous beat noise limited.
In practical situations, the noise figure is degraded by the amplifier input coupling loss.
Noise figureThis lists the signal-spontaneous beat noise limited noise figure. For each signal wavelength, the noise figure is:
(7)
where is the output ASE spectral density (W/Hz) at the signal wavelength, is the input ASE spectral density at the signal wavelength.
Rewriting the ASE spectral density as a function of noise figure value, the noise spectrum can be generated considering the noise figure input parameter. Therefore, the ASE spectrum is obtained from the expression:
(8)
NFoptσsig sp–
2
σsig sh–2 in( )G2
----------------------------------- 2nsp= =
nsp v z,( )N2 z( )
N2 z( ) N1 z( )ε v( )–--------------------------------------------=
ε v( )σa v( )σe v( )-------------=
NoiseFigure dB( ) 10 101G----
Sout λs( )Ghv
-------------------Sin λs( )
hv-----------------–+log×=
Sout λs( ) Sin λs( )
Sout λs( ) G hv 10NoiseFigure dB( )
10------------------------------------- 1
G----–
Sin λs( )hv
-----------------–×=
312
EDFA MEASURED
MeasurementsYou can provide the measurements in the parameter Measured gain and noise figure. Alternatively, the measurements can be loaded from a file using the parameter Gain and noise figure file name. The gain and noise figure curves must be provided in the file containing three columns. The first column refers to the wavelength specified in [nm] units. The second column gives the gain noise curve in [dB] units. The third column gives the noise figure in [dB] units.
Example of input file:
Wavelength ([nm] Gain [dB] NF [dB]
1500.00 20.00 4.00
1510.00 20.00 4.00
1520.00 20.00 4.00
1530.00 20.00 4.00
1540.00 20.00 4.00
1550.00 20.00 4.00
313
EDFA MEASURED
Reference:
[1] T. Okoshi, "Exact Noise-Figure Formulas for Optical Amplifiers and Amplifier-Fiber Cascaded Chains," IEEE/OSA Topical Meeting on Optical Amplifiers and their Applications, Monterrey, PDP11, 1990.
314
ERBIUM DOPED FIBER
Erbium doped fiber
This component simulates a bidirectional Erbium doped fiber considering ESA, Raleigh scattering, ion-ion interactions, and temperature dependence effects. The component solves numerically the rate and propagation equations in the steady-state case, assuming a two-level Erbium system for an inhomogeneous and homogeneous approach.
Ports
Parameters
Main
Name and description Port type Signal type
Input1 Input Optical
Output1 Output Optical
Input2 Input Optical
Output2 Output Optical
Name and description Symbol Default value Default unit
Units Value range
LengthSpecifies the doped fiber length
L 5 m — [0, 1e4]
Er metastable lifetimeSpecifies the Erbium metastable lifetime
10 ms — ]0, +INF[
Input dataDetermines if saturation parameter is used or not
— Fiber specification — — Fiber specification, Saturation parameter
Saturation parameterSpecifies value of saturation parameter
4.4e+015 1/(s.m) — [1e-10, +INF[
Core radiusSpecifies the fiber core radius
a 2.2 µm — [0,1, 10]
τ
ζ
315
ERBIUM DOPED FIBER
Cross-sections
Enhanced
Er doping radiusSpecies the Erbium doped radius
b 2.2 µm — [0.1, 10]
Er ion densitySpecifies the Erbium doping in the fiber
1e+25 m-3 m-3 , ~ppm-wt, ~wt%
[1e23, +INF[
Numerical apertureSpecifies the numerical aperture of the fiber
NA 0.24 — — [0.1,1]
Name and description Default value
Default unit Units Value range
OptiAmplifier formatDetermines if format of cross-section file is an OptiAmplifier file
False — — True, False
File frequency unitDetermines frequency unit of the file with the cross sections
nm — — nm, m, Hz, THz
Cross-section file nameSpecifies Erbium cross-section file name
Erbium.dat — — —
Name and description Symbol Default value Default unit
Units Value range
Background loss data typeDetermines if the loss will be calculated from the loss at 1310nm (constant) or it will be loaded from a file
Constant — — Constant, From file
Loss at 1310 nm
Specifies the fiber loss at 1310nm
3 dB/Km [0, +INF[
Background loss file name
Specifies loss file name
— Loss.dat — — —
Include Rayleigh backscattering
Determines if Rayleigh scattering effect is included or not
False — — True, False
Name and description Symbol Default value Default unit
Units Value range
nt
l λ( )
l1310
316
ERBIUM DOPED FIBER
Rayleigh ConstantSpecifies the value of the Rayleigh constant
150 — dB/Km [0, 1000]
Backscattering capture fractionDetermines if capture fraction values are calculated by the component or loaded from a file
Calculate — — Calculate, From file
Rayleigh capture file nameSpecifies the capture file name
— Capture.dat — — —
Includes ion-ion interaction effectsDetermines whether Er-Er ion interaction effects are included or not
— False — — True, False
Ion-Ion interaction effectDetermines which kind of Er-Er ion interaction is considered
— Homogeneous — — Homogeneous, Inhomogeneous, Combined
Upconversion coefficientSpecifies the two-particle upconversion coefficient
1e-022 [0, 1000]
Ions per clusterSpecifies number of ions in a cluster
2 — — [0, 500]
Relative number of clustersSpecifies the relative number of clusters
K 12 — % [0, 100]
Include Temperature EffectsDetermines if temperature dependence is taken into account
— False — — True, False
TemperatureSpecifies the current temperature
T 20 — C [-273, 500]
Cross-section TemperatureSpecifies the temperature when the cross-section was measured
Tm 20 — C [-273, 500]
Include ESA EffectDetermines if excited stated absorption is taken into account
— False — — True, False
ESA Cross-section file nameSpecifies the ESA cross-section file name
— ESAErbium.dat — — —
Name and description Symbol Default value Default unit
Units Value range
KR
C λ( )
Uc m3 s⁄
mk
317
ERBIUM DOPED FIBER
Numerical
Extract ESA from emissionDetermines if the component has to extract the ESA cross-section from the loaded file
— False — — True, False
Name and description Symbol Default value Default unit
Units Value range
Calculation algorithmDetermines algorithm to be used in simulation
— Giles — Saleh, Jopson, Giles, Inhomogeneous
Relative errorSpecifies maximum acceptable difference between two consecutive iterations to complete the iteration process
0.0001 — — [1e-100, 1]
Max. number of iterationsSpecifies the maximum number of iterations executed
100 — — [1, 1e8]
Number of longitudinal stepsSpecifies the minimum number of longitudinal steps in the fiber
50 [1, 1e8]
Inhomogeneous accuracyIf the inhomogeneous model is selected, this parameter specifies the accuracy in the convolution integrals
— 0.001 — — [1E-10, 0.1]
Overlap factor dataDetermines whether overlap factor values are calculated by the component or loaded from a file
Calculate — — Calculate, From file
Geometrical modelDetermines whether the component calculates the overlap factor using one of the Gaussian approximations, or the LP01 mode
— LP01 — — Marcuse Gaussian, Whitley Gaussian, Desurvire Gaussian, Myslinski Gaussian, LP01
Overlap factorDetermines if overlap factor calculations takes into account the signal and pump power
— Power independent
— — Power independent, Power dependent
Name and description Symbol Default value Default unit
Units Value range
ζ
Nmax
Γ
318
ERBIUM DOPED FIBER
Simulation
Noise
Nr. of transverse integrationsIf PowerDependent is selected for Overlap factor, specifies the number of times that the overlap factor is calculated over the fiber length
— 2 — — [1, 50]
Overlap factor file nameSpecifies the overlap factor file name
— Confinement.dat — — —
Generate homogeneous cr.Generate the homogeneous cross- sections
— False — — True, False
Inhomogeneous linewidthSpecifies the Erbium-doped fiber inhomogeneous linewidth
11.5 nm — ]0, 100]
Number of gaussiansDetermines number of gaussians used in generation of the homogeneous cross-sections
17 — — [8, 28]
Name and description Default value
Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
Enable reflectionsDetermines whether or not the component launches reflections due to backscatterig in the output
False — True, False
Name and description Default value
Default unit Units Value range
Noise center frequencyDetermines the noise center frequency
193.4 THz Hz, THz, nm [30,30e5]
Noise bandwidthBandwidth to create noise bins
13 THz Hz, THz, nm ]0,+INF[
Noise bins spacingSpecifies the noise bins spacing
125 THz Hz, GHz, THz, nm
[1,1000]
Name and description Symbol Default value Default unit
Units Value range
∆λinh
nG
319
ERBIUM DOPED FIBER
Random numbers
Graphs
Noise thresholdMinimum value for adaptation of noise bins
–100 dB — ]-INF,0[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB — [0,+INF[
Convert noise binsDetermines if the generated noise bins are incorporated into the signal
Convert noise bins
— — True, False
Name and description Default value
Units Value range
Generate random seed
Determines if the seed is automatically defined and unique
True — True, False
Random seed index
User-defined seed index for noise generation
0 — [0,4999]
Name and description Default value
Default unit Units Value range
Calculate graphs False — — True, False
Number of distance steps 20 — — [1,1e8]
Number of wavelength steps 20 — — [1,1e8]
Linear scale True — — True, False
Minimum value -50 — dBm ]1e-100, 1e100[
Pump reference wavelength 1400 nm [100, 1900]
Name and description Default value
Default unit Units Value range
320
ERBIUM DOPED FIBER
Technical backgroundThis module presents a rapid numerical solver for the EDF rate and propagation equations for signals, pumps and amplified spontaneous emission (ASE) considering the steady-state case. The propagation and rate equations of a two level system are used to model the Erbium-doped fiber. Several effects are considered, including
interactions, excited state absorption, temperature dependence, and background loss. Furthermore, the component assumes the possibility of considering the inhomogeneous broadening in the EDF.
Propagation and Rate EquationsThe Erbium Doped Fiber component is based on the solution of the rate and propagation equations assuming a two-level model. The use of a two-level model for the amplifier is justified, as for pumping into the 980nm absorption band, the lifetime transition from level is of the order of microseconds for silicate hosts and is reasonable to neglect the population density in the rate equations description. At 1480nm, the pumping is direct to the upper sub-levels of the metastable manifold.
Rate equations are based on energy levels and describe the effects of absorption, stimulated emission, and spontaneous emission on the populations of the ground ( ) and metastable ( ) states.
For a two-level system with optical beams, the rate equations are given by:
where is the Planck constant, is the metastable lifetime parameter, is the frequency, and is the power of the th beam. The absorption and emission cross-section of the th beam are and , respectively, and is the local erbium ion density. The normalized optical intensity is defined as
, where is light intensity distribution of the th beam.
(1)a
(1)b
Er+3 Er-3–
4 11 2⁄N3
n1 n2
k
dn1dt
--------–dn2dt
--------σa vk( )
hvk---------------- ik r φ,( ) Pk z( ) n1 r φ z, ,( )
σe vk( )hvk
---------------- ik r φ,( ) Pk z( ) n2 r φ z, ,( ) 1τ--- n2 r φ z, ,( )⋅–⋅⋅⋅
k∑–⋅⋅⋅
k∑= =
n1 r φ z, ,( ) n2 r φ z, ,( ) nt r φ z, ,( )=+
h τ vkPk k
k σa vk( ) σe vk( ) ntik r φ,( )
ik r φ,( ) Ik r φ z, ,( ) Pk z( )⁄= Ik r φ z, ,( )k
321
ERBIUM DOPED FIBER
The propagation equations describe the propagation of the beams through the doped fiber, and are given by:
where each beam propagates in the forward ( ) or backward ( ) direction, and means the spontaneous emission contribution from the local metastable population . , where the normalized number of modes m is normally 2, and is the noise bandwidth.
Setting the time derivative in Equation 1a to zero and using Equation 1b, the problem is reduced to the steady-state case and the metastable population is defined as:
(2)
(3)
dPkdt
--------- uk σe vk( ) Pk z( ) P0k+( ) n2 r φ z, ,( ) ik r φ,( ) r r φ uk σa vk( ) Pk z( ) .⋅⋅–d⋅d⋅ ⋅⋅
0
∞
∫0
2π
∫⋅ ⋅⋅=
. n1 r φ z, ,( ) ik r φ,( ) r r φd⋅d⋅ ⋅⋅
0
∞
∫0
2π
∫
uk 1= uk 1–=P0k
n2 P0k m h vk ∆vk⋅ ⋅ ⋅=∆vk
n2 r φ z, ,( ) nt
σa vk( ) τ⋅hvk
----------------------- ik r φ,( ) Pk z( )⋅⋅
k 1=
n
∑
σa vk( ) σe vk( )+( ) τ⋅hvk
-------------------------------------------------- ik r φ,( ) Pk z( ) 1+⋅⋅
k 1=
n
∑
--------------------------------------------------------------------------------------------------------------⋅=
322
ERBIUM DOPED FIBER
With the specified boundary conditions at and , Equation 2 and Equation 3 can be integrated over space and frequency.
Figure 1 Example of absorption and emission cross-sections
It is important realize to that the transverse shape of the optical mode and its overlap with the erbium ion distribution profile are very important. It can be parameterized by a factor known as overlap integral factor.
Considering a steady-state case, and substituting Equation 1b in Equation 1a, the rate equation becomes:
Integrating Equation 4 over space:
(4)
z 0= z L=
σa vk( )hvk
---------------- ik r φ,( ) Pk z( ) nt r φ z, ,( )σa vk( )
hvk---------------- ik r φ,( ) Pk z( ) n2 r φ z, ,( ) 1
τ--- n2 r φ z, ,( ) –⋅–⋅⋅⋅
k∑–⋅⋅⋅
k∑
σe vk( )
hvk---------------- ik r φ,( ) Pk z( ) n2 r φ z, ,( ) 1
τ--- n2 r φ z, ,( ) ⋅–⋅⋅⋅
k∑–
1τ--- n2 r φ,( ) π beff
2 σa vk( )hvk
---------------- Pk z( ) nt
ik r φ,( ) nt r φ,( ) r r φd⋅d⋅ ⋅⋅
0
∞
∫0
2π
∫
nt
----------------------------------------------------------------------------- σa vk( )
hvk---------------- Pk z( ) n2 .⋅⋅
k 1=
n
∑–⋅ ⋅⋅k∑=⋅ ⋅⋅
.
ik r φ,( ) n2 r φ,( ) r r φd⋅d⋅ ⋅⋅
0
∞
∫0
2π
∫
n2
------------------------------------------------------------------------------σe vk( )
hvk---------------- Pk z( ) n2 .
ik r φ,( ) n2 r φ,( ) r r φd⋅d⋅ ⋅⋅
0
∞
∫0
2π
∫
n2
------------------------------------------------------------------------------⋅⋅
k 1=
n
∑–
323
ERBIUM DOPED FIBER
where is considered the average density, and is given by:
and is the equivalent radius of the doped region:
when the ion density population is uniform, the effective radius is equal to the doped radius, .
For an effective doped radius , the effective cross-sectional area is .
Then, the overlap integral or confinement factor for the level can be defined as:
If the erbium ions are well confined to the center of the optical modes, then and are nearly equal, and can be replaced with the single constant .
Therefore, using the definition of overlap integral, the average population density for the level 2 is given by:
(5)
(6)
(7)
ni
ni z( )
ni r φ,( ) r r φd⋅d⋅⋅
0
∞
∫0
2π
∫
π beff2⋅
------------------------------------------------------=
beff
beff 2nt r( )nt 0( )------------ r rd⋅ ⋅
0
π
∫
12---
==
b
beffAeff π beff
2⋅=
ith
Γkj z( )
ik r φ,( ) ni r φ,( ) r r φd⋅d⋅ ⋅⋅
0
∞
∫0
2π
∫
ni
----------------------------------------------------------------------------=
Γk 1,Γk 2, Γk
n2 z( )
σa vk( )hvk
---------------- Pk z( ) nt Γk⋅ ⋅⋅
k 1=
n
∑
1τ--- Aeff
σa vk( ) σe vk( )+hvk
-------------------------------------- Pk z( ) Γk⋅⋅
k 1=
n
∑–⋅
----------------------------------------------------------------------------------------------------=
324
ERBIUM DOPED FIBER
and the propagation equation becomes:
Basically, Equation 7 and Equation 8 are the equations solved in the homogeneous case. Slight modifications are made to these equations in order to include other effects.
(8)dPkdz
--------- σe vk( ) σa vk( )+( ) Pk z( ) n2 Γk σa vk( ) Pk z( ) nt Γk P0k σe vk( ) n2 Γk⋅ ⋅⋅+⋅ ⋅⋅–⋅ ⋅⋅=
325
ERBIUM DOPED FIBER
Giles-Desurvire Propagation and Rate EquationsA simpler method of fiber characterization can be done by writing the amplifier equations in terms of absorption coefficient ( ), gain coefficient ( ), and a fiber saturation parameter ( ). These parameters can be obtained by conventional fiber measurement techniques [1].
The saturation parameter can be defined theoretically as:
and the absorption and gain coefficients are expressed in terms of distributions of the ions and optical modes:
For a uniform ion distribution the absorption and gain coefficients can be simplified as:
Giles and Desurvire in [1] rewrote the propagation Equation 8 in terms of saturation parameter, and absorption and emission coefficients:
where is the background loss.
(9)
Er+3 αk gkζ
ζ
ζ π beff2 nt τ⁄⋅ ⋅=
αk λk( ) σa λk( ) ik r φ,( ) nt r φ z, ,( ) r r φd⋅d⋅ ⋅⋅
0
∞
∫0
2π
∫⋅=
gk λk( ) σe λk( ) ik r φ,( ) nt r φ z, ,( ) r r φd⋅d⋅ ⋅⋅
0
∞
∫0
2π
∫⋅=
αk λk( ) Γ λk( ) nt σa λk( )⋅ ⋅=
gk λk( ) Γ λk( ) nt σe λk( )⋅ ⋅=
dPk z( )dz
---------------- uk Pk z( ) gk vk( ) αk vk( )+( )n2
nt
----- αk vk( )– lk–⋅
uk P⋅ 0k gk vk( )n2
nt
-----⋅⋅+⋅⋅=
lk
326
ERBIUM DOPED FIBER
In the same way, the steady-state solution of rate Equation 7 was rewritten as:
Note: The equation for sums over all forward and backward beams, including ASE.
Equation 9 and Equation 10 are referenced further as a Giles model. These equations are solved in the homogeneous line broadening case.
The Giles model provides a full spectral solution. The propagation Equation 9 is integrated back and forth along the fiber, in an iterative numerical process, until the solution converges, or the maximum number of iterations ( ) is reached.
The propagation equation solved by the Giles model can be slightly different from Equation 9, depending on which effects the user has considered in the simulation, such as ESA and Rayleigh scattering. Equation 10 can be different depending on whether the user takes into account the interactions.
Overlap IntegralsThe value of the overlap integral can be calculated using Equation 6. The transverse optical modes distributions are described by their normalized optical intensity.
For a single-mode fiber, the optical mode can be approximated by the mode distribution:
(10)
(11)
n2
nt
----- z( )
Pk z( ) αkvk⋅h vk ζ⋅ ⋅
-----------------------------k 1=
n
∑
1Pk z( ) αk vk( ) gk vk( )+( )⋅
hvk------------------------------------------------------------
k 1=
n
∑+
--------------------------------------------------------------------------------=
n2 z( )
Nmax
Er+3 Er+3–
LP01
i r φ,( )
1π---
vJ0 ur a⁄( )aVJ1 u( )
--------------------------2r a<
1π---
uK0 vr a⁄( )aVK1 v( )
---------------------------2r a≥
=
327
ERBIUM DOPED FIBER
where is the fiber core radius, the fiber number is , and are the eigenvalues found by matching
the solutions at , is the Bessel function of the first kind of order 0, is the Bessel function of the first kind of order 1, is the modified Bessel function of the second kind of order 0, and is the modified Bessel function of the second kind of order 1.
The mode distribution can also be approximated with a Gaussian function:
where the Gaussian mode radius, , has been given by various authors as:
The overlap integrals depend on:• the energy level occupied by the ions, because the distribution is different for
each level• the power, because the ion dopant distribution is power dependent• the wavelength, because the optical mode profile is wavelength dependent
In principle, the overlap integrals are also functions of , due to variations in doping level along the fiber, and mode coupling (if more than one mode is supported).
(12)
(13)
(14)
(15)
(16)
a VV 2 π a ncore
2 nclad2–( ) λ⁄⋅ ⋅ ⋅= u v
r a= J0 J1K0
K1
LP01
i r φ,( ) 2πw2---------- 2 r2⋅
w2------------–
exp=
wGauss
wGauss a 0.65 1.619V 1.5------------- 2.879
V 6-------------+ +
Marcuse=
wGauss a 0.616 1.66V 1.5---------- 0.987
V 6-------------+ +
Whitley=
wGauss a 0.759 1.289V 1.5------------- 1.041
V 6-------------+ +
Desurvire=
wGauss a 0.761 1.237V 1.5------------- 1.429
V 6-------------+ +
Myslinski=
z
328
ERBIUM DOPED FIBER
For a fundamental mode approximated by a Gaussian profile and a uniformly doped fiber with doped radius , the overlap of the mode with the total ion profile is given by:
In the low-power limit, all excited-state overlap integrals with the Gaussian approximation reduce to:
where Equation 18 is an approximated form of the upper levels (1, 2, 3 and 4).
For the mode approximation with a uniformly doped fiber and fiber doped radius , the overlap with the total ion distribution is given by:
Typically, the fiber doped radius is less than or equal to the core radius ( ), and for , the integrals also have weak power dependence [1]. For most cases, therefore, it is reasonable to assume that overlap integrals are power independent and are equal to for ions in all the energy levels.
(17)
(18)
(19)
b nt r φ z, ,( )
Γt 1 e
2b2–w2
-----------
–=
Γ1 2 3 4, , , P 0→( ) bw----
2
1 e
4b2
w2--------–
–
1 e
2b2
w– 2---------
–
--------------------≈
LP01b
Γtub
VaJ1 u( )-------------------
2J0
2 ub a⁄( ) J12 ub a⁄( )+[ ]=
b w 0.8≤⁄b w 0.8≤⁄
Γt
329
ERBIUM DOPED FIBER
Additional Effects
Background LossBackground loss in a fiber amplifier or laser is usually negligible compared to absorption coefficients and discrete losses. However, the background loss may be significant for lightly-doped fibers, for losses at the signal wavelength of a four level ion, for wavelengths far from absorption maxima, and for wavelengths beyond the low-loss region of the host glass. The actual fiber loss is composed of the Rayleigh backscattering loss, and losses from impurities.
Here, the excess loss, , is assumed to be wavelength-independent, and is given by:
where is the total loss at 1310nm and is the loss due the Rayleigh scattering effect at 1310nm.
The user specifies the total loss at 1310 nm ( ), from which the component calculates the excess loss. The loss at any other wavelength then adds an additional term to the propagation equations as:
The user has the possibility of considering the excess loss as wavelength dependent. In this case, a file has to be provided that contains the total loss characteristics for the band of interest. Then, the wavelength dependent excess loss will be defined as:
Note: The effects of background loss are only considered during the Giles algorithm calculation.
Rayleigh ScatteringRayleigh Backscattering is incorporated in the model by coupling each forward and backward traveling signal at a wavelength to a backward-traveling and forward-traveling signal at the same wavelength:
(20)
(21)
(22)
αEL
αEL l1310nm αRS 1310nm( )–=
l1310nm αRS 1310nm( )
a1310nm
dPk+
dz--------- σe vk( ) σa vk( )+( ) Pk
+ z( ) n2 Γk σa vk( ) Pk+ z( ) nt Γk σe vk( ) P0k n2 Γk αRS vk( ) αEL+( ) Pk
+⋅–⋅ ⋅ ⋅+⋅ ⋅⋅–⋅ ⋅⋅=
αEL vk( ) l vk( ) αRS vk( )–=
Pk+
Pk_
Prefk_
Prefk+
dPk+
dz--------- σe vk( ) σa vk( )+( ) Pk
+ z( ) n2 Γk σa vk( ) Pk+ z( ) nt Γk σe vk( ) P0k n2 Γk αRS vk( ) Pk
+⋅–⋅ ⋅ ⋅+⋅ ⋅⋅–⋅ ⋅⋅=
dPrefk_
dz---------------– σe vk( ) σa vk( )+( ) Prefk
_z( ) n2 Γk σa vk( ) Prefk
_z( ) nt Γk C αRS vk( ) Pk
+⋅⋅+⋅ ⋅⋅–⋅ ⋅⋅=
330
ERBIUM DOPED FIBER
where is the background loss caused by Rayleigh scattering, and is the backscattering capture fraction. The component has the option of loading the capture fraction from a file (wavelength dependent) or generating a theoretical capture fraction using the definition given by [2]:
Where is the fiber numerical aperture, is the refractive index of the fiber and depends on the refractive index profile. For single mode fibers a typical value for is 4.55.
The Rayleigh background loss in a fiber is given by [3]:
The first term (0.63 dB/km) is the scattering loss for pure silica fiber at 1000 nm, and the second term accounts for the material and geometrical dependence. The Raleigh constant parameter, , generally is equal to about 70 dB/km for Ge co-doped fiber, and about 150 dB/km for Aluminum co-doped fiber. The index difference can be derived from the numerical aperture, , as:
where it is assumed that the fiber refractive index is approximately 1.45.
In accordance with Equation 20 - Equation 23, the equation that gives the density population in the metastable level, Equation 10, was modified to take into account the reflected powers in the calculation for the steady state case.
(23)
(24)
(25)
(26)
dPk_
dz---------– σe vk( ) σa vk( )+( ) Pk
_z( ) n2 Γk σa vk( ) Pk
_z( ) nt Γk σe vk( ) P0k n2 Γk αRS vk( ) Pk
_⋅–⋅ ⋅ ⋅+⋅ ⋅⋅–⋅ ⋅⋅=
dPrefk+
dz--------------- σe vk( ) σa vk( )+( ) Prefk
+ z( ) n2 Γk σa vk( ) Prefk+ z( ) nt Γk C αRS vk( ) Pk
_⋅⋅+⋅ ⋅⋅–⋅ ⋅⋅=
αRS vk( ) C
C NAno--------
2 1mn------⋅=
NA nomnmn
αRS vk( )
αRS vk( ) 0.63 KR∆n+( ) 1000nmλ nm( )
-------------------- 4
=
KR∆n
NA
∆n NA2
2∗1.45----------------=
n2
331
ERBIUM DOPED FIBER
Double Rayleigh scatteringDouble Rayleigh scattering occurs when a portion of the backscattered signal is reflected again and it is recoupled to the forward direction. It is a problem because it creates paths of different lengths for signals to travel. It is considered in the model changing Equation 22 and Equation 24 by:
The buildup of backscattered light is always included in the Giles calculation, but it can be neglected by setting the capture fraction to zero or not including the Rayleigh scattering in the simulation. The degradation of EDFA performance from internal backscattering has been reported in [3] and [4].
Er3+ - Er3+ Interaction EffectsThe Erbium Doped Fiber Amplifier component allows the user to consider interactions between neighboring ions. The exchange of energy between neighboring ions is also known as "Concentration Quenching". The most important ion-ion interaction for EDFA is the stepwise up-conversion shown in Figure 2. Initially, there are two ions at the metastable level. Energy is transferred from the donor ion, which falls back to the ground level, and the acceptor ion, which returns to the metastable level by phonon transitions, after being excited to one of the upper levels. The net result is that two excited ions become one excited ion so that the quantum efficiency is reduced. Therefore, it has a negative impact on amplifiers.
Figure 2 Stepwise up-conversion
Stepwise up-conversion becomes stronger as the distance between the doped ions decreases, i.e. as the concentration increases. Depending on the fiber material, it
(27)
(28)
dPrefk_
dz---------------– σe vk( ) σa vk( )+( ) Prefk
_z( ) n2 Γk σa vk( ) Prefk
_z( ) nt Γk C αRS vk( ) Pk
+ Prefk++( )⋅⋅+⋅ ⋅⋅–⋅ ⋅⋅=
dPrefk+
dz--------------- σe vk( ) σa vk( )+( ) Prefk
+ z( ) n2 Γk σa vk( ) Prefk+ z( ) nt Γk C αRS vk( ) Pk
_Prefk
_+( )⋅⋅+⋅ ⋅⋅–⋅ ⋅⋅=
332
ERBIUM DOPED FIBER
becomes significant when the concentration is greater than about 1000 ppm. There are three models to account for stepwise up-conversion.
Homogeneous Upconversion
Considering that the ions are independent, i. e., if one ion is excited to the state this would not prevent a neighboring ion from also being excited to the state.
The upconversion fluorescence intensity can be calculated redefining Equation 1 as [5]:
Where is the branching ration between the - transition (980nm) and the - nonradiative transition; is the two-particle upconversion coefficient ( is concentration independent). In [7], the value found for the and
parameters were 1e4 and 1e-22 ( ), respectively. Considering the steady-state case, the rate equation (29) becomes:
Inhomogeneous Pair Induced Quenching
In this model [6] [7], erbium ions exist as two distinct species: single ions (no interaction with others) and clustered ions. The ions residing in each cluster can occupy only two energy levels: State 1 - all the ions in the ground state or State 2 - only one ion per cluster in the excited state. When more than one ion is excited in the cluster, the excitation energy is rapidly transferred from one ion to another, and the upconversion continues until all but one ion in the cluster occupies the metastable excited-state.
Note: It is assumed that all the clusters are of the same size and contain the same number of ions, .
For the total concentration of erbium ions, , the concentration of clustered ions is introduced as , where is the relative number of clusters and
is the percentage of ions in clusters. The concentration of single ions is .
(29)
(30)
I13 2⁄I13 2⁄
dn2 r φ z t, , ,( )dt
--------------------------------σa vk( )
hvk---------------- ik Pk z( ) n1 r φ z, ,( )
σe vk( )hvk
---------------- ik Pk z( ) n2 r φ z, ,( ) _⋅⋅ ⋅–⋅⋅ ⋅k∑=
n2 r φ z t, , ,( )τ
-----------------------------– 1 1 m⁄+( ) Ue n2 r φ z t, , ,( )⋅ ⋅–
m I11 2⁄ I15 2⁄I11 2⁄ I13 2⁄ Uc
Uc mUc m3 s⁄
n2 r φ z t, , ,( )
σa vk( )hvk
---------------- ik Pk z( ) nt r φ z, ,( )⋅⋅ ⋅k∑
σa vk( ) σe vk( )+hvk
-------------------------------------- ik Pk z( ) 1 1 m⁄+( )+⋅ ⋅k∑ Uc n2 r φ z t, , ,( )⋅ 1
τ---+⋅
---------------------------------------------------------------------------------------------------------------------------------------------------------------=
mk
ntnc mk k nt⋅ ⋅= k
mk k⋅ns l mk k⋅–( ) nt⋅=
333
ERBIUM DOPED FIBER
For single ions the rate equations is:
For the steady-state case:
For clustered ions, the rate equation is:
Then, the ion population in the metastable level is:
(31)
(32)
(33)
(34)
(35)
dn2Sdt
-----------σa vk( )
hvk---------------- ik r φ,( ) Pk z( ) n1S r φ z, ,( )
σe vk( )hvk
----------------k∑ ik r φ,( ) Pk z( ) n2S r φ z, ,( ) 1
τ--- n2S r φ z, ,( )⋅–⋅⋅ ⋅–⋅⋅ ⋅
k∑=
n1S n2S+ 1 mk k⋅( ) nt⋅–=
n2S r φ z, ,( )
σa vk( )hvk
---------------- ik r φ,( ) Pk z( ) 1 mk k⋅–( ) nt⋅ ⋅⋅ ⋅k∑
σa vk( ) σe vk( )+hvk
-------------------------------------- ik r φ,( ) Pk z( )⋅ ⋅k∑ 1
τ---+
---------------------------------------------------------------------------------------------------------=
dn2Cdt
------------σa vk( )
hvk---------------- ik r φ,( ) Pk z( ) mk k nt mk n2C⋅–⋅ ⋅( )
σe vk( )hvk
----------------k∑ ik r φ,( ) Pk z( ) n2C r φ z, ,( ) 1
τ--- n2C r φ z, ,( )⋅–⋅⋅ ⋅–⋅⋅ ⋅
k∑=
n2C r φ z, ,( )
σa vk( )hvk
---------------- ik r φ,( ) Pk z( ) mk k⋅ nt⋅ ⋅⋅ ⋅k∑
σe vk( )hvk
---------------- ik r φ,( ) Pk z( )⋅ ⋅k∑
σa vk( )hvk
---------------- ik r φ,( ) Pk z( ) mk k⋅ nt⋅ ⋅⋅ ⋅k∑+
-----------------------------------------------------------------------------------------------------------------------------------------------------------------=
+
σa vk( )hvk
---------------- ik r φ,( ) Pk z( ) 1 mk– k⋅( ) nt⋅ ⋅ ⋅ ⋅k∑
σe vk( )hvk
---------------- ik r φ,( ) Pk z( )⋅ ⋅k∑
σa vk( )hvk
---------------- ik r φ,( ) Pk z( ) mk⋅ 1τ---+⋅ ⋅
k∑+
----------------------------------------------------------------------------------------------------------------------------------------------------------
n2 r φ z t, , ,( ) n2S r φ z t, , ,( ) n2C r φ z t, , ,( )+
σa vk( )hvk
---------------- ik r φ,( ) Pk z( ) 1 mk– k⋅( ) nt⋅ ⋅ ⋅ ⋅k∑
σa vk( ) σe vk( )+hvk
-------------------------------------- ik r φ,( ) Pk z( ) 1τ---+⋅ ⋅
k∑
------------------------------------------------------------------------------------------------------ += =
334
ERBIUM DOPED FIBER
Homogeneous Upconversion and Inhomogeneous Pair Induced Quenching
This case is a combination of the cooperative upconversion and the pair induced upconversion. The combined model is similar to the inhomogeneous model, except that the single ions experience concentration quenching at the same rate as for the homogeneous model. Therefore, the population inversion in the steady-state becomes:
The first term on the right-hand side is for single ions and the second term is for clustered ions.
Temperature dependenceThe temperature dependence exhibited by an erbium doped fiber is mainly attributed to the variation in the occupation probability density of each manifold with temperature. In an EDFA, the gain is temperature dependent through the temperature dependence of the gain and absorption coefficients. Therefore, to represent the temperature dependence of an EDFA, the model needs properly represent the temperature dependence of and (or and ).
The temperature model in the erbium doped fiber amplifier component is based on physical intuition and use fitting parameters to generate modeling parameters at any temperature. It is assumed that the temperature dependence of an EDF is due to the variation in the occupation probability density. Using the Boltzmann's law for the level occupation and the definition that the sum of all occupation probabilities for all states of the manifold must equal unit, integral expressions for and were derived [8]. After a series of approximations, the following equations [8], outline an effective procedure for calculation of the temperature dependence of absorption and emission coefficients:
(36)
(37)
N2 r φ z t, , ,( ) N2S r φ z t, , ,( ) Nn2C r φ z t, , ,( )+=
N2 r φ z t, , ,( )
σa vk( )hvk
----------------k∑ ik Pk z( ) 1 mk– k⋅( ) n⋅ t r φ z, ,( )⋅⋅ ⋅
σa vk( ) σe vk( )+hvk
-------------------------------------- ik r φ,( ) Pk z( ) 1τ---+⋅ ⋅
k∑
------------------------------------------------------------------------------------------------------------ +=
+
σa vk( )hvk
----------------k∑ ik r φ,( ) Pk z( ) mk k⋅ n⋅ t⋅⋅ ⋅
σa vk( )hvk
---------------- ik r φ,( ) Pk z( )σa vk( )
hvk----------------
k∑ ik r φ,( ) Pk z( ) mk
1τ---+⋅ ⋅ ⋅+⋅ ⋅
k∑-----------------------------------------------------------------------------------------------------------------------------------------------------------
g λ( ) α λ( ) σe λ( ) σa λ( )
g λ( ) α λ( )
α λ T,( ) α λ ∞,( ) e
βa λ( )KT
--------------
⋅=
335
ERBIUM DOPED FIBER
where is the Boltzmann's constant, and is the temperature in degrees Kelvin. The fitting parameters and are both temperature independent and can be interpreted as the absorption and gain at "infinite" temperature when all energy levels of each manifolds are equally occupied, according with to Boltzmann statistics. However, a more appropriate interpretation of and is that they represent the absorption and gain coefficient when all levels of the relevant manifolds are uniformly occupied. The parameters and are expected to capture the thermal occupation probability of the initial energy level for the transition at a given wavelength.
In order to calculate functions , , , and , the component requires two sets of measurement data for and at different temperatures. One set of measured and for "infinite" temperature is provided by the component. Another set of measured data for and (or
and ) at a different temperature has to be provided by the user. With these two sets of data for and at different temperatures, the component is able to calculate the functions and . The values of and , at an arbitrary temperature defined by the user, will then be generated by the component in accordance to Equation 37 and Equation 38.
Note that the set of measured data for the gain and absorption coefficients at "infinite" temperature, and , provided by the component, are expected to represent accurately the dependence of EDF spectra for fibers with similar compositions only. However, in [9] is reported that only minor differences for a variety of silica-based, aluminum-codoped EDFs with a wide range of germanium and aluminum levels were observed [9][8]. More information about how temperature dependence can be simulated can be found in the tutorials.
(38)g λ T,( ) g λ ∞,( ) e
βe λ( )KT
-------------
⋅=
K Tα λ ∞,( ) g λ ∞,( )
α λ ∞,( ) g λ ∞,( )
βa λ( ) βe λ( )
α λ ∞,( ) g λ ∞,( ) βa λ( ) βe λ( )g λ( ) α λ( )
g λ( ) α λ( )g λ( ) α λ( )
σe λ( ) σa λ( )g λ( ) α λ( )
βa λ( ) βe λ( ) g λ( ) α λ( )
α λ ∞,( ) g λ ∞,( )
336
ERBIUM DOPED FIBER
Figure 3 Absorption and gain coefficients at infinite "temperature"
Excited-State Absorption Effect (ESA)The excited-state absorption can affect amplifiers in two ways; through parasitic absorption of pump photons, or signal photons. With pump ESA, the pump light at frequency is not absorbed from the ground level (1) of the rare earth ion, but from an excited level (2), due to the existence of a third level (3) whose energy gap
with level (2) happens to closely match the pump photon energy . This happens only if the ESA cross section overlaps with the ground state
absorption (pump absorption cross-section). In the case of signal ESA, the signal light of energy is absorbed from the metastable level (2) to a level (3), due to the same energy gap matching relation . This indicates that both pump and signal ESA result in an excess loss for the pump or the signal.
The ESA effect has been observed to occur in Er-doped fibers in several wavelength bands, but our main interest is in the 980 nm pumping band and in 1500-1620 nm signal band. In the first band, the pump ESA initiated from the metastable level
, is nonexistent near 980 nm [10]. However, pump ESA can be initiated from the energy short-lived level; where the terminal level is . Nevertheless, since the level population is rapidly damped by nonradiative decay, ESA from this level can occur only at high pump power levels [10]. Therefore, the ESA effect in the second band can be more serious in the degradation of amplifier performance, mainly in L-band amplifiers (see lesson about ESA in the tutorials) and it is taken into consideration in the Erbium doped fiber modeling.
α λ ∞,( ) g λ ∞,( )
vp
∆E E3 E2–=h vp⋅
h vs⋅∆E E3 E2 hvs≈( )–=
I413 2⁄
I411 2⁄ F4
7 2⁄
337
ERBIUM DOPED FIBER
To include the ESA effect in our two-level model, Equation 8 was modified to introduce the ESA cross-section :
Additional information about the modeling of the ESA effect can be found in [10].
Figure 4 ESA Cross-sections
Inhomogeneous BroadeningThe previous model considered only homogeneous broadening, which is satisfactory to predict the gain and noise performance of a majority of erbium doped fiber amplifiers. However, to accurately describe the saturation behavior of the amplifier and the effect of spectral-hole burning, inhomogeneous broadening has to be considered. The main assumption in the modeling of this effect is that the variation of the stark splitting from site to site due to the change of the ligand fields leads to randomization of central frequencies of the transition lines; the linewidths, the absorption and emission cross-sections, and the fluorescence lifetime do not change.
The density distribution for inhomogeneous broadening of central frequencies of the transition lines is given for a Gaussian function:
where is the inhomogeneous broadening spectral bandwidth and is the inhomogeneous line width.
(39)
(40)
σESA
dPkdz
--------- σe vk( ) σESA vk( ) σa vk( )+ +( ) Pk z( ) n2 Γk σa vk( ) Pk z( ) nt Γk P0k σa vk( ) n2 Γk⋅ ⋅⋅+⋅ ⋅⋅–⋅ ⋅⋅=
f ω( ) 4 1n 2( )⋅
π ∆ωi2⋅
---------------------- 4 1n 2( ) ω∆ωi---------
2⋅⋅–exp⋅=
∆ωi 2 π c ∆λinh λ2⁄⋅ ⋅ ⋅=∆λinh
338
ERBIUM DOPED FIBER
The observed (measured) inhomogeneous absorption and emission cross-sections, and , are the convolutions of the homogeneous absorption and
emission cross-sections, and , with the normalized inhomogeneous broadening distribution , and can be expressed by:
The description of the inhomogeneous broadening is based on the following form of the propagation equation suggested in [10]:
To include spontaneous emission, a noise source term is introduced in Equation 42.
In order to determine the homogeneous absorption and emission cross-section used in the propagation equation, a deconvolution procedure to resolve Equation 41 is applied.
In Homogeneous cross-sections, there is a description of the procedures used in the component to generate the homogeneous cross-sections.
Homogeneous cross-sectionsHomogeneous cross-sections can be derived from the experimental (inhomogeneous) cross-sections through an inversion Fourier transformation in Equation 41, (a) and (b). However, a direct deconvolution of Equation 41 has a unique
(41)a
(41)b
(42)
σaI v( ) σe
I v( )σa
H v( ) σeH v( )
f v( )
σeI v( ) f v v'–( ) σe
H v( ) v'd⋅⋅
∞–
∞
∫=
σaI v( ) f v v'–( ) σa
H v( ) v'd⋅⋅
∞–
∞
∫=
dP ωk( )dz
------------------ ρ Γk P ωk( ) ωd f ω( ) σaH ωk ω–( )
σeH ωk ω–( )
σaH ωk ω–( )
----------------------------
Pmh v Am⋅ ⋅---------------------σa
H ωm ω–( ) τ⋅m∑
1Pm
h v Am⋅ ⋅--------------------- σa
H ωm ω–( ) σeH ωm ω–( )+( ) τ⋅ ⋅
m∑+
-------------------------------------------------------------------------------------------------------------------------- _⋅ ⋅ ⋅ ⋅
∞–
∞
∫⋅ ⋅ ⋅=
ρ– Γk P ωk( ) ωd f ω( ) σaH ωk ω–( )
1Pm
h v Am⋅ ⋅---------------------σe
H ωm ω–( ) τ⋅m∑+
1Pm
h v Am⋅ ⋅--------------------- σa
H ωm ω–( ) σeH ωm ω–( )+( ) τ⋅ ⋅
m∑+
--------------------------------------------------------------------------------------------------------------------------⋅ ⋅ ⋅
∞–
∞
∫⋅ ⋅ ⋅
339
ERBIUM DOPED FIBER
solution only when the functions , and their evanescent tails are well defined analytically. This is not the case with experimental line shapes.
Nevertheless, there is a possibility of fitting the line shapes with a superposition of Gaussians functions such as
where , , and are the Gaussian line shapes parameters for the fitting. The parameter is the number of Gaussians.
Using this superposition of Gaussian functions; the deconvolution of Equation 41 can be calculated analytically. With the Gaussians functions line shapes parameters found in the numerical fitting, the homogeneous emission and absorption cross-sections can calculated in accordance with the inhomogeneous line width ( ) provided by the user using the definition [10]:
The Erbium-doped fiber component is able to do the fitting of the cross-sections provided by the user using the number of Gaussian functions ( ) determined by the Number of Gaussians parameter.
(43)
σaI λ( ) σe
I λ( )
I λ( ) ai 4 1n 2( )λ λi–( )2
∆λi2
---------------------⋅
⋅–
exp⋅
i
nG
∑=
ai λi ∆λinG
∆λinh
σa e,H λ( ) ai
a e, ∆λi
∆λi2 ∆λinh
2–--------------------------------- 4 1n 2( )
λ λi–( )2
∆λi2
---------------------⋅⋅–
exp⋅ ⋅
i
nG
∑=
nG
340
ERBIUM DOPED FIBER
Figure 5 Homogeneous (a) absorption and (b) emission cross-sections
341
ERBIUM DOPED FIBER
Approximations of Giles-Desurvire rate and propagation equations
Saleh modelThe Saleh model is an approximation of the propagation and rate equations for a two-level system in the steady-state case. This allows for an analytical solution of the equations by means of a transcendental equation, instead of N coupled differential equations [11]. This model could be successfully applied to the study of the small signal gain and saturated gain, optimum fiber length, and saturated power. The theory uses some simplifying assumptions. First, although spontaneous decay is accounted for, amplified spontaneous emission (ASE) is neglected. This is valid for fiber lasers above threshold and for fiber amplifiers when the input signal power is significantly above the equivalent ASE noise input power, as discussed in [11]. Second, it is assumed that there is no excited state absorption (ESA) at any of the pump or signal wavelengths. Third, it is assumed that field and ion distributions are independent of fiber position and power levels. These assumptions are satisfactory in the case of typical doped fibers that have a doped fiber radius less than the core fiber radius. Background loss is also neglected, as with three level ions such as erbium, the absorption by the rare earth ions is typically much greater than other losses.
Using the assumptions, Equation 8 could be integrated analytically from 0 to L [11]. The result is given by the following expression for the output photon flux :
where is the output photon flux for kth signal,
is the input photon flux for kth signal
is the total output photon flux
is the total input photon flux.
Summing Equation 44 over all k signals yields:
which is a implicit equation for the total output photon flux . Note that is completely determined, given the input flux, by the following four fiber parameters;
(fiber length). Solving Equation 45 for allows for the determination of the output fluxes of each individual signal through Equation 44.
Since the Saleh model neglects ASE, it becomes less accurate for cases in which ASE becomes significant, e.g. for low input powers (less than about -20 dBm,
(44)
(45)
Qk
Qkout Qk
in αkL–αk gk+( )
ζ---------------------- Qtot
in Qtotout–( )⋅+
exp=
Qkout Pk
out hvk( )⁄=
Qkin Pk
in hvk( )⁄=
Qtotout Qk
out
k∑=
Qtotin Qk
in
k∑=
Qtotout Qk
in αkL–αk gk+( )
ζ---------------------- Qtot
in Qtotout–( )⋅+
expk∑=
Qtotout Qtot
out
αk gk ζ and L, , , Qtotout
342
ERBIUM DOPED FIBER
depending on the gain and signal wavelengths). In these cases, the accuracy is improved by using an equivalent ASE input, which inputs effective input beams at both ends of the fiber with equivalent input powers:
where for the forward ASE, and for the backward ASE. is the spectral width of the noise beams. The spontaneous emission factor is given by:
where = is the ratio of cross-sections.
The Saleh model has the advantage that longitudinal integrations are not required, so it is much faster to solve. Note that unlike literature that typically uses one or two equivalent ASE beams centered at the spectral peaks near 1532 nm and 1555 nm, this component has an equivalent ASE beam for each of the bins defined in the Noise tab.
Jopson modelThe Saleh model only estimates the pump and signal powers, and equivalent ASE at the doped fiber output. These values are used to estimate the population inversion at the doped fiber ends. However, no information is obtained about the values along the fiber. Jopson and Saleh extended the Saleh model to obtain estimates of the powers and inversion levels along the fiber [12]. The photon flux in distance can be determined by:
where is defined by:
and it is computed from the transcendental equation:
In order to obtain the pump, signals, and equivalent ASE powers and population inversion along the fiber, starting from either end of the fiber, this equation can be solved for in every user-defined step.
(46)
(47)
(48)
(49)
(50)
hvkPkin 2nsp v zin,( )∆v hvk=
zin 0= zin L= ∆v
nsp v zin,( )n2 zin( )
n2 zin( ) n1 zin( )–---------------------------------------- ε v( )⋅=
ε v( ) σa σe⁄
Qk z
Qk z( ) Qk 0( ) ukαkz– ukαk gk+( )
ζ---------------------- Q 0( ) Q z( )–( )⋅+
exp=
Q z( )
Q z( ) ukQk z( )k∑=
Q z( ) ukQk z( )∑ eukαka–
euk Q 0( ) Q z( )–( ) αk gk+( ) ζ⁄⋅[ ]=
343
ERBIUM DOPED FIBER
NoiseThe spontaneous-emission noise at wavelength , of a single polarization, emitted in a single direction by a section of amplifier of length is given by:
where can be determined using Equation 50 and Equation 7.
The amplified spontaneous emission noise (ASE) emitted from the output or input end of the amplifier at wavelength can be obtained by multiplying the spontaneous emission from each section of the amplifier by the amplifier gain at from that section to the desired end of the amplifier. The gain is given by:
, where is the gain from the input ( ) to the length
and
, where is the gain from the length to the output .
λkdz
dP gk n2 z( ) ∆v dz⋅⋅⋅=
n2 z( )
λkλk
Gk 0 z,( ) eukαkz–
euk Q 0( ) Q z( )–( ) αk gk+( ) ζ⁄⋅[ ]= Gk 0 z,( )
z 0= z
Gk z L,( ) eukαk L z–( )–
euk Q z( ) Q L( )–( ) αk gk+( ) ζ⁄⋅[ ]= Gk z L,( )
z L
344
ERBIUM DOPED FIBER
Input Parameters DescriptionMost of the input parameters for the component were described in the sections before and they can be easily linked to a particular effect or equation. However, there are some parameters that were not described yet or they are load from files. In this section those parameter are explained,
Main tabThis tab contains the basic parameters of the erbium-doped fiber. All of them are well described in the technical description. However, there is a new parameter (Input data parameter) that gives the user the choice to enter the saturation parameter or to enter the fiber parameters (core radius, doped radius, numerical aperture, and erbium density population).
Cross-sections tabIn this tab the user defines which cross-section file has to be loaded and what characteristics it has. There are two options available to prepare the cross-section file, which is specified in an ASCII file. The first option is to provide directly the cross-section in an input file with three columns. The first column refers to the wavelength (or frequency) in [m], [nm], [Hz] or [THz] units; the File frequency unit parameter defines the unit of this column. The second column gives the absorption cross-section in [m2] units. The third column gives the emission cross-section file in [m2] units. The unit of the second and third column must be in [m2]. As an example, one possible cross-section file format is:
(nm)
975 1.95386E-25 0
976 2.07791E-25 0
977 2.20195E-25 0
978 2.26852E-25 0
979 2.13394E-25 0
980 1.99935E-25 0
981 1.86477E-25 0
982 1.73019E-25 0
983 1.5956E-25 0
:
:
1450 5.88956E-26 1.78862E-26
1451 6.19338E-26 1.87881E-26
1452 6.50958E-26 1.97301E-26
1453 6.83832E-26 2.06921E-26
λλ nm[ ] σa m2[ ] σe m2[ ]
345
ERBIUM DOPED FIBER
The second option is to provide the absorption and gain coefficients (or Giles parameters) as input parameters that are converted to cross-section by internal routines in the software. The file format in this case contains three columns. The first column refers to the wavelength (or frequency) in [m], [nm], [Hz] or [THz] units; the File frequency unit parameter defines the unit of this column. The second column gives the absorption coefficient in [dB/m] units. The third column gives the emission coefficient in [dB/m] units. The unit of the second and third column must be in [dB/m]. An example of this input file is:
When the EDF component load the cross-section file, it detects whether the file contain the Giles parameters ( and ) or cross-section parameters ( and ).
1454 7.17971E-26 2.16742E-26
1455 7.53386E-26 2.26767E-26
1456 7.90081E-26 2.37003E-26
1457 8.2806E-26 2.4746E-26
1458 8.67324E-26 2.58149E-26
1459 9.07873E-26 2.69085E-26
:
(nm)
977 5 0
978 5 0
979 5 0
980 5 0
981 5 0
:
:
1460 1.357 0.29
1461 1.417 0.309
1462 1.464 0.328
1463 1.525 0.35
1464 1.562 0.365
1465 1.562 0.387
1466 1.562 0.411
:
(nm)λλ nm[ ] σa m2[ ] σe m2[ ]
λλ nm[ ] α dB m⁄[ ] g∗ dB m⁄[ ]
g λ( ) α λ( )σa vk( ) σe vk( )
346
ERBIUM DOPED FIBER
The parameter OptiAmplifier format is used to allow the component load cross-sections files originated from the software OptiAmplier. Therefore, if the user wants to load a cross-section under the crs format (format used in the OptAmplifier software), the OptiAmplifier format parameter has to be set TRUE.
Enhanced tabThe enhanced tab defines the parameters related to the background loss, Rayleigh scattering, interaction effects, ESA, and temperature dependence. First, the user can choose the Background loss data type parameter that determines the background loss through the loss at 1310nm (Loss at 1310 nm parameter) or using a wavelength dependent background loss loaded from a file. In the second case, the user has to specify the name of the file contained the losses in the Background loss file name parameter. The format of this file must be similar to the following example:
The user can include the Rayleigh scattering effect or not in the simulations through the parameter Include Rayleigh scattering. If the Include Rayleigh scattering parameter is TRUE, then the user has to specify the value of the Rayleigh constant. The Backscattering capture parameter determines if the component will generate the capture fraction using Equation 25, or the user will provide a file with the capture fraction - in this case the user should specify the file name in the Rayleigh capture file name parameter and the file has to be in the format similar to the below:
In the case of interaction effects, the user has to decide to include or not this effect through the parameter Include ion-ion interaction effects. If the user chooses to include this effect, the parameter Ion-Ion interaction effect has to specify
(nm)
1460 10
1461 10.5
1462 10.2
1463 10.1
1464 10.3
(nm)
1460 -20
1461 -21.5
1462 -21
1463 -20.5
1464 -20.48
Er+3 Er+3–
λλ nm[ ] α dB km⁄[ ]
λλ nm[ ] C dB[ ]
Er+3 Er+3–
347
ERBIUM DOPED FIBER
which interaction effect will be considered in the simulations; Homogeneous upconversion, pair-induced quenching, or a combination of both. When the ion-ion effect is defined, then the parameters necessaries for that effect will be enabled. Upconversion coefficient, ions per cluster, and relative number of clusters are the parameters that have to be specified depending on the effect considered.
The user can include the temperature dependence in EDF model setting the parameter Include temperature dependence to TRUE. After this, the user has to define in which temperature, the cross-section defined in the cross-sections tab, was measured (Cross-section temperature parameter). With these parameters and the cross-section at infinite temperature stored in the component, it is possible to calculate the parameters and from Equation 37 and Equation 38. The other parameter to be defined is the temperature that will be considered in the simulation (Temperature parameter). For more information, refer to the tutorial about temperature dependence.
The ESA effect can be included in the EDF simulation. In this case the user has to set the parameter Include ESA effect to TRUE. After this, the user has to provide the ESA cross-section. Similar to the cross-sections in the cross-section tab, the ESA cross-section can be in the Giles format [ ] or cross-section format [ ]. The difference is the ESA cross-section file must have only two columns: (1) wavelength (or frequency) in [m], [nm], [Hz] or [THz] units and (2) the ESA cross-section. The unit of the wavelength column has to be the same as defined in the File frequency unit parameter (Cross-sections tab).
The last parameter is Extract ESA from emission. If this parameter is TRUE, it means that the second column of the ESA file contains the ESA cross-section and the emission cross-section together, so the component has to extract the ESA cross-section from this file. If the Extract ESA from emission parameter is FALSE, the component assumes that the second column contains only the ESA cross-section. An example of ESA file is:
(nm)
1449.91984 0.32257
1451.30261 0.35195
1452.68537 0.38317
1454.06814 0.4175
1455.4509 0.4571
:
Er+3 Er+3–
βa λ( ) βe λ( )
dB m⁄ m2
λλ nm[ ] g∗ dB m⁄[ ]
348
ERBIUM DOPED FIBER
For more information, refer to the tutorial about ESA.
Numerical tabThe numerical tab contains most of the options related to the different models or approximations used in the EDF model. In the Calculation algorithm parameter, the user can choose between the four possible models: (1) Saleh, (2) Jopson, (3) Giles, and (4) Inhomogeneous. These four possible models are described in the technical background. If a model is selected, for example the model number 3 (Giles model), the EDF component will start the simulation process from the first model (Saleh) until the model chose by the user (Giles model). Figure 6 details how the component works.
1571.60321 4.08152
1572.98597 3.81553
1574.36874 3.60032
1575.7515 3.37804
1577.13427 3.20419
1578.51703 3.05017
:
1648.98 1.43477
1649.23 1.4325
1649.48 1.49899
1649.73 1.42809
1649.98 1.42593
1650.23 1.49333
(nm)λλ nm[ ] g∗ dB m⁄[ ]
349
ERBIUM DOPED FIBER
Figure 6 Diagram describing the process order of the algorithm models
The EDF component's preprocessing is done to improve the speed of convergence in the model selected by the user. This preprocessing is done in accordance with the complexity of each model.
The user defines the parameter Relative error that indicates the threshold value which the component uses to decide if the results from the iterative process have converged. Another parameter is the Max. number of iterations. This parameter defines the maximum number of iterations allowed for the numerical method to reach the value determined by the Relative error parameter. The parameter Number of longitudinal steps defines the minimum number of steps in the fiber to be considered in the Jopson, Giles, and inhomogeneous method.
If the Inhomogeneous algorithm is chose, then the user has to specify the parameter Inhomogeneous accuracy. This parameter determines the tolerance of the numerical integration of Equation 42, and directly influences the simulation time. Some simulations have shown us that this parameter shoud be between 0.01 and 0.001 to obtain accurate results in a reasonable time.
The user can make their selection via the Overlap factor data parameter, by determining if the component will calculate the overlap integral or the component or load the overlap factor from a file. For the calculation case, the Geometrical model parameter has to be defined. The Geometrical model parameter indicates if the
350
ERBIUM DOPED FIBER
component will use one of the Gaussian approximations (Equation 13 - Equation 16) or the LP01 mode to calculate the overlap integral.
Another possible method to calculate the overlap integral is to consider the power dependence on it. The Overlap factor parameter determines if the power dependence has to be taken into consideration. In this case, Equation 6 is solved numerically for the LP01 mode and the number of integrations to be done in the fiber is defined by the Nr. of transverse integration parameter. In the other way, the confinement factor is calculated in accordance with the Geometrical model parameter.
If the overlap factor is loaded from a file, the user has to specify the file name in the Overlap factor file name parameter, and the file has to be the same as the format below:
If the Inhomogeneous algorithm is chose, then the homogeneous absorption and emission cross-sections are necessary for the inhomogeneous broadening model. In this case, the component generates the homogeneous cross-sections from the measured cross-sections, as explained in the technical background. For this purpose, the user has to specify the number of Gaussians to be used in the fitting and the value of the inhomogeneous linewidth.
(nm)
1449.91984 0.45
1451.30261 0.44
1452.68537 0.43
1454.06814 0.42
1455.4509 0.41
λλ nm[ ] Γ
351
ERBIUM DOPED FIBER
References[1] C. Randy Giles, and Emmanuel Desurvire, "Modeling Erbium-Doped Fiber Amplifiers". IEEE
Journal of Lightwave Technology, Volume: 9 Issue: 2, Feb. 1991, Page(s): 271 - 283.
[2] Fiber Optic Test and Measurement, Edited by Dennis Derickson, 1997.
[3] S. L. Hansen, K. Dybdal, and C. C. Larsen. "Gain Limited in Erbium-Doped Fiber Amplifiers Due to Internal Rayleigh Backscattering". IEEE Photonics Technology Letters, Volume 4, Issue 6, Jun. 1992.
[4] P. F. Wysocki, G. Jacobovitz-Veselka, D. S. Gasper, S. Kosinski, J. Costelloe, and S. W. Granlund. "Modeling, Measurement, and a Simple Analytic Approximation for the Return Loss of Erbium-Doped Fiber Amplifiers". IEEE Photonics Technology Letters, Volume: 7, Issue: 12, Dec. 1995.
[5] P. Blixt, J. Nilsson, T. Carlnas, and B. Jaskorzynska. "Concentration-Dependent Upconversion in Er3+-Doped Fiber Amplifiers: Experiments and Modeling". IEEE Photonics Technology Letters, Volume: 3 Issue: 11, Nov. 1991.
[6] P. Myslink, D. Nguyen, and J. Chrostowski. "Effects of Concentration on the Performance of Erbium-Doped Fiber Amplifiers". Journal of Lightwave Technology, volume 15, Issue 1, Jan. 1997.
[7] Blixt, P.; Jaskorzynska, B.; Nilsson, J. "Performance reduction and design modification of erbium-doped fiber amplifiers resulting from pair-induced quenching". IEEE Photonics Technology Letters , Volume: 5 Issue: 12 , Dec 1993.
[8] M. Bolshtyansky, P. F. Wysocki, N. Conti. "Model of Temperature Dependence for Gain Shape of Erbium-Doped Fiber". Journal of Lightwave Technology, volume 18, Issue 11, Dec 2000.
[9] P. F. Wysocki, N. Conti, and D. Holcomb. "Simple Modeling Approach for the Temperature Dependence of the Gain of Erbium-Doped Fiber Amplifiers". SPIE Conference on Optical Devices for Fiber Communication, Volume 3847, 1999.
[10] Emmanuel Desurvire. "Erbium-Doped Fiber Amplifier: Principles and Applications", John Wiley & Sons.
[11] A. A. M. Saleh, R. M. Jopson, J. D. Evankow, and J. Aspell. "Modeling of Gain in Erbium-Doped Fiber Amplifiers". IEEE Photonics Technology Letters, Volume: 2 Issue: 10, Oct. 1990, Page(s): 714 - 717.
[12] R. M. Jopson, A. A. M Saleh. "Modeling of Gain and Noise in Erbium-Doped Fiber Amplifiers". Fiber Laser Sources and Amplifiers, SPIE Volume: 1581, 1991, Page(s): 114 - 119.
[13] C. R. Giles, C. A. Burrus, D. J. DiGiovanni, N. K. Dutta, and G. Raybon. "Characterization of Erbium-Doped Fibers and Application to Modeling 980 nm and 1480 nm Pumped Amplifiers". IEEE Photonics Technology Letters, Volume: 3 Issue: 4, Apr. 1991, Page(s): 363 -365.
[14] "Rare-Earth-Doped Fiber Laser and Amplifiers", Edited by M. J. F. Digonnet, 2001.
[15] P. C. Becker, N. A. Olsson, and J. R. Simpson. "Erbium-Doped Fiber Amplifiers: Fundamentals and Technology". Optics and Photonics, 1999.
352
ER-YB CODOPED FIBER
Er-Yb codoped fiber
This component simulates a bidirectional Erbium-Ytterbium codoped fiber. The component solves numerically the rate and propagation equations for the steady-state case.
Ports
Parameters
Main
Name and description Port type Signal type
Input1 Input Optical
Output1 Output Optical
Input2 Input Optical
Output2 Output Optical
Name and description Default value
Default unit Units Value range
Length
Doped fiber length
1 m — [0,1000000]
Core radius
Doped fiber core radius
2 µm — [1,1e100]
Doping radius
Doped radius
2 µm — [1,1e100]
Numerical aperture
Specifies numerical aperture of fiber
0.15 — — [0.1,1]
Loss data type Constant Constant, FromFile
Signal loss
Fiber loss at signal range
0.10 dB/m — [0,1e100]
353
ER-YB CODOPED FIBER
Doping
Cross-sections
Pump loss
Fiber loss at pump range
0.15 dB/m — [0,1e100]
Loss vs. wavelength Loss.dat — — —
Name and description Default value
Default unit Units Value range
Er ion density
Specifies Erbium doping in the fiber
5.14e+025 m-3 — [1,1e100]
Yb ion density
Specifies Ytterbium doping in the fiber
6.2e+026 m-3 — [1,1e100]
Er metastable lifetime
Specifies the Erbium metastable lifetime
10 ms — [1e-100, 1e100]
Yb metastable lifetime
Specifies the Ytterbium metastable lifetime
1.5 ms — [1e-100, 1e100]
Name and description Default value
Default unit Units Value range
OptiAmplifier format
Determines if format of cross-section file is an OptiAmplifier file
False — — True, False
File frequency unit
Determines if the filter will down sample the signal bandwidth to the filter sample rate
nm — — nm, m, Hz, THz
Er cross-section file name
Specifies Erbium cross-section file name
Erbium.dat — — —
Yb cross-section file name
Specifies Ytterbium cross-section file name
Ytterbium.dat — — —
Name and description Default value
Default unit Units Value range
354
ER-YB CODOPED FIBER
Enhanced
Numerical
Name and description Default value
Default Unit Units Value range
Calculate upconversion
Component calculates C16 and C14 based on ion density
True — — True, False
C14
Cross relaxation coefficient between level 1 and 4
5.2834e-024 — m-3/s [1e-100, 1e100]
C16
Cross relaxation coefficient between level 1 and 6
3.44e-022 — m-3/s [1e-100, 1e100]
Cup
Homogeneous upconversion coefficient from level 2
5.2834e-024 — m-3/s [1e-100, 1e100]
A32
Nonradiative emission rate from level 3 to level 2
1000000000 — 1/s [1,1e100]
A43
Nonradiative emission rate from level 4 to level 3
1000000000 — 1/s [1,1e100]
Name and description Default value
Default unit Units Value range
Relative error
Specifies maximum acceptable difference between two consecutive iterations to complete the iteration process
0.0001 — — [1e-100,1]
Maximum number of iterations
Specifies the maximum number of times for iteration process
150 — — [1,1e8]
Longitudinal steps
Specifies the number of longitudinal steps in the fiber
100 — — [1,1e8]
Radial steps
Specifies the number of radial steps for integration
50 — —
355
ER-YB CODOPED FIBER
Graphs
Simulation
Noise
Numerical solverDefines whether the numerical solver is used instead of analytical solutions for the rate equations.
False — — True, False
Name and description Default value
Default unit Units Value range
Calculate graphs False — — True, False
Number of distance steps 20 — — [1,1e8]
Number of wavelength steps 20 — — [1,1e8]
Linear scale True — — True, False
Minimum value -50 — dBm ]1e-100, 1e100[
Pump reference wavelength 1400 nm [100, 1900]
Name and description Default value
Default unit Units Value range
Enabled
Defines whether the component is enabled or not
True — — True, False
Longitudinal monitor True — — True, False
Number of monitors 10 — — [1,1000]
Name and description Default value
Default unit Units Value range
Noise center frequency
Determines the noise center frequency
193.4 THz Hz, THz, nm [30, 30e5]
Noise bandwidth
Bandwidth to create noise bins
13 THz Hz, THz, nm ]0,+INF[
Noise bins space
Specifies the noise bins spacing
125 THz Hz, GHz, THz, nm
[1,1000]
Name and description Default value
Default unit Units Value range
356
ER-YB CODOPED FIBER
Random numbers
Noise threshold
Minimum value for adaptation of noise bins
-100 dB — ]-INF, 0[
Noise dynamic
Threshold ratio for adaption of noise bins
3 dB — [0, +INF[
Convert noise bins
Determines if generated noise bins are incorporated into signal
Convert noise bins
— — True, False
Name and description Default value
Default unit Units Value range
Generate random seed
Determines if the seed is automatically defined and unique
True — — True, False
Random seed index
User-defined seed index for noise generation
0 — — [0, 4999]
Name and description Default value
Default unit Units Value range
357
ER-YB CODOPED FIBER
Technical background
Er-Yb Codoped Fiber Propagation and Rate EquationsIn order to give flexibility to change the waveguiding parameters of the Er3+ - Yb3+ codoped fiber for large signal and high pump power applications the extended model for Er3+ - Yb3+ codoped fiber presented in [1] is used.
Figure 1 Energy levels for Er3+ - Yb3+ system
Population densities of the levels of have been included together with the upconversion from the pump level . The model takes into account propagation of the forward and backward amplified spontaneous powers for both the pump and the signal wavelength range.
Depending on the pump wavelength, pump energy can be absorbed by both the Er ions in the and by the ions in the ground levels. Ytterbium ions excited to the level transfer their energy to neighboring Erbium ions in the
ground level, exciting them to the pump level from where they rapidly relax to the metastable level. The backtransfer from the Er pump level to the Yb ground level is neglected.
4 11 2⁄ and 4 9 2⁄ Er3+
4 11 2⁄
4 15 2⁄ Yb3+ F27 2⁄
F25 2⁄
4 15 2⁄ 4 11 2⁄4 13 2⁄
358
ER-YB CODOPED FIBER
Let us denote the , , and the levels of as levels 1, 2, 3, and 4, and the and the levels of as levels 5 and 6, and their population densities as N1, N2, N3, N4, N5, and N6, respectively. The uniform upconversion mechanisms from the erbium metastable and pump levels are modeled by quadratic terms in N2 and N3, with a concentration dependent upconversion coefficient. The pair induced energy transfer process from to is described by a cross relaxation coefficient [2]. The rate equations for the above atomic populations are:
In these equations, the terms represent the stimulated transition rates between the i and j levels, , are the spontaneous emission lifetimes for and
levels, , are the nonradiative relaxation rates, and are the upconversion and cross-relaxation coefficients. The signal absorption, signal emission, pump absorption, and pump emission rates, are given by:
(1)
(2)
(3)
(4)
(5)
(6)
4 15 2⁄ 4 13 2⁄ 4 11 2⁄ 4 9 2⁄ Er3+
F27 2⁄ F2
5 2⁄ Yb3+
Yb3+ Er3+
∂N1∂t
--------- W12N1 W13N1–N2τEr------- W21N2 CupN2
2 C14N1N4– CupN32 CcrN1N6–+ + + +–=
∂N2∂t
--------- W12N1 W21N2–N2τEr-------– A32N3 2CupN2
2– 2C14N1N4+ +=
∂N3∂t
--------- W13N1 A32N3– A43N4 2CupN32– CerN1N6+ +=
∂N4∂t
--------- 2CupN22 C14N1N4– A43N4– CupN3
2+=
∂N6∂t
--------- W56N5 N6τYb--------– W65N6– CerN1N6–=
WijτEr τYb 4 13 2⁄
F25 2⁄ A32 A43 Cup C14 C16, ,
W12 W21 W13 W56 W65, , , ,
W12 r z,( )σ12 vs( )
hvs------------------Ps z( ) E r vs,( ) 2 σ12 v( )
hv---------------- PASE
+ z v,( ) PASE_
z v,( )+[ ] E r v,( ) 2⋅ vd0
∞
∫+=
359
ER-YB CODOPED FIBER
where are the frequency dependent and emission and absorption cross sections, respectively, is the
Planck’s constant, , are the forward and backward propagating optical powers at frequency in a frequency interval , and at a longitudinal fiber coordinate . They represent the forward and backward ASE powers due to the - transition at , and also the ASE powers due to the - transition at .
is the signal power, the pump power, are the signal and pump frequencies, and is the field distribution of the mode normalized according to
The total and ion density distributions , are assumed to be constant within the whole or a part of the fiber core, and along the fiber length (top hat shaped with the diameter of 2b).
(7)
(8)
(9)
(10)
(11)
W21 r z,( )σ21 vs( )
hvs------------------Ps z( ) E r vs,( ) 2 σ21 v( )
hv---------------- PASE
+ z v,( ) PASE_
z v,( )+[ ] E r v,( ) 2⋅ vd0
∞
∫+=
W13 r z,( )σ13 vp( )
hvp------------------Pp z( ) E r vp,( ) 2 σ13 v( )
hv---------------- PASE
+ z v,( ) PASE_
z v,( )+[ ] E r v,( ) 2⋅ vd0
∞
∫+=
W56 r z,( )σ56 vp( )
hvp------------------Pp z( ) E r vp,( ) 2 σ56 v( )
hv---------------- PASE
+ z v,( ) PASE_
z v,( )+[ ] E r v,( ) 2⋅ vd0
∞
∫+=
W65 r z,( )σ65 vp( )
hvp------------------Pp z( ) E r vp,( ) 2 σ65 v( )
hv---------------- PASE
+ z v,( ) PASE_
z v,( )+[ ] E r v,( ) 2⋅ vd0
∞
∫+=
σ21 v( ) σ65 v( ) σ12 v( ) σ13 v( ) and σ56 v( ),,,,Er3+ Yb3+ h
PASE+ z v,( ) PASE
_z v,( )
v ∆vz
4 13 2⁄ 4 15 2⁄ 1400nm λ 1650nm< <F2
5 2⁄ F27 2⁄ 850nm λ 1100nm< <
Ps z( ) Pp z( ) vs vp,E r v,( ) LP01
2π E r v,( ) 2r rd0
∞
∫ 1=
Er3+ Yb3+ NEr t NYb
t
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ER-YB CODOPED FIBER
They satisfy the conservation equations
Propagation of the pump power along the active fiber is described by the following differential equation:
where is the radius of - codoped part of the fiber core. The signal power and the ASE powers in both the pump and the signal wavelength range are amplified according to:
where is the frequency dependent background loss of the active fiber and the emission and absorption factors , are determined from the corresponding emission and absorption cross sections as overlap integrals between the intensity distribution and the population densities of the , and
, levels defined in:
(12)
(13)
(14)
(15)
(16)
(17)
NEr t N1 r z,( ) N2 r z,( ) N3 r z,( ) N4 r z,( )+ + +=
NYb t N5 r z,( ) N6 r z,( )+=
∂Pp z vp,( )∂z
------------------------- 2π σ56 vp( )N5 r z,( ) σ13 vp( )N1 r z,( ) σ65 vp( )N6 r z,( )–+[ ] E r vp,( ) 2rdr α vp( )+0
b
∫ Pp z vp,( )=
b Er3+ Yb3+
∂Ps z vs,( )∂z
------------------------ ge z vs,( ) ga z vs,( )– α vs( )–[ ]Ps z vs,( )=
∂PASE ± z v,( )
∂z---------------------------- 2hv∆vge z vs,( ) ge z v,( ) ga z v,( )– α v( )–[ ]±± z vs,( )PASE
± z v,( )=
α v( )ge z v,( ) z v,( )
LP01 F25 2⁄ 4 13 2⁄F2
7 2⁄ 4 15 2⁄
ge z v,( )2πσ65 v( ) N6 r z,( ) E r v,( ) 2r r…850nm λ 1100nm< <d
0
b
∫
2πσ21 v( ) N2 r z,( ) E r v,( ) 2r r…1400nm λ 1650nm< <d0
b
∫
=
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ER-YB CODOPED FIBER
These equations form a system of coupled differential equationsthat are solved by numerical integration along the active fiber, using the Runge-Kutta method. Population densities , , , , , and
are derived from the steady-state solutions to the rate equations [1] - [5] together with conservation laws, equations [12] and [13] are substituted. Due to quadratic terms appearing in the rate equations, it is not possible to eliminate densities , , , and analytically, and so the numerical approach must be used. It was assumed that and that the upconversion coefficient and the cross-relaxation coefficient are linearly increasing functions of and respectively.
References:[1] M. Karasek, "Optimum Design of Er3+ - Yb3+ Codoped Fibers for Large-Signal High-Pump-
Power Applications", IEEE Journal of Quantum Electronics, vol. 33, pp 1699-1705, 1997.
[2] M. Federighi, F. Di Pasquale, "The Effect of Pair-induced Energy Transfer on the Performance of Silica Waveguide Amplifiers with High Er3+-Yb3+ Concentrations", IEEE Photon. Technol. Lett., vol 7, pp. 303-305, 1995.
(18)
(19)
(20)
ga z v,( )2πσ56 v( ) N5 r z,( ) E r v,( ) 2r r…850nm λ 1100nm< <d
0
b
∫
2πσ12 v( ) N1 r z,( ) E r v,( ) 2r r…1400nm λ 1650nm< <d0
b
∫
=
N1 r z,( ) N2 r z,( ) N3 r z,( ) N4 r z,( ) N5 r z,( )N6 r z,( )
N1 r z,( ) N2 r z,( ) N5 r z,( ) N6 r z,( )C14 Cup=
Cup CcrNEr
1 NYb1
Cup 3.5 10 24–× 2.41 10 49–× NEr1 4.4 1025×–( )+=
Ccr 1.0 10 22–× 4.0 10 49–× NYb1 1.0 1025×–( )+=
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ER-YB CODOPED WAVEGUIDE AMPLIFIER
Er-Yb codoped waveguide amplifier
This component simulates an Er-Yb codoped waveguide amplifier based on basic parameters.
Ports
Parameters
Main
Name and description Port type Signal type
Input1 Input Optical
Output1 Output Optical
Input2 Input Optical
Output2 Output Optical
Name and description Default value
Default unit Units Value range
Waveguide length 0.03 — m ]0,+INF[
Signal background loss
Represents the intrinsic material losses, given by the losses at 1300nm.
0 — db/m [0,+INF[
Pump background loss
Represents the intrinsic material losses, given by the losses at 1300nm.
0 db/m [0,+INF[
Refractive index data fileSame as OptiBPM’s refractive index file. Contains a uniform refractive index distribution and follows the format defined in OptiBPM. Also contains the number of points used to discretize the domain.
Index.rid — — —
Er ion density distribution fileSame as Refractive index data file, contains the Erbium ion density distribution. File must have the same discretization as the Refractive index data file, and must be filled with ones and zeros.
Erdensity.dat — — —
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ER-YB CODOPED WAVEGUIDE AMPLIFIER
Doping
Yb ion density distribution fileSame as Er ion density distribution file, contains the Ytterbium ion density distribution. File must have the same discretization as the Refractive index data file, and must be filled with ones and zeros.
Ybdensity.dat — — —
Calculate mode in all wavelengthsIdentifies if a mode must be calculated for all the signal wavelengths. If selected, the mode solver is activated, using the refractive index distribution defined in a file for all the signal wavelengths.
True — — True, False
Wavelength to calculate the modeIf Calculate mode in all wavelength is not selected, a signal mode, calculated at the defined wavelength, is shared for all signals. This selections makes the calculation faster after the part of the execution time is spent calculating the modes.
1550 nm [1490, 3000]
Recalculate modes every runningIdentifies if all the modes, in the pump and signal wavelengths, must be recalculated. It is suggested that this option not be selected, due to the excessive time spent recalculating the modes.
False — — False, True
Polarization for signal mode calculationPolarization used to calculate the signal modes.
TE — — TE, TM
Number of modes at pump wavelengthNumber of modes that are calculated at the pump wavelength. Read-only value. To change it, edit the “Power ratio for each pump mode” option.
2 — — [1, 10]
Polarization for pump mode calculationPolarization used to calculate the pump’s modes.
TE — — TE, TM
Power ratio for each pump modePower ratio for each pump mode. Number of elements in the list must be equal to the number of modes at the pump wavelength, and the sum of the ratios must be 1.
0.5 0.5 — — any string with numbers
Name and description Default value
Default unit Units Value range
Er ion densitySpecifies Erbium doping in the fiber
1e+025 m-3 [0, +INF[
Name and description Default value
Default unit Units Value range
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ER-YB CODOPED WAVEGUIDE AMPLIFIER
Cross-sections
Er metastable lifetimeSpecifies the Erbium metastable lifetime
11 ms ]0, +INF[
Er signal excess lossRepresents the losses, due to the introduction of Erbium in the material by diffusion or by another implantation method, at the signal wavelength. Backscattering is a typical effect observed in this case. Note: This isn’t a commonly observed absorption loss in the 1550nm wavelength range.
0 dB/m [0, +INF[
Er pump excess lossRepresents the losses, due to the introduction of Erbium in the material by diffusion or by another implantation method, at the pump wavelength. Backscattering is a typical effect observed in this case. Note: This isn’t a commonly observed absorption loss at 980nm.
0 dB/m [0, +INF[
Yb ion densitySpecifies Ytterbium doping in the fiber
1e+025 m-3 [0, +INF[
Yb metastable lifetimeSpecifies the Ytterbium metastable lifetime
11 ms ]0, +INF[
Yb signal excess lossRepresents the losses, due to the introduction of Ytterbium in the material by diffusion or by another implantation method, at the signal wavelength. Backscattering is a typical effect observed in this case.
0 dB/m [0, +INF[
Yb pump excess lossRepresents the losses, due to the introduction of Ytterbium in the material by diffusion or by another implantation method, at the pump wavelength. Backscattering is a typical effect observed in this case.
0 dB/m [0, +INF[
Name and description Default value
Default unit Units Value range
EDFA design formatDetermines if format of cross-section file uses EDFA file format
False — — True, False
File frequency unitDetermines if the filter will down sample the signal bandwidth to the filter sample rate
nm — — nm, m, Hz, THz
Name and description Default value
Default unit Units Value range
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ER-YB CODOPED WAVEGUIDE AMPLIFIER
Enhanced
ESA cross section value at 1480 5.53-026 m2 ]0, +INF[
Er cross-section file nameSpecifies Erbium cross-section file name. File contains erbium absorption and emission cross sections.
Erbium.dat — — —
Yb cross-section file nameSpecifies Ytterbium cross-section file name. File contains the ytterbium absorption and emission cross sections.
Ytterbium.dat — — —
Name and description Default value
Default Unit Units Value range
Number of ASE modelsQuantity of excited modes by the ASE. Normally this number is the total number of modes (TE and TM) present in the waveguide at the signal wavelength.
2 — — [1, 1e+008]
A32Nonradiative emission rate from level 3 to level 2
1000000000 — 1/s ]0, +INF[
A43Nonradiative emission rate from level 4 to level 3
1000000000 — 1/s ]0, +INF[
Fraction of ion in pairFraction of ion in pair due to the pair-induced quenching PIQ phenomenon.
0 — — [0, 1]
Fast nonradiative upconversion lifetime 5e-006 s ]0, +INF[
Calculate upconversion effectsDefine whether the upconversion effects are calculated or just approximated.
True — — True, False
CupHomogeneous upconversion coefficient from level 2
1e-022 — m3/s ]0, +INF[
C3Homogeneous upconversion coefficient from level 3
1e-022 — m3/s ]0, +INF[
C14Cross relaxation coefficient between level 1 and 4
7e-023 — m3/s ]0, +INF[
Name and description Default value
Default unit Units Value range
366
ER-YB CODOPED WAVEGUIDE AMPLIFIER
Numerical
Graphs
Simulation
Noise
C16Cross relaxation coefficient between level 1 and 6
7e-023 — m3/s ]0, +INF[
Name and description Default value
Default unit Units Value range
Relative errorSpecifies maximum acceptable error in solving the propagation equations
5e-007 — — ]0, 1]
Longitudinal stepsSpecifies the number of divisions necessary to discretize the waveguide length
130 — — [1,1e+008[
Name and description Default value
Default unit Units Value range
Calculate graphs True — — True, False
Longitudinal power graphs True — — True, False
Nornalized population density graphs True — — True, False
Name and description Default value
Default unit Units Value range
Enabled
Defines whether the component is enabled or not
True — — True, False
Name and description Default value
Default unit Units Value range
Noise center frequency
Determines the noise center frequency
193.4 THz Hz, THz, nm [30, 30e5]
Noise bandwidth
Bandwidth to create noise bins
13 THz Hz, THz, nm ]0,+INF[
Name and description Default value
Default Unit Units Value range
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ER-YB CODOPED WAVEGUIDE AMPLIFIER
Technical BackgroundThe Er-Yr codoped waveguide amplifier solves the propagation of electromagnetic fields on Erbium doped, or on Erbium doped and Ytterbium co-doped waveguides. The pump wavelength must be in the region of 980 nm or 1480 nm, and can be co-and counter-propagating. Multiple co- and counter-propagating input signals may be considered in different wavelengths (DWDM).
In order to run this component, the following data must be provided: the Erbium and Ytterbium doping profiles, with their respective cross sections (parameters located in the cross-sections tab); the pump wavelength ( ) with the co- and counter-propagant pump powers ( ); and the WDM signal wavelengths ( ) with its respective powers. Notice that a signal is characterized by its wavelength, and may have different co and counter-propagant powers ( ).
The main characteristics of this component are:• co- and counter-propagant pump at 980nm region or 1480nm region;• multiple signals (co- and counter-propagant) at different wavelengths (DWDM);• multimode operation for the pump and signals;• co- and counter-propagant ASE noise due to Erbium concentration;• homogeneous upconversion (HUC) 1 from levels;• pair-induced quenching - PIQ;• nine energy levels considered.
Model implementationThis model is based on the solution of the propagation equations, using, directly, the solutions of the involved electromagnetic fields and the exact Erbium and Ytterbium transversal distributions.
Noise bins space
Specifies the noise bins spacing
125 GHz Hz, GHz, THz, nm
[1,1000[
Noise thresholdMinimum value for adaptation of noise bins
-100 dB — ]-INF, 0[
Noise dynamicThreshold ratio for adaption of noise bins
3 dB — [0, +INF[
Convert noise binsDetermines if generated noise bins are incorporated into signal
Convert noise bins
— — True, False
Name and description Default value
Default unit Units Value range
λpPp+ Pp_,
λs1…λs
WDM
λsi P s+
i and P s-i→
4 13 2⁄ e 4 11 2⁄
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ER-YB CODOPED WAVEGUIDE AMPLIFIER
Propagation equations
The propagation equations describe the power evolution of the propagating electromagnetic fields in the optical amplifier and are described as:
This set of equations forms a system of 2+2WDM+2M coupled ones, and must be solved with the following boundary conditions:
where
is the device length
, , , and are the signals, pumps and ASE (Amplified Spontaneous Emission) longitudinal power distributions in the direction of propagation , with the signs (+) and (-) meaning, respectively, the co- and counter propagant direction;
and are the attenuation coefficients in the wavelengths for signal and pumping, respectively.
The index in refers to the -th signal, centered in the frequency , of a total number of WDM signals that can propagate simultaneously within the amplifier, as in systems with Dense Wavelength Division Multiplex - DWDM. The ASE± spectrum is discretized in M intervals (slots) with spectral width , centered in the frequencies
, in such a way, that (see Equation 3) refers to the -th spectral
(1)
(2)
(3)
(4)
(5)
(6)
dPp+_ z( )dz
---------------------- γp z( )Pp+_ z( ) αpPp+_ z( )+−+−=
dP s+_i z vs
i,( )
dz----------------------------- γ 21 z vs
i,( ) γ12 z vsi,( )–[ ]P s
i z vsi,( ) αpP s
i z vsi,( ) i,+−+− 1 … WDM, ,= =
dP jASE +_ z vj,( ) γ21 z vj,( ) γ12 z vj,( )–[ ]P j
ASE +_ z vs,( ) +±=
mhvj∆vjγ21 z vj,( ) αsPjASE +_ z vs,( ) j,±± 1 … M, ,=
Pp+ 0( ) Pp0 Pp_ L( ), PpL= =
P s+i 0 vs
i,( ) Ps0 vsi( ) and P s_
i L vsi,( ) PsL vs
i( ) i, 1 …WDM,= = =
PASE + 0 vs,( ) PASE_ L vj,( ) 0 j, 1 … M, ,= = =
L
P s+_i Pp+_ e P j
ASE +_
z
αs αp
i P s+_i i vs
i
∆vjvj P j
ASE +_ j
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ER-YB CODOPED WAVEGUIDE AMPLIFIER
component of ASE±. Also in Equation 3, we have as the total number of modes present in the waveguide, and is the Planck constant. In Equation 1 - Equation 3, the gain coefficients , , and are given by:
where , , and , are the populations of Erbium ions of the ground ( ), meta-stable( ) and pump levels ( if pumped in 1480nm, or if pumped in 980nm). and are the populations of Ytterbium ions of levels
and .
The populations of three possible states of an excited pair exist:
- no ion excited
- one ion excited
- two ions excited
due to the phenomenon of pair-induced quenching - PIQ. , , , and are the absorption and emission cross sections of the Erbium doped material,
at the signal (12 and 21) and pump (13 and 31) wavelengths. The parameters and are the absorption and emission cross sections of the Ytterbium doped/co-doped material at the pump wavelength in the region of 980nm. When the amplifier is pumped at 980nm, the level 3 corresponds to the main level of the Stark Split. However, when the amplifier is pumped in the 1480nm region, the pump level is confounded with the main level . Thus, according to Equation 7a or
(7)a
(7)b
(8)
(9)
mh
γp γ12 γ21
γp z( ) Ψp x y,( ) σa13 N1 x y z, ,( ) 2N0p x y z, ,( ) N1p x y z, ,( )+ +( )[∫A∫=
σe31N3 x y z, ,( )– σa56N5 x y z, ,( ) σe65N6 x y z, ,( ) ]dxdy–+
γp z( ) Ψp x y,( ) σa13 N1 x y z, ,( ) 2N0p x y z, ,( ) N1p x y z, ,( )+ +( ) + [∫A∫=
σ– e31 N2 x y z, ,( ) N3 x y z, ,( ) 2N0p x y z, ,( ) N1p x y z, ,( )+ + +( ) ]dxdy
γ12 z vi,( ) Ψs x y,( )σa12 N1 x y z, ,( ) 2N0p x y z, ,( ) N1p x y z, ,( )+ +( ) xd yd∫A∫=
γ21 z vi,( ) Ψs x y,( )σe21 N2 x y z, ,( ) 2N2p x y z, ,( ) N1p x y z, ,( )+ +( ) xd yd∫A∫=
N1 N2 N3 4 15 2⁄4 13 2⁄ 4 13 2⁄ 4 11 2⁄
N5 N6F2
7 2⁄ F25 2⁄
N0p
N1p
N2p
σa13 σe31 σa12σe21
σa56σe65
4 11 2⁄
4 13 2⁄
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ER-YB CODOPED WAVEGUIDE AMPLIFIER
Equation 7b, the coefficient of gain is taken when the amplifier is pumped at 980nm or 1480nm, respectively. In Equation 7 through to Equation 9, and
are the normalized intensity profiles obtained from the modal analysis of the waveguide (see the section on "Multimode operation"), in such a way that the intensity distributions of the signal, pump and ASE± can be written as:
where it should be noted that the same normalized intensity profile has been used for ASE and signal, because the difference between the central wavelengths of the intervals used to discretize the ASE and the signal wavelength is relatively small and may be considered . The correlation between the field distribution of the fundamental mode at 1530nm and 1650nm is higher than 95% for a typical optical fiber/waveguide.
Rate equationsThe populations , and also the population of the three possible states of an excited pair ( , , and ) in Equation 7 through to Equation 9, are the solutions of the rate equations for the energetic systems of Figure 1 or Figure 2, when it is considered the pumping in 980nm or 1480nm, respectively.
(10)
(11)
(12)
γpΨs x y,( )
Ψp x y,( )
Is x y z, ,( ) Ψs x y,( )Ps z( )=
Ip x y z, ,( ) Ψp x y,( )Pp z( )=
I jASE +_ x y z, ,( ) Ψs x y,( )P j
ASE +_ z( )=
M
ΨASEj Ψs
i≈
N1 N6→N0p N1p N2p
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ER-YB CODOPED WAVEGUIDE AMPLIFIER
Figure 1 Coupled Er+3/Yb+3 system, pumped in 980nm region
Note: There are nine relevant energy levels considered (four levels due to the presence of the Erbium ions, two due to the Ytterbium dopant, and three due to the formation of Erbium paired-induced ions). 's and 's are the pump and signal stimulated rates,and the 's are the nonradioactive rate from level i to j. A21 is the fluorescent rate. Cup and C3 are the homogeneous upconversion coefficients. C14 and C16 are the cross-relaxation coefficients. Figure 1 also shows the population densities of the three possible states of an excited pair ( (no ions excited), (one ion excited), and (two ions excited), due to the PIQ effect.
In Figure 1, for the 980nm-pumping region, we have representations of the , , , and energy levels (due to the Erbium dopant), with
corresponding population densities of , respectively. The and energy levels are also shown, with population densities , due to
the Ytterbium dopant. The populations of the three possible states of an excited ion
Rij WijAij
N0p N1p N2p
4 15 2⁄4 13 2⁄ 4 11 2⁄ 4 9 2⁄
Ni i 1 4,=( ) F27 2⁄
F25 2⁄ Ni i 5 6,=( )
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ER-YB CODOPED WAVEGUIDE AMPLIFIER
( , , and ) are also shown. is the fast nonradiative upconversion lifetime, and can be calculated as:
with being the distance between two ions in a pair. Experimental measurements report typical value of the order of few microseconds. We know that
‘s are pump rates (stimulated absorption and emission) between levels , and 's are the absorption and emission stimulated rates at the signals wavelength. The non-radiative rates between levels are represented by . A21 is the fluorescence rate. Cup and C3 are the homogeneous upconversion coefficients from levels 2 and 3. The homogeneous upconversion is modeled through the quadratic terms in N2 and N3 in the rate equations. These terms are dependent on the Erbium concentration, and can be calculated using reference [1]. C14 and C16 are the cross-relaxation coefficients between levels and . The cross-relaxation between levels is the main energy transfer mechanism between the Ytterbium and Erbium ions, and the approached value of the coefficient can be obtained from [1]. Due to the short lifetime of level 3 ( ), the back energy transfer process (from Erbium to Ytterbium ions) is not being considered in this model. However, the fact that all Erbium ions are surrounded by Ytterbium ions is taken into account. Special attention should be paid to the Ytterbium concentration in relation to the Erbium concentration. Geometrically, it is observed that the Ytterbium concentration must be in the interval . If the Ytterbium concentration ( ) is less than , the formation of clusters may occur and the energy transference form Ytterbium ions ( ) to the Erbium ones ( ) may not be so efficient. On the other hand, if the Ytterbium concentration is too high, Ytterbium clusters may form, which means there won't be any energy transference to the Erbium ions, the pump energy will be wasted, and consequently, the efficiency of the amplifier device will be reduced. It is believed that the homogeneous upconversion that occurs from level 3 doesn't reach level and relaxes very quickly to level 4 ( ).
(13)
N0p N1p N2p τ21p
τ21pdpair
3
Cup-----------=
dpair
Rij i j→Wij
i j→ Aij
4 1→ 6 1→6 1→
1 A32⁄
4NEr NYb 20NEr< <NYb 4NEr
Yb+3 Er+3
F47 2⁄ 4 9 2⁄
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ER-YB CODOPED WAVEGUIDE AMPLIFIER
The rate equations for the energy system of Figure 2 is given by:
The presence of the crossed terms for the solutions of the population , suggests the use of a special numeric treatment due to its non-linear
nature. However, the system for the paired-induced population is a linear one and can be solved by a straightforward solution.
(14)
∂N1∂t
--------- W12N1– R13N1– R31N3 A21N2 W21N2 ++ + +=
+ CupN22 C14N1N4– C3N3
2 C16N1N6–+
∂N2∂t
--------- W12N1 A21N2– W21– N2 A22N3 + +=
2CupN22– 2C14N1N4+
∂N3∂t
--------- R13N1 R31N3– A32– N3 A43N4 2C3N32– C16N1N6++=
N1 N2 N3 N4+ + + 1 2p–( )NEr=
∂N5∂t
--------- R56– N5 A65N6 R65N6 C16N1N6+ + +=
N5 N6+ NYb=
∂N0p∂t
------------ 2R13– N0p A21N1p 2W12N0p– W21N1p+ +=
∂N1p∂t
------------ + 2R13N0p A– 21N1p 2+ W12N0p W– 21N1p 2A21N2p ++=
R13– N1p W12– N1p 2W21N2pN2pτ21p---------+ +
N0p N1p N2p+ + pNEr=
NiNjNi i 1 6→=( )
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ER-YB CODOPED WAVEGUIDE AMPLIFIER
The solution for the paired-induced population when the amplifier is pumped at 980nm is given by:
Figure 2 shows the system of energy levels that are being taken into account for the 1480nm pumping wavelength, as well as the numbering of these levels. In this case the pump energy level belongs to the main level 2 ( ). However, due to the presence of the nonradioactive transitions inside the level , we have named the pump level as "level 3". Note that it should not be confused with the level , when the system is pumped at 980nm region.
Figure 2 Coupled Er+3/Yb+3 system, pumped at 1480nm region
(15)
N0p N( 1p pNEr– 3A21N1pτ21p N1pR13τ21p 2A21pNErτ21p– N1pτ21pW12+ + + +–=
3N1pτ21pW21 2pNErτ21pW21 ) 1 2A21τ21p 2R13τ21p– 2τ21pW12– 2τ21pW21+ +( )⁄–
N1p2N0p R13 W12+( )( )
A21 W21+( )----------------------------------------------=
N2p pNEr N0p– N1p–=
4 13 2⁄4 13 2⁄
4 11 2⁄
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ER-YB CODOPED WAVEGUIDE AMPLIFIER
Note: There are nine relevant energy levels considered (four levels due to the presence of the Erbium ions, two due to the Ytterbium dopant, and three due to the formation of Erbium paired-induced ions). 's and 's are the pump and signal stimulated rates,and the 's are the nonradioactive rate from level i to j. A21 is the fluorescent rate. Cup and C3 are the homogeneous upconversion coefficients. C14 and C16 are the cross-relaxation coefficients. Figure 2 also shows the population densities of the three possible states of an excited pair ( (no ions excited), (one ion excited), and (two ions excited), due to the PIQ effect.
When the system is pumped in the 1480nm region, levels 5 and 6 (Ytterbium levels) are considered to be empty.
It is known that the effects of ESA cannot be disregarded when the pumping wavelength is at 1480nm region, because the ESA cross section is approximately 10% of the peak value of the absorption cross section. The non-radioactive rate embodies the non-radioactive rates between levels and
, in such a way that level is not considered. In this case, the system of rate equations is then described as:
(16)
Rij WijAij
N0p N1p N2p
A434 9 2⁄ 4 11 2⁄→
4 11 2⁄ 4 13 2⁄→ 4 11 2⁄
∂N1∂t
--------- W12N1– R13N1– R31N3 A21N2 W21N2 CupN22 C14N1N4–+ + + +=
∂N2∂t
--------- W12N1 A21N2– W21– N2 A32N3 2CupN22– 2C14N1N4 R24
ESAN2–++=
∂N3∂t
--------- R13N1 R31N3– A32– N3 A43N4+=
N1 N2 N3 N4+ + + 1 2p–( )NEr=
∂N0p∂t
------------ 2R13– N0p A21N1p 2W12N0p– W21N1p+ +=
∂N1p∂t
------------ + 2R13N0p R– 31N1p A– 21N1p 2W12N0p W– 21N1p 2A21N2p ++ +=
R13– N1p 2R31 N2p W– 12N1p 2W21N2pN2pτ21p---------+ + +
N0p N1p N2p+ + pNEr=
376
ER-YB CODOPED WAVEGUIDE AMPLIFIER
and are the simulated rates between levels , at the pump ( ) and signals ( ) wavelengths. are the non-radioactive rates between levels , and A21 is the fluorescence rate. Cup and C14 are the homogeneous upconversion and the cross-relaxation coefficients. is the ESA rate for level 2 and level 4. The presence of the crossed terms in Equation 16 suggests the use of a numeric solution for the populations . However, the system for the paired-induced population is a linear one and can be solved by a straightforward solution. The solution for the paired-induced population when the amplifier is pumped at 1480nm is given by:
In the stationary state, the solutions of the rate Equation 14 and Equation 16 are obtained by nullifying the left side of these equations. As we have previously stated, the systems of Equation 14 and Equation 16 are non-linear due to the presence of the crossed terms and , and must be solved numerically. The stimulated rates and are written as:
(17)
(18)a
Rij Wij i j→ RW Aij i j→
R24ESA
NiNjN1 N6→
N0p pNEr 1 2A21τ21p 2R31τ21p 2τ21pW21+ + +( )( ) 1–( 2A21 2R13τ21p 2R31τ21p– 2τ21pW21 _+ +–⁄–=
2 R13 W12+( ) 1 3A21τ21p R13τ21p 3R31τ21p τ21pW12 3τ21pW21+ + + + +( ) A21 R31 W21+ +( )⁄ )
N1p2N0p R13 W12+( )( )A21 R31 W21+ +( )
-----------------------------------------------=
N2p pNEr N0p– N1p–=
N1N4 N1N6Wij Rij
W12 x y z vs, , ,( )σa12
i vsi( )
hvsi
-------------------- Is+i x y z vs
i, , ,( ) Is_i x y z vsi, , ,( )+( ) +
i 1=
WDM
∑=
+ σa12
j v j( )
hv j-------------------- IASE+
j x y z v j, , ,( ) IASE_j x y z v j, , ,( )+( )
j 1=
M
∑
377
ER-YB CODOPED WAVEGUIDE AMPLIFIER
where when the pumping wavelength is in the 980nm region. When the pumping wavelength is in the 1480nm region, we have and . In Equation 18, it is presumed that the propagation of WDM signals with frequencies and intensities ; pumping intensities ; and ASE(Amplified Spontaneous Emission) with its spectrum discretized in slots of
(18)b
(18)c
(18)d
(18)e
(18)f
(18)g
W21 x y z vs vp, , , ,( )σe21
i vsi( )
hvsi
-------------------- Is+i x y z vs
i, , ,( ) Is_i x y z vsi, , ,( )+( ) +
i 1=
WDM
∑=
+ σep21 vp( )
hvp----------------------- Ip+ x y z vp, , ,( ) Ip_ x y z vp, , ,( )+( ) +
+ σe21
j v j( )
hv j------------------- IASE+
j x y z v j, , ,( ) IASE_j x y z v j, , ,( )+( )
j 1=
M
∑
R13 x y z vp, , ,( )σa13 vp( )
hvp--------------------- Ip+ x y z vp, , ,( ) Ip_ x y z vp, , ,( )+( )=
R31 x y z vp, , ,( )σe31 vp( )
hvp-------------------- Ip+ x y z vp, , ,( ) Ip_ x y z vp, , ,( )+( )=
R56 x y z vp, , ,( )σa56 vp( )
hvp--------------------- Ip+ x y z vp, , ,( ) Ip_ x y z vp, , ,( )+( )=
R65 x y z vp, , ,( )σe65 vp( )
hvp-------------------- Ip+ x y z vp, , ,( ) Ip_ x y z vp, , ,( )+( )=
R24ESA x y z vs vp, , , ,( )
σa24 vsi( )
hvsi
-------------------- Is+i x y z vs
i, , ,( ) Is_i x y z vsi, , ,( )+( ) +
i 1=
WDM
∑=
+ σa24 vp( )
hvp--------------------- Ip+ x y z vp, , ,( ) Ip_ x y z vp, , ,( )+( ) +
+ σa24
j v j( )
hv j-------------------- IASE+
j x y z v j, , ,( ) IASE_j x y z v j, , ,( )+( )
j 1=
M
∑
R24ESA σep21 0= =
σep21 σep31=R56 R65 0= =
vsi I
s +_ Ip +_M
378
ER-YB CODOPED WAVEGUIDE AMPLIFIER
width with intensity . The sign "+" refer to the co-propagant waves, and the sign "-" to the counter-propagant waves. The use of the homogeneous upconversion and the cross-relaxation coefficients and consideration of the PIQ phenomenon in Equation 14 and Equation 16 allows for the adequate modeling of Erbium doped and Ytterbium co-doped waveguides. In general, for Erbium concentrations in the order of 100ppm ("1024 ions/m3) these effects are not important. However, the present applications of optical amplifiers demand Erbium concentrations higher than 1000ppm, and, therefore, such effects cannot be ignored.
Multimode operationThe doped waveguide may present more than one mode at the pump or at the signal frequencies/wavelength. This is common in integrated optics, in which the discontinuity between the refraction index of the core and the cladding is raised on purpose to provoke a high confinement of the pump field and, thus, obtain higher gain [1].
We can presume that the device is externally excited by a beam with gaussian field distribution , with different spatial widths at the pump and signal wavelengths. This supposition is experimentally sustained when a beam that it is being coupled through a set of lenses excites an integrated optical device. Consider that at the wavelengths and (signal and pump wavelength, respectively), and modes with fields distributions can propagate. The input beam can then be described through a modal expansion of the modes present in the waveguide, that is:
where can assume and , and represents the coupling coefficient between the field of the gaussian input beam and the field of the corresponding -th mode. Then, the fraction of the total power allocated in each expansion mode for the pumping and for the signal will be:
(19)
(20)
∆v IASE +_
Φ x y ω, ,( )
λs λp NsNp φi x y λs p⁄, ,( )
Φ x y λs p⁄, ,( )gauss ciφ x y λs p⁄, ,( )ii 1=
Nq
∑=
Nq Ns Np cii
ηpicpicpi∗
cpjcpj∗
j 1=
Np
∑
-------------------------- ηsicsicsi∗
csjcsj∗
j 1=
Ns
∑
------------------------- ==
379
ER-YB CODOPED WAVEGUIDE AMPLIFIER
In this way, for multimode waveguides, the normalized intensity profile for the signals and the pump can be calculated as:
where and are the normalized intensity profiles at the signals and the pump wavelength, respectively.
References:[1] M. Federighi, F. Di Pasquale, "The Effect of Pair-Induced Energy Transfer on the Performance
of Silica Waveguide Amplifiers with High Er+3/Yb+3 Concentration", IEEE Photonics Technology Letters, Vol.7, No.3, pp.303-305, March 1995.
[2] S. Honkanen, S.I. Najafi e W.J. Wang, "Composite Rare-Earth Doped Glass Waveguides", IEEE Electronics Letters, Vol.28, No.8, pp.746-747, abril, (1992).
(21)Ψs p⁄ ηsi pi⁄ Ψs p⁄i
i 1=
Nq
∑=
Ψsi x y,( ) Ψp
i x y,( )
380
SEMICONDUCTOR OPTICAL AMPLIFIER
Semiconductor Optical Amplifier
Performs lumped amplification with traveling wave semiconductor optical amplifiers (SOA). The rate-equation approximation has been used in which the electrical field is described by the wave equation and the carrier density by means of the rate equation. Such model is applicable to describe the amplification of CW and optical pulsed signals.
Ports
Parameters
Main
Physical
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value Units Value range
Injection current 0.15 A [0,1]
Name and description Default value Units Value range
Length 0.0005 m ]0,1e-3]
Width 3e-006 m ]0,500e-6]
Height 8e-008 m ]0,10e-6]
Optical confinement factor 0.15 — ]0,1]
Loss 4000 1/m [0,10e-4]
Differential gain 2.78e-020 m2 ]0,50e-20]
Carrier density at transparency 1.4e+024 m3 ]0,10e-25]
Linewidth enhancement factor 5 — [–30,30]
Recombination coefficient A 143e+008 1/s ]0,1e-15]
Recombination coefficient B 1e-016 m3/s ]0,1e-10]
381
SEMICONDUCTOR OPTICAL AMPLIFIER
Numerical
Simulation
Technical backgroundThis module performs lumped amplification with traveling wave semiconductor optical amplifiers (SOA) [AGR, 1993] and [SHI, 1994]. The rate-equation approximation has been used in which the electrical field is described by the wave equation and the carrier density by means of the rate equation [1-4]. Such model is applicable to describe the amplification of CW and optical pulse signals. The pulse widths have to be much larger than the intraband relaxation time that governs the dynamics of the induced polarization. Typically, the intraband relaxation time is 0.1 ps. Therefore, the model can be used for pulse widths larger than 1 ps [3-4].
The basic approximation done in the wave equation for the electrical field in the SOA is a linear dependence between the carrier induced susceptibility and the carrier density [6-8]. In the framework of this approximation the material gain coefficient gm is related to carrier density N(t) by,
(1)
where N0 is the carrier density at transparency point and Ag is the differential gain coefficient [2].
Recombination coefficient C 3e-041 m6/s [0,1e-30]
Initial carrier density 3e+024 m–3 ]0,10e-25]
Name and description Value Units Mode
Integration type Runge Kutta 4th order — Normal
Relative tolerance 1e-006 — Normal
Maximum number of steps 100000 — Normal
Interpolation type Polynomial — Normal
Order of polynomial 4 — Normal
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False]
Name and description Default value Units Value range
gm t( ) Ag N t( ) N0–[ ]=
382
SEMICONDUCTOR OPTICAL AMPLIFIER
The net gain coefficient g is related to the material gain gm by,
(2)where α is an effective loss coefficient which includes scattering and absorption losses and Γ is the optical confinement factor defined as a fraction of the mode power within the active layer.
It is also assumed that the amplifier supports a single wave-guide mode and it does not change the polarization state during the amplification. Linearly polarized input light is presumed. The group velocity dispersion in the SOA is neglected. The amplified spontaneous emission noise is not taken into account. In the framework of these assumptions, the gain G for a traveling wave SOA for a distance z is:
(3)
The carrier density rate equation expresses the conservation of carriers inside the active layer. It takes into account the current density and the net rate of carrier generation and recombination averaged over the active layer. The recombination rate consists of spontaneous and stimulated recombinations. The spontaneous recombination rate includes the radiative and nonradiative components. The nonradiative recombination takes into account the Auger recombination, which is generally the dominant nonradiative process in long wavelength lasers. The spontaneous recombination rate can be characterized by a quantity known as the carrier lifetime :
(4)
where RA is the non-radiative coefficient due to recombination at defects and traps, RB is the spontaneous radiative recombination coefficient, and RC is the Auger recombination coefficient.
Neglecting the carrier diffusion, the amplified spontaneous emission noise and the shot noise the equation for the carrier density N(t) is [3-4]:
(5)
where I is the light intensity, J is the injection current density, q is the electron charge, h is the Planck’s constant, f is the light frequency, t is the time, and d is the active layer thickness.
Equation 5 can be rewritten as:
(6)
where Ip is the pump current (or injection current), V = L w d is the volume of the active region, and L and w are the length and the width of the amplifier respectively.
g t( ) Γgm t( ) α–=
G t z,( ) e g t( )z[ ]=
τs
N t( )τs
---------- RAN t( ) RBN2 t( ) RcN3 t( )+ +=
dNdt------- J
qd------ N
τs----Ag N N0–( ) I
hf-----–=
dNdt-------
IpqV------- N
τs----– ΓAg N t( ) N0–( )P N t,( )L
Vhf--------------------–=
383
SEMICONDUCTOR OPTICAL AMPLIFIER
The amplifier power P(N,t), which is the average power over the length of the amplifier, is by:
(7)
The output optical field is:
(8)
where δ is the linewidth enhancement factor.
This parameter takes into account the coupling between the gain and refractive index of the amplifying medium. The output power to parameterized signals is:
(9)
To include multiple frequency bands, the term P(N,t) / f in Equation 6 should be substituted with:
(10)
where fk is the center frequency for each frequency band.
Basic physical effects described by the model for single wavelength channel are gain saturation, gain-saturation induced self-phase modulation, and gain recovery [3-5].
Gain-saturation induced self-phase modulation is responsible for important changes in the spectrum of amplified pulses:• appearance of multi-peak spectral structure• red shift of the spectrum• appearance of the positive chirp
In addition, the shape and the spectral pulse distortions depend on the shape and the initial frequency pulse modulation.
Gain saturation and gain recovery effects for Gaussian, super Gaussian, and chirped Gaussian pulses for an SOA are in OptiSystem Tutorials — Introduction to the
P N t,( ) P N z,( )L
----------------- zd0
L
∫PinG t z,( )
L-----------------------
0
L
∫ Pine g t( )L[ ] 1–
g t( )-----------------------= = =
Eout t( ) Ein t( )e1 jδ+( )g t( )L[ ]
2------------------------------
=
Pout Pine g t( )L[ ]=
Pk N t,( )fk
------------------k∑
384
SEMICONDUCTOR OPTICAL AMPLIFIER
basic gain saturation and gain recovery characteristics of the SOA. A strong agreement with [3-4] can be identified in this section.
Generally, gain saturation effect is a serious obstacle for an SOA as an inline amplifier. In the case of single-channel transmission, gain saturation effect leads to a pattern effect. Pattern effect is demonstrated for 10 Gb/s average soliton transmission over a 500 km SMF optical link in OptiSystem Tutorials — Basic application of the OSA as an inline amplifier.
In the case of multi-channel transmission, gain saturation effect leads to inter-channel crosstalk. Independent of the problems connected with applying an SOA as an inline amplifier, they are used near the 1.3 wavelength in SMF. The fundamental reason for this is the possibility of avoiding the large group velocity dispersion of SMF at 1.55 [6-11]. This idea following [11] is demonstrated in OptiSystem Tutorials — Basic application of the OSA as an inline amplifier.
Some undesirable properties of applying an SOA as an inline amplifier have found other applications. For example, the positive pulse chirp created during the process of amplification can be used for pulse compression if you can propagate the pulse in a dispersive media with a proper sign of the group velocity dispersion. Pulse compression with the help of SMF following [12] is described in OptiSystem Tutorials — Applying the gain saturation properties of the SOA to obtain pulse compression.
SOAs have found new applications as wavelength converters, fast switches for wavelength routing in WDM networks, and nonlinear elements for clock recovery and demultiplexing in TDM systems [5, 13-14]. In OptiSystem Tutorials — Application of the SOA as a wavelength converter, SOA wavelength conversion is demonstrated based on four-wave mixing and cross-saturation effects.
References
[1] M.J. Adams, H.J. Westlake, M.J. O’Mahony, I.D. Henning, “A Comparison of Active and Passive Optical Bistability in Semiconductors”, IEEE Journal of Quantum Electronics, Vol. QE-21, N 9, September 1985.
[2] M.J. O’Mahoney, “Semiconductor Laser Optical Amplifier for use in Fiber Systems,” Journal of Lightwave Technology, Vol. 6, N 4, April 1988.
[3] G.P. Agrawal and N.A. Olsson, “Self-Phase Modulation and Spectral Broadening of optical pulses in semiconductor Laser Amplifiers”, IEEE J. of Quantum Electronics, Vol. QE-25, N 11, pp. 2297-2306, November 1989.
[4] N.A. Olsson and G.P. Agrawal, “Spectral shift and distortion due to self-phase modulation of picosecond pulses in 1.5 mm optical amplifiers”, Appl. Phys. Lett. 55, N 1, pp. 13-15, July 1989.
[5] G.P. Agrawal, “Fiber-Optic Communication Systems”, Second edition, John Wiley & Sons, Inc. 1997.
µm
µm
385
SEMICONDUCTOR OPTICAL AMPLIFIER
[6] J.J. Reid, C.T.H.F. Liendenbaum, L.F. Tiemeijer, A.J. Boot, P.I. Kuindersma, I. Gabitov, and A. Mattheus, in Proceedings of the 20th European Conference on Optical Communication (Instituto Internationale delle Communicaziono, Genova, Italy, 1994).
[7] A. Mecozzi, “Optics Letters,” 20, 1616-1618, 1995.
[8] S. Wabnitz, “Optics Letters,” 20, 1979-1982, 1995.
[9] S.K. Turitsyn, Phys. Rev. E 54, R3125, 1996.
[10] I.M. Uzunov, M. Golles, and F. Lederer, “Optics Letters,” 22, 1406-1408, 1997.
[11] M. Settembre, F. Matera, V. Hagele, I. Gabitov, A.W. Mattheus, and S. Turitsyn, “Journal of Lightwave Technology,” Vol. 15, pp. 962-967, 1997.
[12] G.P. Agrawal and N.A. Olsson, “Optics Letters,” 14, 500-502, 1989.
[13] T. Durhuus, B. Mikkelsen, and K.E. Stubkjaer, “Journal of Lightwave Technology,” Vol. 10, pp. 1056-1065, 1992.
[14] T. Durhuus, B. Mikkelsen, C. Joergensen, S.L. Danielsen, and K.E. Stubkjaer, “Journal of Lighwave Technology,” Vol. 14, pp. 942-954, 1992.
Technical references
[AGR, 1993] G.P. Agrawal and N.K. Dutta, “Semiconductor lasers,” Second edition, International Thomson Publishing, Inc., 1993.
[BAS, 1992] S.P. Bastien, H. R. D. Sunak, B. Sridhar, V. E. Kalomiris “Temporal, spatial and spectral modeling of erbium doped fiber amplifiers”, SPIE – Physic and Simulations of Optoelectronic Devices, pp. 2-11, 1992
[BUR, 1998] J. Burgmeier, A. Cords, R. März, C. Schäffer, B. Stummer “A black box model of EDFA’s operating in WDM systems”, Journal of LIghtwave Technology, Vol. 16, N. 7, pp. 1271-1275, 1998
[DES, 1994] E. Desurvire, “Erbium-Doped Fiber Amplifiers – Principles and Applications”, John Wiley & Sons, Inc., USA, 1994
[GIL, 1991] C.R. Giles, E. Desurvire, "Modeling erbium-doped fiber amplifiers," Journal of LIghtwave Technology, Vol. 9, N. 2, pp. 271-283, 1991
[KAR, 1998] J. A. Vallés, “Analysis of channel addition/removal response in all-optical gain-controlled cascade of erbium-doped fiber amplifiers”, Journal of Lightwave Technology, Vol. 16, N. 10, pp. 1795-1803, 1998
[OKO, 1990] T. Okoshi, "Exact Noise-Figure Formulas for Optical Amplifiers and Amplifier-Fiber Cascaded Chains," IEEE/OSA Topical Meeting on Optical Amplifiers and their Applications, Monterrey, PDP11, 1990
[SHI, 1994] S. Shimada, H. Ishio, “Optical Amplifiers and their Applications”, John Wiley & Sons, Chichester, 1994.
386
LIMITING AMPLIFIER
Limiting Amplifier
This component is an electrical limiting amplifier. The minimum and maximum output signal values are user-defined parameters.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Units Value range
Max. output voltageThe maximum value of the output signal.
0.5 Volt ]INF,+INF[
Min. output voltageThe minimum value of the output signal.
-0.5 Volt ]INF,+INF[
Name and description Default value
Units Value range
EnabledDetermines whether or not the component is enabled
True —
387
LIMITING AMPLIFIER
Technical backgroundThis component measures the input signals and compares the amplitude with the parameters Max. output voltage and Min. output voltage. If the signal value is outside of the range between the min and max values, the signal will be clipped. This component does not affect the noise amplitude, only the signal amplitude.
388
ELECTRICAL AMPLIFIER
Electrical Amplifier
Electrical amplifier with additive thermal noise.
Ports
Parameters
Main
Simulation
Noise
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Units Value range
Gain 10 dB [-1e+100, 1e+100]
Name and description Default value
Units Value range
EnabledDetermines whether or not the component is enabled
True —
Name and description Default value
Default unit Units Value range
Include noise Yes — —
PSDDetermines whether the power is defined as PSD or the average power in time
Yes — —
389
ELECTRICAL AMPLIFIER
Random numbers
Noise powerValue of the PSD or the average power
–60 dBm W, mW, dBm [-1e+100, 1e+100]
Add noise to signal No — —
Name and description Default value
Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
Name and description Default value
Default unit Units Value range
390
TRANSIMPEDANCE AMPLIFIER
Transimpedance Amplifier
DescriptionThis component is an electrical transimpedance amplifier with user defined noise figure. It has linear gain and additive thermal noise.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Units Value range
Voltage gainThe linear gain of the amplifier.
600 Ohm, kOhm, dB
[0,+INF[
Include NoiseDefines whether the noise will included in the output
True — True, false
Noise figureAmplifer noise figure
6 dB [0,+INF]
Input noise densityMinumum input noise
4e-21 A/Hz-1, W/Hz, mW/Hz, dBm/Hz
[0,+INF]
Name and description Default value
Units Value range
EnabledDetermines whether or not the component is enabled
True —
391
TRANSIMPEDANCE AMPLIFIER
Noise
Random numbers
Technical backgroundThis component amplifies the input electrical signal and adds thermal noise to the signal output. The value of the thermal noise is calculated from the input SNR and the user defined parameter Noise figure.
Since OptiSystem can have noiseless electrical signals, the parameter Input noise density assures a minimum value for the noise floor at the input signal.
Name and description Default value
Default unit Units Value range
Include noise Yes — —
PSDDetermines whether the power is defined as PSD or the average power in time
Yes — —
Noise powerValue of the PSD or the average power
–60 dBm W, mW, dBm [-1e+100, 1e+100]
Add noise to signal No — —
Name and description Default value
Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
392
AGC AMPLIFIER
AGC Amplifier
This component is an electrical limiting amplifier with user defined noise figure. It inputs signal dependent gain and additive thermal noise.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Units Value range
Output voltageThe peak value of the output signal.
0.005 Volt [0,+INF[
Include NoiseDefines whether the noise will included in the output
False — True, false
Noise figureAmplifer noise figure
6 dB [0,+INF]
Input noise densityMinumum input noise
4e-21 A/Hz-1, W/Hz, mW/Hz, dBm/Hz
[0,+INF]
Name and description Default value
Units Value range
EnabledDetermines whether or not the component is enabled
True —
393
AGC AMPLIFIER
Noise
Random numbers
Technical backgroundThis component amplifies/attenuates the input electrical signal and adds thermal noise to the signal output. The output signal will have a peak value defined by the parameter Output voltage. The value of the thermal noise is calculated from the input SNR and the user defined parameter Noise figure.
Since OptiSystem can have noiseless electrical signals, the parameter Input noise density assures a minimum value for the noise floor at the input signal.
Name and description Default value
Default unit Units Value range
Include noise Yes — —
PSDDetermines whether the power is defined as PSD or the average power in time
Yes — —
Noise powerValue of the PSD or the average power
–60 dBm W, mW, dBm [-1e+100, 1e+100]
Add noise to signal No — —
Name and description Default value
Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
394
Filters LibraryThis section contains information on the following filters.
Optical
• Optical IIR filter• Measured Optical filter• Measured Group Delay Optical filter• Rectangle Optical filter• Trapezoidal Optical filter• Gaussian Optical filter• Butterworth Optical filter• Bessel Optical filter• Fabry Perot Optical filter• Acousto Optical filter• Mach-Zehnder Interferometer• Inverted Optical IIR filter• Inverted Rectangle Optical filter• Inverted Trapezoidal Optical filter• Inverted Gaussian Optical filter• Inverted Butterworth Optical filter• Inverted Bessel Optical filter
FBG
• Fiber Bragg Grating (FBG)• Uniform Fiber Bragg Grating• Ideal Dispersion Compensation FBG
395
Electrical
• Low Pass IIR filter (Electrical)• Low Pass Rectangle filter (Electrical)• Low Pass Gaussian filter (Electrical)• Low Pass Butterworth filter (Electrical)• Low Pass Bessel filter (Electrical)• Low Pass Chebyshev filter (Electrical)• Low Pass RC filter (Electrical)• Low Pass Raised Cosine filter (Electrical)• Low Pass Cosine Roll Off filter (Electrical)• Low Pass Squared Cosine Roll Off filter (Electrical)• Band Pass IIR filter (Electrical)• Measured filter (Electrical)• Band Pass Rectangle filter (Electrical)• Band Pass Gaussian filter (Electrical)• Band Pass Butterworth filter (Electrical)• Band Pass Bessel filter (Electrical)• Band Pass Chebyshev filter (Electrical)• Band Pass RC filter (Electrical)• Band Pass Raised Cosine filter (Electrical)• Band Pass Cosine Roll Off filter (Electrical)• Band Pass Square Cosine Roll Off filter (Electrical)• S Parameters Measured filter (Electrical)
Filter Analyzers
• Optical Filter analyzer• Electrical Filter analyzer
396
OPTICAL IIR FILTER
Optical IIR filter
Infinite impulse response filter (IIR) for optical signals.
Ports
Parameters
Main
Numerator coefficients
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
193.1 THz Hz, THz, nm [0,+INF[
Filter sample rate
User-defined sample rate independent from the signal sample rate
1000 GHz Hz, GHz, THz, nm
[1e-9,+INF[
Additional loss
Loss applied to the signal after filtering
0 dB — [0,+INF[
Filter coefficients type
Type of numerator and denominator coefficients for the filter
Z domain — — Frequency domain, Poles and zeros, Z domain
Name and description Default value Units Value range
Numerator coefficients
Number of numerator coefficients
3 — [1,+INF[
Numerator[0].real 0.64 — ]-INF,+INF[
397
OPTICAL IIR FILTER
Denominator coefficients
Simulation
Numerator[0].imag 0 — ]-INF,+INF[
Numerator[1].real 1.28 — ]-INF,+INF[
Numerator[1].imag 0 — ]-INF,+INF[
Numerator[2].real 0.64 — ]-INF,+INF[
Numerator[2].imag 0 — ]-INF,+INF[
Name and description Default value Units Value range
Denominator coefficients
Number of denominator coefficients
3 — [1,+INF[
Denominator[0].real 5.05 — ]-INF,+INF[
Denominator[0].imag 0 — ]-INF,+INF[
Denominator[1].real –4.75 — ]-INF,+INF[
Denominator[1].imag 0 — ]-INF,+INF[
Denominator[2].real 2.26 — ]-INF,+INF[
Denominator[2].imag 0 — ]-INF,+INF[
Name and description Default value
Default unit Units Value range
Enabled
Determines whether or not the component is enabled
True — — True, False
Resample
Determines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rate
New output signal sample rate
500 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value Units Value range
398
OPTICAL IIR FILTER
Noise
Technical backgroundThe infinite impulse response filter is a recursive digital filter. The transfer function can be expressed in the z domain as:
where H(z) is the filter transfer function in the Z domain, α is the parameter for Additional loss, N is the parameter number of Numerator coefficients, an are the coefficients for the numerator, M is the parameter number of Denominator coefficients, and bm are the coefficients for the denominator.
Also,
where fc is the filter center frequency defined by the parameter Frequency, fs is the parameter Filter sample rate, and f is the frequency.
According to the parameter Filter coefficients type, the filter transfer function can be given in the z (Z domain) or in the frequency domain. In the second case, the filter is determined by the numerator and the denominator polynomial, which can be expressed by their roots (Poles and zeros) or by the polynomial coefficients (in Frequency domain).
Name and description Default value
Units Value range
Noise threshold
Minimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamic
Threshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
H z( )
α anz n–
n 0=
N
∑
bmz m–
m 0=
M
∑------------------------=
z j2π f fc–( ) fs⁄( )exp=
399
MEASURED OPTICAL FILTER
Measured Optical filter
Filter based on measurements.
Ports
Parameters
Main
Measurements
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value
Default unit Units Value range
User-defined frequency
Determines whether you can define the filter center frequency or use the value from the measurements
True — — True, False
Frequency
User-defined filter center frequency
193.1 THz Hz, THz, nm [0,+INF[
Name and description Default value
Units Value range
File frequency unit
Determines the frequency unit of the file with the measurements
Hz — Hz, THz, m, nm
File format
Determines the format of the file with the measurements
Power — Power, Power Phase, Real Imag, phase
Linear scale
Determines whether the measured data is in linear scale or not
True — ]-INF,+INF[
400
MEASURED OPTICAL FILTER
Numerical
Simulation
Noise
Filter filename
Filename with the measured data
Filter.dat — —
Name and description Default value
Units Value range
Interpolation
Determines the interpolation algorithm for the measured data
Linear — Linear, Cubic
Name and description Default value
Default unit Units Value range
Enabled
Determines whether or not the component is enabled
True — — True, False
Resample
Determines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rate
New output signal sample rate
500 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value
Units Value range
Noise threshold
Minimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamic
Threshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
Name and description Default value
Units Value range
401
MEASURED OPTICAL FILTER
Graphs
Technical backgroundThe input file is formatted containing two items per line — frequency and filter measurement. The parameter File frequency unit determines the frequency or wavelength unit of the first item. It can be in Hz, THz, m, or nm.
According to the parameter File format, the second item can be one value (Power or Phase) or two values (Power and Phase or Real and Imag):
Power (Phase is set to zero, assuming frequency unit is THz)
Power Phase
Name and description X Title Y Title
Filter transmission - real part Frequency (Hz) Amplitude (a.u.)
Filter transmission - imag part Frequency (Hz) Amplitude (a.u.)
193.10 0
193.11 0.5
193.12 0.5
193.13 0
...
193.10 0 0
193.11 0.5 3.14
193.12 0.5 3.14
193.13 0 0
...
402
MEASURED OPTICAL FILTER
Real Imag
Phase (Power is set to one)
The parameter User defined frequency determines if you can enter the center frequency. This means that the filter data is shifted from the measured center frequency to the user center frequency that you define in the parameter Frequency.
193.10 0
193.11 –0.5 7.9e-4
193.12 –0.5 7.9e-4
193.13 0 0
...
193.10 0
193.11 3.14
193.12 3.14
193.13 0
...
403
MEASURED GROUP DELAY OPTICAL FILTER
Measured Group Delay Optical filter
Loads files with the filter amplitude and group delay ripple measurements. This FBG was designed mainly for dispersion compensation.
Ports
Parameters
Main
Measurements
Name and description Port type Signal type
Input Input Optical
Transmission Output Optical
Name and description Default value
Default unit Units Value range
User-defined frequency
Determines whether you can define the filter center frequency or use the value from the measurements
True — — True, False
Frequency
User-defined filter center frequency
193.1 THz Hz, THz, nm [0,+INF[
Name and description Default value
Units Value range
File frequency unit
Determines the frequency unit of the file with the measurements
m — nm, m
Group delay unit
Determines the group delay unit of the file with the measurements
ps — s, pss
404
MEASURED GROUP DELAY OPTICAL FILTER
Numerical
Simulation
Noise
File format
Determines the format of the file with the measurements
Delay — Power, Power Delay, Delay
Linear scale
Determines whether or not the measured data is in linear scale
True — True, False
Filename
Filename with the measured data
GroupDelay.dat — —
Name and description Default value
Units Value range
Interpolation Linear — Linear, Cubic
Name and description Default value
Default unit Units Value range
Enabled
Determines whether or not the component is enabled
True — — True, False
Resample
Determines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rate
New output signal sample rate
500 GHz Hz, GHz, THz [1e-9,+INF[
Name and description Default value
Units Value range
Noise threshold
Minimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamic
Threshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
Name and description Default value
Units Value range
405
MEASURED GROUP DELAY OPTICAL FILTER
Graphs
Technical backgroundThis model is a filter with measured group delay. The filter transfer function is
where f is the frequency dependence phase of the filter.
The group delay is defined by Equation 1:
Writing Equation 2 as a function of wavelength:
where c is the speed of light.
You define by entering the table with the measurements.
Name and description X Title Y Title
Filter transmission — Amplitude Wavelength (m) Amplitude (a.u.)
Filter transmission — Phase Wavelength (m) Phase (rad)
(1)
(2)
(3)
H f( ) ejφ f( )=
τ f( ) 12π------dφ
df------–=
τ λ( ) λ2
2πc---------dφ
dλ------–=
τ
406
MEASURED GROUP DELAY OPTICAL FILTER
Typically, this measurement looks like the graph in Figure 1, where X is the wavelength in nm and Y is the group delay in ps:
Figure 1 Group delay measurement
Calculate the phase from this curve in order to calculate the filter transfer function.
Phase calculationThe phase is calculated with Equation 3:
File formatThe input file is formatted with two items per line — the wavelength and the filter measurement. The parameter File frequency unit determines the wavelength unit of the first item, and can be in m or in nm. The parameter Group delay unit determines the group delay unit, and can be in s or in ps.
According to the parameter File format, the second item can be one value (Power or Delay) or two values (Power and Delay).
(4)φ 2πc τ λ( ) 1λ2----- λd∫–=
407
MEASURED GROUP DELAY OPTICAL FILTER
Example of input file:
Power (Delay is set to zero)
Power Delay
Delay (Power is set to one)
The parameter User defined frequency determines if you can enter the center frequency. This means that the filter data is shifted from the measured center frequency to the user center frequency that you define in the parameter Frequency.
References[1] Madsen, C. K. and Zhao, J H., Optical Filter Design and Analysis: A Signal Processing
Approach. John Wiley & Sons, USA, (1999).
1551 0
1551.1 0.5
1551.2 0.5
1551.3 0
...
1551 0 0
1551.1 0.5 –10
1551.2 0.5 –20
1551.3 0 –30
...
1551 0
1551.1 –10
1551.2 –20
1551.3 –30
...
408
RECTANGLE OPTICAL FILTER
Rectangle Optical filter
Optical filter with a rectangle frequency transfer function.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
193.1 THz Hz, THz, nm [0,+INF[
Bandwidth
3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
]0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
409
RECTANGLE OPTICAL FILTER
Simulation
Noise
Technical backgroundThe filter transfer function is:
where H(f) is the filter transfer function, α is the parameter Insertion loss, d is the parameter Depth, fc is the filter center frequency defined by the parameter Frequency, B is the parameter Bandwidth , and f is the frequency.
Name and description Default value
Default unit Units Value range
Enabled
Determines whether or not the component is enabled
True — — True, False
Resample
Determines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rate
New output signal sample rate
500 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value
Units Value range
Noise threshold
Minimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamic
Threshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
H f( )α,d,
=fc B 2 f fc B 2⁄+< <⁄–
otherwise
410
TRAPEZOIDAL OPTICAL FILTER
Trapezoidal Optical filter
Optical filter with a trapezoidal frequency transfer function.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
193.1 THz Hz, THz, nm [0,+INF[
Zero dB bandwidth
Filter bandwidth at 0 dB
10 GHz Hz, GHz, THz, nm
]0,+INF[
Bandwidth
Filter bandwidth at cutoff magnitude
100 GHz Hz, GHz, THz, nm
]0,+INF[
Cutoff magnitude
Attenuation at the filter bandwidth
3 dB — [0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
411
TRAPEZOIDAL OPTICAL FILTER
Simulation
Noise
Technical backgroundThe filter transfer function is:
where
and H(f) is the filter transfer function, α is the parameter Insertion loss, fc is the filter center frequency defined by the parameter Frequency, B is the parameter Bandwidth at the cutoff magnitude, B0dB is the parameter Zero dB bandwidth, and f is the frequency.
Name and description Default value
Default unit Units Value range
Enabled
Determines whether or not the component is enabled
True — — True, False
Resample
Determines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rate
New output signal sample rate
500 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value
Units Value range
Noise threshold
Minimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamic
Threshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
H f( )α.10
1 A–10B B0dB–------------------------------- f f2–( )
,α,
α.101 A–
10B B0dB–------------------------------- f f1–( )
,
=
f f2>
f1 fc f2< <
f f1<
f1 fc B0dB 2⁄–=f2 fc B0dB 2⁄+=
412
GAUSSIAN OPTICAL FILTER
Gaussian Optical filter
Optical filter with a Gaussian frequency transfer function.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
193.1 THz Hz, THz, nm [0,+INF[
Bandwidth
3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
]0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Order
Order of the function
1 — — [1,100]
413
GAUSSIAN OPTICAL FILTER
Simulation
Noise
Technical backgroundThe filter transfer function is:
where H(f) is the filter transfer function, α is the parameter Insertion loss, fc is the filter center frequency defined by the parameter Frequency, B is the parameter Bandwidth, N is the parameter Order, and f is the frequency.
Name and description Default value
Default unit Units Value range
Enabled
Determines whether or not the component is enabled
True — — True, False
Resample
Determines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rate
New output signal sample rate
500 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value
Units Value range
Noise threshold
Minimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamic
Threshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
H f( ) αe 1n 2–
2 f fc–( )2N
B--------------------------
=
414
BUTTERWORTH OPTICAL FILTER
Butterworth Optical filter
Optical filter with a Butterworth frequency transfer function.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
193.1 THz Hz, THz, nm [0,+INF[
Bandwidth
3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
]0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Order
Order of the function
1 — — [1,100]
415
BUTTERWORTH OPTICAL FILTER
Simulation
Noise
Technical backgroundButterworth filters are a class of all-pole filters with maximally flat frequency response. The filter transfer function is:
where
and H(f) is the filter transfer function, α is the parameter Insertion loss, fc is the filter center frequency defined by the parameter Frequency, B is the parameter Bandwidth, N is the parameter Order, and f is the frequency.
Name and description Default value
Default unit Units Value range
Enabled
Determines whether or not the component is enabled
True — — True, False
Resample
Determines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rate
New output signal sample rate
500 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value
Units Value range
Noise threshold
Minimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamic
Threshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
H f( ) α B 2⁄( )N
j f fc–( ) pk–( )k 0=
N 1–
∏------------------------------------------=
pkB2--- e
jπ2--- 1 2k 1+
N---------------+
⋅=
416
BESSEL OPTICAL FILTER
Bessel Optical filter
Optical filter with a Bessel frequency transfer function.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
193.1 THz Hz, THz, nm [0,+INF[
Bandwidth
3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
]0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Order
Order of the function
1 — — [1,100]
417
BESSEL OPTICAL FILTER
Simulation
Noise
Technical backgroundBessel filters have a transfer function of the form:
α is the parameter Insertion loss, N is the parameter Order, and
is a normalizing constant and BN(s) is an nth-order Bessel polynomial of the form
where
Name and description Default value
Default unit Units Value range
Enabled
Determines whether or not the component is enabled
True — — True, False
Resample
Determines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rate
New output signal sample rate
500 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value
Units Value range
Noise threshold
Minimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamic
Threshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
H s( ) αd0
BN s( )-------------=
d02N( )!
2N N!⋅----------------=
BN s( ) dksk
k 0=
N
∑=
dk2N k–( )!
2N k– k! N k–( )!⋅---------------------------------------=
418
BESSEL OPTICAL FILTER
and
where fc is the filter center frequency defined by the parameter Frequency, B is the parameter Bandwidth, and Wb denotes the normalized 3 dB bandwidth and can be approximated by
for N≥ 3
s j 2 f fc–( ) wb⋅B
----------------------------- =
wb 2N 1–( ) 2ln⋅≈
419
FABRY PEROT OPTICAL FILTER
Fabry Perot Optical filter
Optical filter with a Fabry Perot frequency transfer function.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
193.1 THz Hz, THz, nm [0,+INF[
Bandwidth
3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
]0,+INF[
Free spectral range 500 GHz Hz, GHz, THz, nm
]0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
420
FABRY PEROT OPTICAL FILTER
Simulation
Noise
Technical backgroundThe filter transfer function is:
where H(f) is the filter transfer function, α is the parameter Insertion loss, fc is the filter center frequency defined by the parameter Frequency, B is the parameter Bandwidth, and f is the frequency.
where
where FSR is the parameter Free spectral range.
Name and description Default value
Default unit Units Value range
Enabled
Determines whether or not the component is enabled
True — — True, False
Resample
Determines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rate
New output signal sample rate
500 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value
Units Value range
Noise threshold
Minimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamic
Threshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
H f( ) α 1 R–
1 R∗e2πJ
f fc–( )
B-----------------
–
-----------------------------------=
R2 πB
FSR-----------
2
2 πBFSR-----------+
2
4––+
2---------------------------------------------------------------------------=
421
ACOUSTO OPTICAL FILTER
Acousto Optical filter
Optical filter with an Acousto optical frequency transfer function.
Ports
Parameters
Main
Channels
Name and description Port type Signal type
Input Input Optical
Transmission Ouput Optical
Reflection Output Optical
Name and description Default value
Default unit Units Value range
Bandwidth
3 dB filter bandwidth
100 GHz Hz, GHz, THz, nm
]0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Name and description Default value
Default unit Units Value range
Number of channels
Number of filter channels
4 — — [1,+INF[
Frequency[0]
Filter center frequency 0
193.1 THz Hz, THz, nm [0,+INF[
422
ACOUSTO OPTICAL FILTER
Simulation
Noise
Frequency[1]
Filter center frequency 1
193.2 THz Hz, THz, nm [0,+INF[
Frequency[2]
Filter center frequency 2
193.3 THz Hz, THz, nm [0,+INF[
Frequency[3]
Filter center frequency 3
193.4 THz Hz, THz, nm [0,+INF[
Name and description Default value
Default unit Units Value range
Enabled
Determines whether or not the component is enabled
True — — True, False
Resample
Determines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rate
New output signal sample rate
500 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value
Units Value range
Noise threshold
Minimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamic
Threshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
Name and description Default value
Default unit Units Value range
423
ACOUSTO OPTICAL FILTER
Technical backgroundThe filter transfer function is described using a sum of power transfer functions of the type
where k=2.78311475, Hn(f) is the filter transfer function for each channel, α is the parameter Insertion loss, fnc is the filter center frequency defined by the parameter Frequency for each channel n, B is the parameter Bandwidth, and f is the frequency.
Hn f( ) αk f fc–( ) B⁄( )sin
k f fnc–( ) B⁄( )---------------------------------------=
424
MACH-ZEHNDER INTERFEROMETER
Mach-Zehnder Interferometer
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Output 1 Output Optical
Output 2 Output Optical
Name and description Default value
Default unit Units Value range
Delay
Time delay of the first path
0 s s, ms, ns [1e-9,+INF[
Coupling coefficient
Cross coupling coefficients
0.5 — — [0,1]
Additional loss
Loss applied to the signal at the output
0 dB — [0,+INF[
425
MACH-ZEHNDER INTERFEROMETER
Technical backgroundThe Mach-Zehnder filter is tunable and consists of two couplers, which are connected by two waveguides. The filter transfer function for such a case is defined by:
where H(f) is the filter transfer function and f is the frequency.
with:
where α is the parameter Coupling coefficient, and
where t is the parameter time Delay.
H f( ) Hcoupler f( )HτHcoupler f( )=
Hcoupler f( )1 α–
j α=
j α
1 α–
Hτ f( ) e j2πfτ–
0= 0
1
426
INVERTED OPTICAL IIR FILTER
Inverted Optical IIR filter
Inverted infinite impulse response filter (IIR) for optical signals.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
193.1 THz Hz, THz, nm [0,+INF[
Filter sample rate
User-defined sample rate independent from the signal sample rate
10 GHz Hz, GHz, THz, nm
[1e-9,+INF[
Additional loss
Loss applied to the signal after filtering
0 dB — [0,+INF[
Filter coefficients type
Type of numerator and denominator coefficients for the filter
Z domain — — Frequency domain, Poles and zeros, Z domain
427
INVERTED OPTICAL IIR FILTER
Numerator coefficients
Denominator coefficients
Simulation
Name and description Default value Units Value range
Numerator coefficients
Number of numerator coefficients
3 — [1,+INF[
Numerator[0].real 0.64 — ]-INF,+INF[
Numerator[0].imag 0 — ]-INF,+INF[
Numerator[1].real 1.28 — ]-INF,+INF[
Numerator[1].imag 0 — ]-INF,+INF[
Numerator[2].real 0.64 — ]-INF,+INF[
Numerator[2].imag 0 — ]-INF,+INF[
Name and description Default value Units Value range
Denominator coefficients
Number of denominator coefficients
3 — [1,+INF[
Denominator[0].real 5.05 — ]-INF,+INF[
Denominator[0].imag 0 — ]-INF,+INF[
Denominator[1].real –4.75 — ]-INF,+INF[
Denominator[1].imag 0 — ]-INF,+INF[
Denominator[2].real 2.26 — ]-INF,+INF[
Denominator[2].imag 0 — ]-INF,+INF[
Name and description Default value
Default unit Units Value range
Enabled
Determines whether or not the component is enabled
True — — True, False
Resample
Determines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rate
New output signal sample rate
500 GHz Hz, GHz, THz ]0,+INF[
428
INVERTED OPTICAL IIR FILTER
Noise
Technical backgroundThe transfer function is of the form:
where H(f) is the filter transfer function, α is the parameter Insertion loss, HIIR(f) is the IIR filter transfer function (see Optical IIR filter), and f is the frequency.
Name and description Default value
Units Value range
Noise threshold
Minimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamic
Threshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
H f( ) α 1 HIIR f( )– 2=
429
INVERTED RECTANGLE OPTICAL FILTER
Inverted Rectangle Optical filter
Optical filter with an inverted rectangle frequency transfer function.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
193.1 THz Hz, THz, nm [0,+INF[
Bandwidth
3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
]0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
430
INVERTED RECTANGLE OPTICAL FILTER
Simulation
Noise
Technical backgroundThe transfer function is of the form:
where H(f) is the filter transfer function, α is the parameter Insertion loss, HRect(f) is the rectangle filter transfer function (see Rectangle Optical filter), and f is the frequency.
Name and description Default value
Default unit Units Value range
Enabled
Determines whether or not the component is enabled
True — — True, False
Resample
Determines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rate
New output signal sample rate
500 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value
Units Value range
Noise threshold
Minimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamic
Threshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
H f( ) α 1 HRect f( ) 2–=
431
INVERTED TRAPEZOIDAL OPTICAL FILTER
Inverted Trapezoidal Optical filter
Optical filter with an inverted trapezoidal frequency transfer function.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
193.1 THz Hz, THz, nm [30,3e5]
Zero dB bandwidth 10 GHz Hz, GHz, THz, nm
[1e-9,+INF[
Bandwidth
3 dB filter bandwidth
100 GHz Hz, GHz, THz, nm
[1e-9,+INF[
Cutoff magnitude 3 dB — [0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
432
INVERTED TRAPEZOIDAL OPTICAL FILTER
Simulation
Noise
Name and description Default value
Default unit Units Value range
Enabled
Determines whether or not the component is enabled
True — — True, False
Resample
Determines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rate
New output signal sample rate
500 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value
Units Value range
Noise threshold
Minimum value for adaptation of noise bins
–100 dB ]-INF,0[
Noise dynamic
Threshold ratio for adaptation of noise bins
3 dB [0,+INF[
433
INVERTED GAUSSIAN OPTICAL FILTER
Inverted Gaussian Optical filter
Optical filter with an inverted gaussian frequency transfer function.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
193.1 THz Hz, THz, nm [0,+INF[
Bandwidth
3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
]0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Order
Order of the function
1 — — [1,100]
434
INVERTED GAUSSIAN OPTICAL FILTER
Simulation
Noise
Technical backgroundThe transfer function is:
where H(f) is the filter transfer function, α is the parameter Insertion loss, HGauss(f) is the filter transfer function (see Gaussian Optical filter), and f is the frequency.
Name and description Default value
Default unit Units Value range
Enabled
Determines whether or not the component is enabled
True — — True, False
Resample
Determines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rate
New output signal sample rate
500 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value
Units Value range
Noise threshold
Minimum value for adaptation of noise bins
–100 dB ]-INF,0[
Noise dynamic
Threshold ratio for adaptation of noise bins
3 dB [0,+INF[
H f( ) α 1 HGauss f( )– 2=
435
INVERTED BUTTERWORTH OPTICAL FILTER
Inverted Butterworth Optical filter
Optical filter with an inverted Butterworth frequency transfer function.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
193.1 THz Hz, THz, nm [0,+INF[
Bandwidth
3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
]0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Order
Order of the function
1 — — [1,100]
436
INVERTED BUTTERWORTH OPTICAL FILTER
Simulation
Noise
Technical backgroundThe transfer function is:
where H(f) is the filter transfer function, α is the parameter Insertion loss, HB(f) is the filter transfer function (see Butterworth Optical filter), and f is the frequency.
Name and description Default value
Default unit Units Value range
Enabled
Determines whether or not the component is enabled
True — — True, False
Resample
Determines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rate
New output signal sample rate
500 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value
Units Value range
Noise threshold
Minimum value for adaptation of noise bins
–100 dB ]-INF,0[
Noise dynamic
Threshold ratio for adaptation of noise bins
3 dB [0,+INF[
H f( ) α 1 HB f( )– 2=
437
INVERTED BESSEL OPTICAL FILTER
Inverted Bessel Optical filter
Optical filter with an inverted Bessel frequency transfer function.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
193.1 THz Hz, THz, nm [0,+INF[
Bandwidth
3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
]0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Order
Order of the function
1 — — [1,100]
438
INVERTED BESSEL OPTICAL FILTER
Simulation
Noise
Technical backgroundThe transfer function is:
where H(f) is the filter transfer function, α is the parameter Insertion loss, HB(f) is the filter transfer function (see Bessel Optical filter), and f is the frequency.
Name and description Default value
Default unit Units Value range
Enabled
Determines whether or not the component is enabled
True — — True, False
Resample
Determines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rate
New output signal sample rate
500 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value
Units Value range
Noise threshold –100 dB ]-INF,0[
Noise dynamic 3 dB [0,+INF[
H f( ) α 1 HB f( )– 2=
439
FIBER BRAGG GRATING (FBG)
Fiber Bragg Grating (FBG)
Simulates an FBG.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Transmission Output Optical
Reflection Output Optical
Name and description Default value
Default unit Units Value range
Frequency
Optical frequency of the center of the Fiber Bragg Grating reflection spectrum
193.1 THz Hz, THz, nm [30,3e5]
Effective index
Modal index of the optical fiber grating
1.45 — — [1,10]
Length
Length of the optical fiber grating
2 nm — [1e-6,1e3]
440
FIBER BRAGG GRATING (FBG)
Apodization
Chirp
Name and description Default value Units Value range
Apodization function
Modulates the grating intensity over the grating length.
Uniform — Uniform, Gaussian, Tanh, user-defined
Gauss parameter
Apodization is defined by a Gaussian function using the S parameter. See Technical Background for the definition.
0.5 — [0.01,100]
Tanh parameter
Apodization is defined by an hyperbolic tangent function using the S parameter. See Technical Background for the definition.
0.5 — [0.01,100]
Apodization filename
You supply a file for the apodization. The ith element of this file is applied as the local apodization for the ith segment of the grating.
Apodization.dat — —
Modulation AC
Index modulation when the apodization is unity. The product of this number with the apodization function determines the local index modulation.
0.00001 — ]0,1e3]
Modulation DC
Modifies the modal index of the fiber in proportion to the apodization function.
0 — ]0,1e3]
Name and description Default value Units Value range
Chirp function
Period that the grating can be changed over the length of the fiber.
None — None, Linear, Quadratic, Square root, Cubic root, user-defined
Linear parameter
Period varies in a linear way, as defined in the Technical Background.
0.00001 µm [0.01,100]
Quadratic parameter
Period varies in a quadratic way, as defined in the Technical Background.
0.00001 µm [0.01,100]
Square root parameter
Period varies as defined in the Technical Background.
0.00001 µm [0.01,100]
441
FIBER BRAGG GRATING (FBG)
Calculation
Simulation
Cubic root parameter
Period varies as defined in the Technical Background.
0.00001 µm [0.01,100]
Chirp filename
In the user-defined file, the ith entry is used as the period for the ith segment of the chirped grating.
ChirpPeriod.dat — —
Name and description Default value
Units Value range
Number of segments
The non-uniform grating will be divided into this number of equal length uniform segments to calculate the spectrum
101 — [1,1e9]
Max. number of spectral points
Maximum nuber of points for the transmission and reflection complex spectrum
1000 — [100,1e6]
Name and description Default value
Default unit Units Value range
Enabled
Determines whether or not the component is enabled
True — — True, False
Resample
Determines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rate
New output signal sample rate
500 GHz Hz, GHz, THz [1e-9,+INF[
Name and description Default value Units Value range
442
FIBER BRAGG GRATING (FBG)
Noise
Technical backgroundThe non-uniform (chirped and apodized) grating [1] is divided into Number of Segments uniform gratings. The coupled mode theory is used to calculate the scattering matrix of each uniform segment, and the spectral response of the whole grating is found by connecting the uniform segments using the transfer matrix theory. The apodization functions Gaussian and Hyperbolic tangent are defined with the following parameters:
Gaussian
Hyperbolic tangent
Name and description Default value
Default unit Units Value range
Noise threshold
Minimum value for adaptation of noise bins
–100 dB — ]-INF,0[
Noise dynamic
Threshold ratio for adaptation of noise bins
3 dB — [0,+INF[
Noise calculation bandwidth
Calculation bandwidth — outside of this range, calculation is replaced by the attenuation
1 THz Hz, GHz, THz, nm
[0, 1e+100]
A z( ) 2 2 z L 2⁄–( )⋅s L⋅
-------------------------------2
⋅ln–
exp=
A z( ) s z L⁄⋅( ) s 1 z L⁄–( )⋅[ ] 1 h s 2⁄( )2tan–+tanh⋅tanh=
443
FIBER BRAGG GRATING (FBG)
When the parameter Apodization function is user-defined, you provide a file with the data describing the apodization. The input file is formatted containing two items per line — the length in mm and the apodization value.
The chirp functions depend on a parameter, ∆, which is used as follows:
Linear
Quadratic
Square Root
0 7.99437714249507e-007
0.2 2.39785072153609e-006
0.4 3.99496320824255e-006
0.6 5.58995679966756e-006
0.8 7.18201727067935e-006
1.0 8.770334716246e-006
1.2 1.03541096905246e-005
.
.
.
Λ z( ) Λ0z L 2⁄–
L------------------∆–= ∆ Λ0«
Λ z( ) Λ0zL---
2 1
4---+ ∆–= ∆ Λ0«
Λ z( ) Λ0zL--- 1
2-------– ∆–= ∆ Λ0«
444
FIBER BRAGG GRATING (FBG)
Cubic Root
When the parameter Chirp function is user-defined, you provide a file with the data describing the chirp. The input file is formatted containing two items per line — the length in mm and the chirp value in µm.
References[1] Erdogan, R., “Fiber Grating Spectra”, J. Light. Technol., 15, 1277-1294, (1997).
0 0.53368353843689
0.2 0.53369003534317
0.4 0.533694565296173
0.6 0.533698260784149
0.8 0.533701419830322
1.0 0.533704221248627
1.2 0.533706843852997
.
.
.
Λ z( ) Λ0zL---3
123
-------– ∆–= ∆ Λ0«
445
UNIFORM FIBER BRAGG GRATING
Uniform Fiber Bragg Grating
Simulates a Uniform FBG.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Transmission Output Optical
Reflection Output Optical
Name and description Default value
Default unit Units Value range
Frequency
Optical frequency of the center of the Fiber Bragg Grating reflection spectrum
193.1 THz Hz, THz, nm [30,3e5]
Bandwidth
Width of the reflection stop band of the Fiber Bragg Grating
125 GHz Hz, GHz, THz, nm
[0,+INF[
Reflectivity
Desired maximum reflectivity of the grating (maximum is at the centre wavelength)
0.99 — — [ 1e-100, 1]
446
UNIFORM FIBER BRAGG GRATING
Simulation
Noise
Technical backgroundThe solution to the coupled mode equations for a uniform grating is used. The unknown parameters in the grating (grating period, grating modulation intensity) are found by employing the information about maximum reflectivity and bandwidth. The result is a module for the calculation of the reflection and transmission spectra [1].
References[1] Agrawal, G.P., Fiber-Optic Communication Systems. John Wiley & Sons, New York, (1997).
Name and description Default value
Default unit Units Value range
Enabled
Determines whether or not the component is enabled
True — — True, False
Resample
Determines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rate
New output signal sample rate
500 GHz Hz, GHz, THz [1e-9,+INF[
Name and description Default value
Default unit Units Value range
Noise threshold
Minimum value for adaptation of noise bins
–100 dB — ]-INF,0[
Noise dynamic
Threshold ratio for adaptation of noise bins
3 dB — [0,+INF[
Noise calculation bandwidth
Calculation bandwidth, outside of this range calculation is replaced by the attenuation
1 THz Hz, GHz, THz, nm
[0, 1e+100]
447
IDEAL DISPERSION COMPENSATION FBG
Ideal Dispersion Compensation FBG
Approximation of an ideal chirped FBG designed for dispersion compensation.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Transmission Output Optical
Reflection Output Optical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
193.1 THz Hz, THz, nm [0,+INF[
Bandwidth
3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
]0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Dispersion
Group delay slope
800 ps/nm ps/nm s/m ] -INF, +INF[
448
IDEAL DISPERSION COMPENSATION FBG
Simulation
Noise
Technical backgroundThis model is a filter with user-defined group delay. The filter transfer function is:
where f is the frequency dependence phase of the filter.
The group delay is defined by [1]:
Writing Equation 2 as a function of wavelength:
where c is the speed of light.
Name and description Default value
Default unit Units Value range
Enabled
Determines whether or not the component is enabled
True — — True, False
Resample
Determines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rate
New output signal sample rate
500 GHz Hz, GHz, THz [1e-9,+INF[
Name and description Default value
Units Value range
Noise threshold
Minimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamic
Threshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
(1)
(2)
(3)
H f( ) ejφ f( )=
τ f( ) 12π------dφ
df------–=
τ λ( ) λ2
2πc---------dφ
dλ------–=
449
IDEAL DISPERSION COMPENSATION FBG
You define by entering the center wavelength , bandwidth , and the group delay slope D in s/m:
This generates the following group delay curve:
Figure 1 Group delay
Calculate the phase from this curve to calculate the filter transfer function.
Phase calculationThe phase is calculated from Equation 3 and Equation 4:
(4)
:
(5)
τ λc ∆λ
τ λ( )
τ0
D.λτλc ∆λ 2⁄+
=λ λc ∆λ 2⁄–≤
λc ∆λ 2 λ λc ∆λ 2⁄+≤<⁄–λ λc ∆λ 2⁄+>
φ 2πc τ λ( ) 1λ2----- λd∫–=
λ λc ∆λ 2⁄–≤
φ 2πcτ01λ2----- λd
λ1
λ
∫– 2πcτ01λ--- 1
λ1-----–
= =
λ1 ∞ τ0,– 0= =φ 0=
450
IDEAL DISPERSION COMPENSATION FBG
:
(6)
:
(7)
λc ∆λ 2 λ λc≤<⁄– ∆λ 2⁄+
φ 2πcD λ λ1–( )λ2
------------------- λ φλc ∆λ 2⁄–+dλ1
λ
∫ 2πcD λ( ) 2πcDλ1
λ-----– φλc ∆λ 2⁄–+ln= =
φλc ∆λ 2⁄– 2πcD λ1( ) 2πcD λ1,–ln λc ∆λ 2⁄–( )= =
φ 2πcD λ( ) 2πcD λc ∆λ 2⁄–( )λ
----------------------------– 2πcD λc ∆λ 2⁄–( ) 2πcD–ln+ln=
λ λc ∆λ 2⁄+>
φ 2πcτλc ∆λ 2⁄–1λ2----- λ φλc ∆λ 2⁄–+d
λ1
λ
∫– 2πcτλc ∆λ 2⁄–1λ--- 1
λ1-----–
φλc ∆λ 2⁄–+= =
λ1 λc ∆λ 2⁄+( ) λ2, λ τλc ∆λ 2⁄–, D ∆λ( )–= = =
φλc ∆λ 2⁄– 2πcD λc ∆λ 2⁄+( ) 2πcD λc ∆λ 2⁄–( )λc ∆λ 2⁄+( )
-----------------------------– 2πcD λc ∆λ 2⁄–( ) 2πcD–ln+ln=
φ 2πcD∆λ– 1λ--- 1
λc ∆λ 2⁄+( )-----------------------------–
+= =
2πcD λc ∆λ 2⁄+( ) 2πcD λc ∆λ 2⁄–( )λc ∆λ 2⁄+( )
-----------------------------– 2πcD λc ∆λ 2⁄–( ) 2πcD–ln+ln
451
IDEAL DISPERSION COMPENSATION FBG
This generates the following typical phase curve (for :
Figure 2 Cumulative phase
References[1] Madsen, C. K. and Zhao, J H., Optical Filter Design and Analysis: A Signal Processing
Approach. John Wiley & Sons, New York, (1999).
D 0.8s m⁄–=
452
LOW PASS IIR FILTER (ELECTRICAL)
Low Pass IIR filter (Electrical)
Infinite impulse response filter (IIR) for electrical signals.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Units Value range
Filter sample rate
User-defined sample rate independent from the signal sample rate
10 GHz Hz, GHz [1e-9,+INF[
Additional loss
Loss applied to the signal after filtering
0 dB dB [0,+INF[
Filter coefficients type
Type of numerator and denominator coefficients for the filter
Z domain — — Frequency domain, Poles and zeros, Z domain
453
LOW PASS IIR FILTER (ELECTRICAL)
Numerator coefficients
Denominator coefficients
Simulation
Name and description Default value
Units Value range
Numerator coefficients
Number of numerator coefficients
3 — [1,+INF[
Numerator[0].real 0.64 — ]-INF,+INF[
Numerator[0].imag 0 — ]-INF,+INF[
Numerator[1].real 1.28 — ]-INF,+INF[
Numerator[1].imag 0 — ]-INF,+INF[
Numerator[2].real 0.64 — ]-INF,+INF[
Numerator[2].imag 0 — ]-INF,+INF[
Name and description Default value
Units Value range
Denominator coefficients
Number of denominator coefficients
3 — [1,+INF[
Denominator[0].real 5.05 — ]-INF,+INF[
Denominator[0].imag 0 — ]-INF,+INF[
Denominator[1].real –4.75 — ]-INF,+INF[
Denominator[1].imag 0 — ]-INF,+INF[
Denominator[2].real 2.26 — ]-INF,+INF[
Denominator[2].imag 0 — ]-INF,+INF[
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
454
LOW PASS IIR FILTER (ELECTRICAL)
Technical backgroundThe infinite impulse response filter is a recursive digital filter. The transfer function can be expressed in the z domain as:
where H(z) is the filter transfer function in the Z domain, α is the parameter related to Additional loss, N is the parameter number of Numerator coefficients, an are the coefficients for the numerator, M is the parameter number of Denominator coefficients, and bm are the coefficients for the denominator.
Also
where fs is the parameter Filter sample rate, and f is the frequency.
According to the parameter Filter coefficients type, the filter transfer function can be given in the z (z domain) or in the frequency domain. In the second case, the filter is determined by the numerator and the denominator polynomial, which can be expressed by their roots (Poles and zeros) or by the polynomial coefficients (in Frequency domain).
H z( ) α
anz n–
n 0=
N
∑
bmz m–
m 0=
M
∑-----------------------=
z j2πf fs⁄( )exp=
455
LOW PASS RECTANGLE FILTER (ELECTRICAL)
Low Pass Rectangle filter (Electrical)
Optical filter with a rectangle frequency transfer function.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Units Value range
Cutoff frequency
3 dB cutoff frequency of the filter
0.75 * bit rate Hz Hz, MHz, GHz [0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
456
LOW PASS RECTANGLE FILTER (ELECTRICAL)
Technical backgroundThe filter transfer function is:
where H(f) is the filter transfer function,α is the parameter Insertion loss, d is the parameter Depth, fc is the cutoff frequency, and f is the frequency.
H f( )α,d,
=0 f fc< <
otherwise
457
LOW PASS GAUSSIAN FILTER (ELECTRICAL)
Low Pass Gaussian filter (Electrical)
Optical filter with a Gaussian frequency transfer function.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Units Value range
Cutoff frequency
3 dB cutoff frequency of the filter
0.75 * bit rate Hz Hz, MHz, GHz [0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Order
Order of the function
1 — — [1, 100]
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
458
LOW PASS GAUSSIAN FILTER (ELECTRICAL)
Technical backgroundThe filter transfer function is:
where H(f) is the filter transfer function, α is the parameter Insertion loss, fc is the filter cutoff frequency, N is the parameter Order, and f is the frequency.
H f( ) αe2 f
2N
fc--------
ln–
=
459
LOW PASS BUTTERWORTH FILTER (ELECTRICAL)
Low Pass Butterworth filter (Electrical)
Optical filter with a Butterworth frequency transfer function.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Units Value range
Cutoff frequency
3 dB cutoff frequency of the filter
0.75 * bit rate Hz Hz, MHz, GHz [0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Order
Order of the function
1 — — [1, 100]
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
460
LOW PASS BUTTERWORTH FILTER (ELECTRICAL)
Technical backgroundButterworth filters are a class of all-pole filters with maximally flat frequency response. In this case. the filter transfer function is:
where
where H(f) is the filter transfer function, α is the parameter Insertion loss, fc is the filter cutoff frequency, N is the parameter Order, and f is the frequency.
H f( ) αfc( )N
j f( ) pk–( )k 0=
N 1–
∏--------------------------------=
pk fc ejπ2-- 1 2k 1+
N--------------+
⋅=
461
LOW PASS BESSEL FILTER (ELECTRICAL)
Low Pass Bessel filter (Electrical)
Filter with a Bessel frequency transfer function.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Units Value range
Cutoff frequency
3 dB cutoff frequency of the filter
0.75 * bit rate Hz Hz, MHz, GHz [0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Order
Order of the function
4 — — [1, 100]
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
462
LOW PASS BESSEL FILTER (ELECTRICAL)
Technical backgroundBessel filters have the following transfer function:
where α is the parameter Insertion loss, N is the parameter Order, and
being a normalizing constant and BN(s) an nth-order Bessel polynomial of the form:
where
and
where fc is the filter cutoff frequency defined by the parameter Frequency and Wb denotes the normalized 3 dB bandwidth and can be approximated by:
for N≥ 3
H s( ) αd0
BN s( )-------------=
d02N( )!
2N N!⋅----------------=
BN s( ) dksk
k 0=
N
∑=
dk2N k–( )!
2N k– k! N k–( )!⋅---------------------------------------=
s j f wb⋅fc
------------ =
wb 2N 1–( ) 2ln⋅≈
463
LOW PASS CHEBYSHEV FILTER (ELECTRICAL)
Low Pass Chebyshev filter (Electrical)
Filter with a Chebyshev frequency transfer function.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Units Value range
Cutoff frequency
3 dB cutoff frequency of the filter
0.75 * bit rate Hz Hz, MHz, GHz [0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Order
Order of the function
1 — — [1, 100]
Ripple factor
Ripple parameters
0.5 — — [0, 1]
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
464
LOW PASS CHEBYSHEV FILTER (ELECTRICAL)
Technical backgroundChebychev of order N filters have the following transfer function:
where α is the parameter Insertion loss and N is the parameter Order.
Also
and
where fc is the filter cutoff frequency.
The parameters:
and
where
where rp is the parameter ripple factor.
H s( ) α
sk
k 0=
N 1–
∏
s sk–( )k 0=
N 1–
∏-------------------------⋅–=
s jf=
sk fc δ βk j δ βksin⋅cosh⋅+cos⋅sinh( )⋅=
δ 1N----ar r 1–( )sinh=
βkπ 2 k 1+( ) N 1–+( )
2N------------------------------------------------=
r 11 rp–------------- 1–=
465
LOW PASS RC FILTER (ELECTRICAL)
Low Pass RC filter (Electrical)
Filter with an RC frequency transfer function.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Units Value range
Cutoff frequency
3 dB cutoff frequency of the filter
0.75 * bit rate Hz Hz, MHz, GHz [0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
466
LOW PASS RC FILTER (ELECTRICAL)
Technical backgroundRC filter has the following transfer function:
where α is the parameter Insertion loss and fc is the filter cutoff frequency.
H f( ) α 1
1 j ffc---+
---------------⋅=
467
LOW PASS RAISED COSINE FILTER (ELECTRICAL)
Low Pass Raised Cosine filter (Electrical)
Filter with a raised cosine frequency transfer function.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Units Value range
Cutoff frequency
3 dB cutoff frequency of the filter
0.75 * bit rate Hz Hz, MHz, GHz [0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Roll-off factor 0.5 — — [0, 1]
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
468
LOW PASS RAISED COSINE FILTER (ELECTRICAL)
Technical backgroundRaised cosine filter has the following transfer function:
where
where α is the parameter Insertion loss, fc is the filter cutoff frequency, and rp is the parameter Roll off factor.
H f( )
α
α cos2 π2rp∆f------------- f( )
1 rp–( )2
------------------∆f–⋅
0
=
f 1 rp–( )2
------------------∆f<
1 rp–( )2
------------------∆f f 1 rp+( )2
------------------∆f<≤
1 rp+( )2
------------------∆f f≤
∆f 2fc1
1 rp– 4 π rp arc 24cos⋅ ⋅⁄+--------------------------------------------------------------------⋅=
469
LOW PASS COSINE ROLL OFF FILTER (ELECTRICAL)
Low Pass Cosine Roll Off filter (Electrical)
Filter with a cosine roll off frequency transfer function.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Units Value range
Cutoff frequency
3 dB cutoff frequency of the filter
0.75 * bit rate Hz Hz, MHz, GHz [0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Roll off factor 0.5 — — [0, 1]
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
470
LOW PASS COSINE ROLL OFF FILTER (ELECTRICAL)
Technical backgroundCosine Roll Off Filter has the following transfer function:=
where a is the parameter Insertion loss, fc is the filter cutoff frequency, and rp is the parameter Roll off factor.
The parameters f1 and f2 are:
and
H f( )
α
0.5 α2 1 f f1–rp ∆fFWHM⋅------------------------- π⋅
cos+⋅ ⋅
0
=
f f1<
f1 f f2<≤
f2 f≤
f1 1 rp–( )fc= 0 rp 1≤ ≤
f2 1 rp+( )fc= 0 rp 1≤ ≤
471
LOW PASS SQUARED COSINE ROLL OFF FILTER (ELECTRICAL)
Low Pass Squared Cosine Roll Off filter (Electrical)
Filter with a square cosine roll off frequency transfer function.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Units Value range
Cutoff frequency
3 dB cutoff frequency of the filter
0.75 * bit rate Hz Hz, MHz, GHz [0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Roll-off factor 0.5 — — [0, 1]
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
472
LOW PASS SQUARED COSINE ROLL OFF FILTER (ELECTRICAL)
Technical backgroundSquare cosine roll off filter has the following transfer function:
where α is the parameter Insertion loss and rp is the roll off factor.
The parameter is related to the filter frequency cutoff by:
where fc is the filter cutoff frequency.
H f( )
α
0.5 α 1 f f1–rp ∆f⋅-------------- π⋅
cos+⋅ ⋅
0
=
f f1<
f1 f f2<≤
f2 f≤
∆f
∆f 2fc
1 2π--- arc 2 1–( ) 1–cos⋅ rp⋅+
-------------------------------------------------------------------------------=
473
BAND PASS IIR FILTER (ELECTRICAL)
Band Pass IIR filter (Electrical)
Infinite impulse response filter (IIR) for electrical signals.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
10 GHz Hz, MHz, GHz [0,+INF[
Filter sample rate
User-defined sample rate independent from the signal sample rate
10 GHz Hz, GHz [1e-9,+INF[
Additional loss
Loss applied to the signal after filtering
0 dB — [0,+INF[
Filter coefficients type
Type of numerator and denominator coefficients for the filter
Z domain — — Frequency domain, Poles and zeros, Z domain
474
BAND PASS IIR FILTER (ELECTRICAL)
Numerator coefficients
Denominator coefficients
Simulation
Name and description Default value
Units Value range
Numerator coefficients
Number of numerator coefficients
3 — [1,+INF[
Numerator[0].real 0.64 — ]-INF,+INF[
Numerator[0].imag 0 — ]-INF,+INF[
Numerator[1].real 1.28 — ]-INF,+INF[
Numerator[1].imag 0 — ]-INF,+INF[
Numerator[2].real 0.64 — ]-INF,+INF[
Numerator[2].imag 0 — ]-INF,+INF[
Name and description Default value
Units Value range
Denominator coefficients
Number of denominator coefficients
3 — [1,+INF[
Denominator[0].real 5.05 — ]-INF,+INF[
Denominator[0].imag 0 — ]-INF,+INF[
Denominator[1].real –4.75 — ]-INF,+INF[
Denominator[1].imag 0 — ]-INF,+INF[
Denominator[2].real 2.26 — ]-INF,+INF[
Denominator[2].imag3 0 — ]-INF,+INF[
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
475
BAND PASS IIR FILTER (ELECTRICAL)
Technical backgroundThe infinite impulse response filter is a recursive digital filter. The transfer function can be expressed in the z domain as:
where H(z) is the filter transfer function in the Z domain, α is the parameter related to Additional loss, N is the parameter number of Numerator coefficients, an are the coefficients for the numerator, M is the parameter number of Denominator coefficients, and bm are the coefficients for the denominator.
Also
where fc is the filter center frequency defined by the parameter Frequency, fs is the parameter Filter sample rate, and f is the frequency.
According to the parameter Filter coefficients type, the filter transfer function can be given in the z (Z domain) or in the frequency domain. In the second case, the filter is determined by the numerator and the denominator polynomial, which can be expressed by their roots (Poles and zeros) or by the polynomial coefficients (Frequency domain).
H z( ) α
anz n–
n 0=
N
∑
bmz m–
m 0=
M
∑----------------------=
z j2π f fc–( ) fs⁄( )exp=
476
MEASURED FILTER (ELECTRICAL)
Measured filter (Electrical)
Filter based on measurements.
Ports
Parameters
Main
Measurements
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Units Value range
User-defined frequency
Determines whether you can define the filter center frequency or use the value from the measurements
True — — True, False
Frequency
User-defined filter center frequency
0 GHz Hz, MHz, GHz [0,+INF[
Name and description Default value
Units Value range
File frequency unit
Determines the frequency unit of the file with the measurements
Hz — Hz, THz
File format
Determines the format of the file with the measurements
Power — Power, Power Phase, Real Imag, phase
Linear scale
Determines whether or not the measured data is in linear scale
True — ]-INF,+INF[
477
MEASURED FILTER (ELECTRICAL)
Numerical
Simulation
Technical backgroundThe input file is formatted containing two items per line, the frequency and filter measurement. The parameter File frequency unit determines the frequency or wavelength unit of the first item; It can be in Hz or THz.
According to the parameter File format the second item can be one value (Power or Phase) or two values (Power and Phase or Real and Imag):
Filename
Filename with the measured data
Filter.dat — —
Name and description Default value
Units Value range
Interpolation
Determines the interpolation algorithm for the measured data
Linear — Linear, Cubic
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
Name and description Default value
Units Value range
478
MEASURED FILTER (ELECTRICAL)
Power (Phase is set to zero, assuming frequency unit is THz)
Power Phase
Real Imag
193.10 0
193.11 0.5
193.12 0.5
193.13 0
...
193.10 0 0
193.11 0.5 3.14
193.12 0.5 3.14
193.13 0 0
...
193.10 0
193.11 –0.5 7.9e-4
193.12 –0.5 7.9e-4
193.13 0 0
...
479
MEASURED FILTER (ELECTRICAL)
Phase (Power is set to one)
The parameter User defined frequency determines if you can enter the center frequency.
From the measured data,
where is the center frequency of the loaded file, is the maximum frequency of the file, and is the minimum frequency of the file. If the option 'User Defined Frequency' is selected, then the center frequency of the loaded file becomes centered at the user defined frequency.
193.10 0
193.11 3.14
193.12 3.14
193.13 0
...
Fc Max Min+( ) 2⁄=
Fc MaxMin
480
BAND PASS RECTANGLE FILTER (ELECTRICAL)
Band Pass Rectangle filter (Electrical)
Optical filter with a rectangle frequency transfer function.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
10 GHz Hz, MHz, GHz [0,+INF[
Bandwidth
3 dB filter bandwidth
1.5 * bit rate Hz Hz, MHz, GHz [0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
481
BAND PASS RECTANGLE FILTER (ELECTRICAL)
Technical backgroundThe filter transfer function is:
where H(f) is the filter transfer function, α is the parameter Insertion loss, d is the parameter Depth, fc is the filter center frequency defined by the parameter Frequency, B is the parameter Bandwidth, and f is the frequency.
H f( )α,d,
=
fc B 2 f fc B 2⁄+< <⁄–otherwise
482
BAND PASS GAUSSIAN FILTER (ELECTRICAL)
Band Pass Gaussian filter (Electrical)
Optical filter with a Gaussian frequency transfer function.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
10 GHz Hz, MHz, GHz [0,+INF[
Bandwidth
3 dB filter bandwidth
1.5 * bit rate Hz Hz, MHz, GHz [0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Order
Order of the function
1 — — [1, 100]
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
483
BAND PASS GAUSSIAN FILTER (ELECTRICAL)
Technical backgroundThe filter transfer function is:
where H(f) is the filter transfer function, α is the parameter Insertion loss, fc is the filter center frequency defined by the parameter Frequency, B is the parameter Bandwidth, N is the parameter Order, and f is the frequency.
H f( ) αe2 2
f fc–( )2N
B-----------------------
ln–
=
484
BAND PASS BUTTERWORTH FILTER (ELECTRICAL)
Band Pass Butterworth filter (Electrical)
Optical filter with a Butterworth frequency transfer function.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
10 GHz Hz, MHz, GHz [0,+INF[
Bandwidth
3 dB filter bandwidth
1.5 * bit rate Hz Hz, MHz, GHz [0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Order
Order of the function
1 — — [1, 100]
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
485
BAND PASS BUTTERWORTH FILTER (ELECTRICAL)
Technical backgroundButterworth filters are a class of all-pole filters with maximally flat frequency response. The filter transfer function is:
where
where H(f) is the filter transfer function, α is the parameter Insertion loss, fc is the filter center frequency defined by the parameter Frequency, B is the parameter Bandwidth, N is the parameter Order, and f is the frequency.
H f( ) α B 2⁄( )N
j f fc–( ) pk–( )k 0=
N 1–
∏
------------------------------------------=
pkB2--- e
jπ2--- 1 2k 1+
N---------------+
⋅=
486
BAND PASS BESSEL FILTER (ELECTRICAL)
Band Pass Bessel filter (Electrical)
Filter with a Bessel frequency transfer function.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
10 GHz Hz, MHz, GHz [0,+INF[
Bandwidth
3 dB filter bandwidth
1.5 * bit rate Hz Hz, MHz, GHz [0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Order
Order of the function
4 — — [1, 100]
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
487
BAND PASS BESSEL FILTER (ELECTRICAL)
Technical backgroundBessel filters have the following transfer function:
where α is the parameter Insertion loss, N is the parameter Order, and
is a normalizing constant and BN(s) is an nth-order Bessel polynomial of the form
where
and
where fc is the filter center frequency defined by the parameter Frequency, B is the parameter Bandwidth, and Wb denotes the normalized 3 dB bandwidth and can be approximated by:
for N≥ 3
H s( ) αd0
BN s( )-------------=
d02N( )!
2N N!⋅----------------=
BN s( ) dksk
k 0=
N
∑=
dk2N k–( )!
2N k– k! N k–( )!⋅---------------------------------------=
s j 2 f fc–( ) wb⋅B
-------------------------- =
wb 2N 1–( ) 2ln⋅≈
488
BAND PASS CHEBYSHEV FILTER (ELECTRICAL)
Band Pass Chebyshev filter (Electrical)
Filter with a Chebyshev frequency transfer function.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
10 GHz Hz, MHz, GHz [0,+INF[
Bandwidth
3 dB filter bandwidth
1.5 * bit rate Hz Hz, MHz, GHz [0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Order
Order of the function
1 — — [1, 100]
Ripple factor
Bandpass ripple parameter
0.01 — — [0, 1]
489
BAND PASS CHEBYSHEV FILTER (ELECTRICAL)
Simulation
Technical backgroundChebychev of order N filters have the following transfer function:
where is the parameter Insertion loss and N is the parameter Order.
with
where fc is the filter center frequency defined by the parameter Frequency.
Here, Sk are the poles of the filter defined by:
where B is the parameter Bandwidth.
and
where rp is the parameter ripple factor.
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
H s( ) α
sk
k 0=
N 1–
∏
s sk–( )k 0=
N 1–
∏-------------------------⋅=
α
s j f fc–( )=
skB2--- δ βk j δ βksin⋅cosh⋅+cos⋅sinh( )⋅=
r 11 rp–------------- 1–=
δ 1N----ar r 1–( )sinh=
490
BAND PASS CHEBYSHEV FILTER (ELECTRICAL)
and
βkπ 2 k 1+( ) N 1–+( )
2N------------------------------------------------=
491
BAND PASS RC FILTER (ELECTRICAL)
Band Pass RC filter (Electrical)
Filter with an RC frequency transfer function.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
10 GHz Hz, MHz, GHz [0,+INF[
Bandwidth
3 dB filter bandwidth
1.5 * bit rate Hz Hz, MHz, GHz [0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
492
BAND PASS RC FILTER (ELECTRICAL)
Technical backgroundRC filter has the following transfer function:
where α is the parameter Insertion loss, fc is the filter center frequency defined by the parameter Frequency, and B is the parameter Bandwidth.
H f( ) α 1
1 j2f fc–B
-----------+--------------------------⋅=
493
BAND PASS RAISED COSINE FILTER (ELECTRICAL)
Band Pass Raised Cosine filter (Electrical)
Filter with a raised cosine frequency transfer function.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
10 GHz Hz, MHz, GHz [0,+INF[
Bandwidth
3 dB filter bandwidth
1.5 * bit rate Hz Hz, MHz, GHz [0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Roll off factor 0.5 — — [0, 1]
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
494
BAND PASS RAISED COSINE FILTER (ELECTRICAL)
Technical backgroundRaised cosine filter has the following transfer function:
where
where α is the parameter Insertion loss, fc is the filter center frequency defined by the parameter Frequency, B is the parameter Bandwidth, and rp is the parameter Roll off factor.
H f( )
α
α cos2 π2rp∆f------------- f fc–( )
1 rp–( )2
------------------∆f–⋅
0
=
f fc– 1 rp–( )2
------------------∆f<
1 rp–( )2
------------------∆f f fc– 1 rp+( )2
------------------∆f<≤
1 rp+( )2
------------------∆f f fc–≤
∆f B 11 rp– 4 π rp arc 24cos⋅ ⋅⁄+--------------------------------------------------------------------⋅=
495
BAND PASS COSINE ROLL OFF FILTER (ELECTRICAL)
Band Pass Cosine Roll Off filter (Electrical)
Filter with a cosine roll off frequency transfer function.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
10 GHz Hz, MHz, GHz [0,+INF[
Bandwidth
3 dB filter bandwidth
1.5 * bit rate Hz Hz, MHz, GHz [0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Roll-off factor 0.5 — — [0, 1]
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
496
BAND PASS COSINE ROLL OFF FILTER (ELECTRICAL)
Technical backgroundCosine Roll Off Filter has the following transfer function:
where α is the parameter Insertion loss, fc is the filter center frequency defined by the parameter Frequency, B is the parameter Bandwidth, and rp is the parameter Roll off factor.
The parameters f1 and f2 are:
and
H f( )
α
0.5 α2 1 f fc– f1–rp ∆fFWHM⋅------------------------- π⋅
cos+⋅ ⋅
0
=
f fc– f1<
f1 f fc– f2<≤
f2 f fc–≤
f11 rp–
2-------------B= 0 rp 1≤ ≤
f11 rp+
2-------------B= 0 rp 1≤ ≤
497
BAND PASS SQUARE COSINE ROLL OFF FILTER (ELECTRICAL)
Band Pass Square Cosine Roll Off filter (Electrical)
Filter with a square cosine roll off frequency transfer function.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Units Value range
Frequency
Filter center frequency
10 GHz Hz, MHz, GHz [0,+INF[
Bandwidth
3 dB filter bandwidth
1.5 * bit rate Hz Hz, MHz, GHz [0,+INF[
Insertion loss
Insertion loss of the filter
0 dB — [0,+INF[
Depth
Maximum attenuation value for the filter
100 dB — [0,+INF[
Roll off factor 0.5 — — [0, 1]
498
BAND PASS SQUARE COSINE ROLL OFF FILTER (ELECTRICAL)
Simulation
Technical backgroundSquare cosine roll off filter has the following transfer function:
where α is the parameter Insertion loss, fc is the filter center frequency defined by the parameter Frequency, and rp is the roll off factor.
The parameter is related to the filter bandwidth by:
(2)
where B is the parameter Bandwidth.
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
H f( ) 0.5 α 1
α
f fc– f1–rp ∆f⋅
----------------------- π⋅
0
cos+f fc– f1<
f1 f fc– f2<≤
f2 f fc–≤
⋅ ⋅
=
∆f
∆f B
1 2π--- arc 2 1–( ) 1–cos⋅ rp⋅+
-------------------------------------------------------------------------------=
499
S PARAMETERS MEASURED FILTER (ELECTRICAL)
S Parameters Measured filter (Electrical)
Loads files with S Parameter measurements. You can load files directly from measurements by using the Touchstone (.s2p) format.
Ports
Parameters
Main
Measurements
Name and description Port type Signal type
Input Input Electrical
Transmission Output Electrical
Reflection Output Electrical
Name and description Default value
Default unit Units Value range
User-defined frequency
Determines whether you can define the filter center frequency or use the value from the measurements
True — — True, False
Frequency
User-defined filter center frequency
0 GHz Hz, MHz, GHz [0, 1e+100]
Name and description Default value
Units Value range
Filename (.s2p)
Filename with the measured data
Device.s2p — —
500
S PARAMETERS MEASURED FILTER (ELECTRICAL)
Numerical
Simulation
Graphs
Technical backgroundThe Touchstone Format is a common standard for S Parameter data. The model expects the .s2p file to be in the following general format (lines starting with the comment symbol '!' and blank lines are ignored):
# freq_unit param_type data_form term_type term_val
f1 s11a s11b s21a s21b s12a s12b s22a s22b
f2 s11a s11b s21a s21b s12a s12b s22a s22b
.
.
.
fn s11a s11b s21a s21b s12a s12b s22a s22b
where: • freq_unit: Specifies the frequency units — can be Hz, kHz, MHz, or GHz.• param_type: Usually set to S to indicate S Parameter file.
Name and description Default value
Units Value range
Interpolation
Determines the interpolation algorithm for the measured data
Linear — Linear, Cubic
Name and description Default value
Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
Name and description X Title Y Title
Reflection - real part Frequency (Hz) Amplitude (a.u.)
Reflection - imag part Frequency (Hz) Amplitude (a.u.)
Transmission - real part Frequency (Hz) Amplitude (a.u.)
Transmission - imag part Frequency (Hz) Amplitude (a.u.)
501
S PARAMETERS MEASURED FILTER (ELECTRICAL)
• data_form: Either RI (for real imaginary), MA (for magnitude & angle) or DB (for magnitude in dB scale & angle). Indicates how the component should treat the pair of S Parameter values.
• term_type: Termination type (R for real or Z for terminating impedance). Usually R.
• term_val: Termination value (if R, then the value in Ohms, else a pair representing the impedance).
The header is followed by the data. Each line has nine values — the frequency and the eight values representing four S Parameters. This model loads only the S11 and S21 (direct reflection and transmission).
The following example was generated by a network analyzer. The units are in Hz and the data is in real and imaginary values.
The parameter User defined frequency determines if you can enter the center frequency. This means that the filter data is shifted from the measured center frequency to the user center frequency that you define by the parameter Frequency.
! Network Analyzer
! Model 1
! 16 Dec 1999 15:02:50
!Frequency S11 S21 S12 S22
# HZ S RI R 50
3000 2.17788E-1 0.24215E-1 -5.69091E0 4.64843E-1 3.02257E-2 0.33741E-2 -6.33483E-1 0.40252E-1
30029850 1.72088E-1 -1.57524E-1 -5.98193E0 -1.68359E0 4.33025E-2 1.31721E-2 -4.84573E-1 1.45126E-1
60029700 0.49133E-1 -2.12097E-1 -7.35302E0 -2.20703E0 5.24978E-2 1.82323E-2 -3.78585E-1 1.96167E-1
90029550 -4.32815E-2 -2.02163E-1 -8.36279E0 -2.04736E0 5.92289E-2 1.87740E-2 -2.99804E-1 1.91909E-1
120029400 -9.79766E-2 -1.74827E-1 -8.99023E0 -1.67724E0 6.32743E-2 1.8013E-2 -2.49618E-1 1.72729E-1
.
.
.
502
S PARAMETERS MEASURED FILTER (ELECTRICAL)
Notes:
503
OPTICAL FILTER ANALYZER
Optical Filter analyzer
Extracts the frequency response of an optical component by comparing a reference optical signal before and after the calculation.
Ports
Parameters
Main
Name and description Port type Signal type
From DUT output Input Optical
To DUT input Output Optical
Name and description Default value
Default unit Units Value range
Frequency
Signal center frequency
193.1 THz Hz, THz, nm [0,3e5[
Bandwidth
Signal bandwidth or sample rate
100 GHz Hz, GHz, THz, nm
[0,+INF[
Frequency unit
Unit scale for the graphs
nm — — nm, m, Hz, THz
Linear scale
Determines whether or not the graph is in linear scale
False — — True, False
Minimum value
Minimum value when using log scale
–100 dBm — ]-INF,+INF[
504
OPTICAL FILTER ANALYZER
Results
Export
Graphs
Results
Name and description Default value
Units Value range
Cutoff magnitude
Reference cutoff magnitude for bandwidth result calculation
3 dB [0,100]
Name and description Default value Units Value range
Save to file
Determines if the filter transmission will be saved as a file
False — True, False
Filename
Filename with the filter data
Filter.dat — —
Name and description X Title Y Title
Transmission function Frequency (Hz) Power (dB)
Transmission Phase X
Phase at the polarization X
Frequency (Hz) Phase (rad)
Name and description Unit
Frequency at Max. Transmission Hz
Filter Bandwidth (BandPass) at Cut off Hz
Frequency at Max. Transmission nm
Filter Bandwidth (BandPass) at Cut off nm
Frequency at Min. Transmission Hz
Filter Bandwidth (Band-Reject) at Cut off Hz
Frequency at Min. Transmission nm
Filter Bandwidth (Band-Reject) at Cut off nm
505
ELECTRICAL FILTER ANALYZER
Electrical Filter analyzer
Extracts the frequency response of an electrical component by comparing a reference electrical signal before and after the calculation.
Ports
Parameters
Main
Results
Name and description Port type Signal type
From DUT output Input Electrical
To DUT input Output Electrical
Name and description Default value
Default unit Units Value range
Bandwidth
Signal bandwidth or sample rate
100 GHz Hz, GHz, THz [0,+INF[
Frequency unit
Unit scale for the graphs
Hz — — Hz, THz
Linear scale
Determines whether or not the graph is in linear scale
False — — True, False
Minimum value
Minimum value when using log scale
–100 dBm — ]-INF,+INF[
Name and description Default value
Units Value range
Cutoff magnitude
Reference cutoff magnitude for bandwidth result calculation
3 dB [0,100]
506
ELECTRICAL FILTER ANALYZER
Export
Graphs
Results
Name and description Default value Units Value range
Save to file
Determines if the filter transmission will be save as a file
False — True, False
Filename
Filename with the filter data
Filter.dat — —
Name and description X Title Y Title
Transmission function Frequency (Hz) Power (dB)
Name and description Unit
Frequency at Max. Transmission Hz
Filter Bandwidth (BandPass) at Cut off Hz
Frequency at Min. Transmission Hz
Filter Bandwidth (Band-Reject) at Cut off Hz
507
WDM Multiplexers Library
This section contains information on the following WDM Multiplexers.
Add and Drop
• WDM Add• WDM Drop• WDM Add and Drop
Demultiplexers
• WDM Demux 1x2• WDM Demux 1x4• WDM Demux 1x8• WDM Demux• WDM Demux ES• Ideal Demux
Multiplexers
• WDM Mux 2x1• WDM Mux 4x1• WDM Mux 8x1• WDM Mux• WDM Mux ES• Ideal Mux
507
Notes:
508
WDM ADD
WDM AddAdds a WDM channel and a WDM signal.
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Output Output Optical
Name and description Default value Default unit Units Value range
Frequency 193.1 THz Hz, THz, nm [30, 300000]
Bandwidth3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
[0,+INF[
Insertion lossInsertion loss of the demux
0 dB — [0,+INF[
DepthMaximum attenuation value for the filter
100 dB — [0,+INF[
Filter typeInternal filter type
Bessel — — Rectangle, Gaussian, Bessel
Filter orderOrder of the function when using Gaussian or Bessel filter type
2 — — [1,1000]
509
WDM ADD
Simulation
Noise
Technical background
The input signals are filtered by an optical filter and are combined in one signal. The first signal is filtered by an inverse filter. The optical filters can be a Rectangle, Gaussian, or Bessel optical filter. The subsystem is illustrated in Figure 1.
Figure 1 WDM Add subsystem
Defining crosstalk
The level of crosstalk for both MUX and DEMUX components, is defined by bandwidth, ripple, and depth of the filter. These 3 factors will determine how much power, from neighboring channels, will act as crosstalk terms when calculating the performance of a specific channel. The most important parameter is depth, as it will play the most significant role in determining the power levels of the neighboring channels.
Name and description Default value Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
ResampleDetermines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rateNew output signal sample rate
128 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value Units Value range
Noise thresholdMinimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
510
WDM DROP
WDM DropDrops a WDM channel from a WDM signal.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output 1 Output Optical
Output 2 Output Optical
Name and description Default value Default unit Units Value range
Frequency 193.1 THz Hz, THz, nm [30, 300000]
Bandwidth3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
[0,+INF[
Insertion lossInsertion loss of the demux
0 dB — [0,+INF[
DepthMaximum attenuation value for the filter
100 dB — [0,+INF[
Filter typeInternal filter type
Bessel — — Rectangle, Gaussian, Bessel
Filter orderOrder of the function when using Gaussian or Bessel filter type
2 — — [1,1000]
511
WDM DROP
Simulation
Noise
Technical background
The input signal is split into two signals. Each signal is filtered by an optical filter. The first signal is filtered by an inverse filter. The optical filters can be a Rectangle, Gaussian, or Bessel optical filter. The subsystem is illustrated in Figure 1.
Figure 1 WDM Drop subsystem
Defining crosstalk
The level of crosstalk for both MUX and DEMUX components, is defined by bandwidth, ripple, and depth of the filter. These 3 factors will determine how much power, from neighboring channels, will act as crosstalk terms when calculating the performance of a specific channel. The most important parameter is depth, as it will play the most significant role in determining the power levels of the neighboring channels.
Name and description Default value Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
ResampleDetermines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rateNew output signal sample rate
128 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value Units Value range
Noise thresholdMinimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
512
WDM ADD AND DROP
WDM Add and DropWDM Add and Drop multiplexer. Equivalent to a subsystem based on the WDM Add and WDM Drop components.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output (Drop) Output Optical
Input (Add) Input Optical
Output Output Optical
Name and description Default value Default unit Units Value range
Frequency 193.1 THz Hz, THz, nm [30, 300000]
Bandwidth3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
[0,+INF[
Insertion lossInsertion loss of the demux
0 dB — [0,+INF[
Depth Maximum attenuation value for the filter
100 dB — [0,+INF[
Filter typeInternal filter type
Bessel — — Rectangle, Gaussian, Bessel
Filter orderOrder of the function when using Gaussian or Bessel filter type
2 — — [1,1000]
513
WDM ADD AND DROP
Simulation
Noise
Technical background
In the drop section, the input signal is divided in two signals. Each signal is filtered by an optical filter. An inverse filter filters the first signal.
In the add section, the input signals are filtered by an optical filter and are combined in one signal. An inverse filter filters the first signal.
The optical filters can be a Rectangle, Gaussian, or Bessel optical filter. The subsystem is illustrated in Figure 1.
Name and description Default value Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
ResampleDetermines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rateNew output signal sample rate
128 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value Units Value range
Noise thresholdMinimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
514
WDM ADD AND DROP
Figure 1 WDM Add and drop subsystem
Defining crosstalk
The level of crosstalk for both MUX and DEMUX components, is defined by bandwidth, ripple, and depth of the filter. These 3 factors will determine how much power, from neighboring channels, will act as crosstalk terms when calculating the performance of a specific channel. The most important parameter is depth, as it will play the most significant role in determining the power levels of the neighboring channels.
515
WDM ADD AND DROP
Notes:
516
WDM DEMUX 1X2
WDM Demux 1x2Demultiplexes two WDM signal channels.
Ports
Parameters
Main
Channels
Name and description Port type Signal type
Input Input Optical
Output 1 Output Optical
Output 2 Output Optical
Name and description Default value Default unit Units Value range
Bandwidth3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
[0,+INF[
Insertion lossInsertion loss of the demux
0 dB — [0,+INF[
DepthMaximum attenuation value for the filter
100 dB — [0,+INF[
Filter typeInternal filter type
Bessel — — Rectangle, Gaussian, Bessel
Filter orderOrder of the function when using Gaussian or Bessel filter type
2 — — [1,1000]
Name and description Default value Default unit Units Value range
Frequency[0]Filter center frequency for channel 0
193.1 THz Hz, THz, nm [30,3e5]
Frequency[1]Filter center frequency for channel 1
193.2 THz Hz, THz, nm [30,3e5]
517
WDM DEMUX 1X2
Ripple
Simulation
Noise
Name and description Default value Units Value range
Ripple[0]Additional loss of the filter for channel 0
0 dB ]-INF,+INF[
Ripple[1] Additional loss of the filter for channel 1
0 dB ]-INF,+INF[
Name and description Default value Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
ResampleDetermines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rateNew output signal sample rate
128 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value Units Value range
Noise thresholdMinimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
518
WDM DEMUX 1X2
Technical backgroundThe input signal is split into two signals that are filtered by an optical filter. The optical filter can be a Rectangle, Gaussian, or Bessel optical filter. The subsystem is illustrated in Figure 1.
Figure 1 Demultiplexer subsystem
Defining crosstalk
The level of crosstalk for both MUX and DEMUX components, is defined by bandwidth, ripple, and depth of the filter. These 3 factors will determine how much power, from neighboring channels, will act as crosstalk terms when calculating the performance of a specific channel. The most important parameter is depth, as it will play the most significant role in determining the power levels of the neighboring channels.
519
WDM DEMUX 1X2
Notes:
520
WDM DEMUX 1X4
WDM Demux 1x4Demultiplexes four WDM signal channels.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output 1 Output Optical
Output 2 Output Optical
Output 3 Output Optical
Output 4 Output Optical
Name and description Default value Default unit Units Value range
Bandwidth3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
[0,+INF[
Insertion lossInsertion loss of the demux
0 dB — [0,+INF[
DepthMaximum attenuation value for the filter
100 dB — [0,+INF[
Filter typeInternal filter type
Bessel — — Rectangle, Gaussian, Bessel
Filter orderOrder of the function when using Gaussian or Bessel filter type
2 — — [1,1000]
521
WDM DEMUX 1X4
Channels
Ripple
Simulation
Noise
Name and description Default value Default unit Units Value range
Frequency[0]Filter center frequency for channel 0
193.1 THz Hz, THz, nm [30,3e5]
Frequency[1]Filter center frequency for channel 1
193.2 THz Hz, THz, nm [30,3e5]
Frequency[2]Filter center frequency for channel 2
193.3 THz Hz, THz, nm [30,3e5]
Frequency[3]Filter center frequency for channel 3
193.4 THz Hz, THz, nm [30,3e5]
Name and description Default value Units Value range
Ripple[0]Additional loss of the filter for channel 0
0 dB ]-INF,+INF[
Ripple[1] Additional loss of the filter for channel 1
0 dB ]-INF,+INF[
Ripple[2]Additional loss of the filter for channel 2
0 dB ]-INF,+INF[
Ripple[3]Additional loss of the filter for channel 3
0 dB ]-INF,+INF[
Name and description Default value Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
ResampleDetermines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rateNew output signal sample rate
128 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value Units Value range
Noise thresholdMinimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
522
WDM DEMUX 1X4
Technical backgroundThe input signal is split into four signals that are filtered by an optical filter. The optical filter can be a Rectangle, Gaussian, or Bessel optical filter. The subsystem is illustrated in Figure 1.
Figure 1 Demultiplexer subsystem
Defining crosstalk
The level of crosstalk for both MUX and DEMUX components, is defined by bandwidth, ripple, and depth of the filter. These 3 factors will determine how much power, from neighboring channels, will act as crosstalk terms when calculating the performance of a specific channel. The most important parameter is depth, as it will play the most significant role in determining the power levels of the neighboring channels.
523
WDM DEMUX 1X4
Notes:
524
WDM DEMUX 1X8
WDM Demux 1x8Demultiplexes eight WDM signal channels.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output 1 Output Optical
Output 2 Output Optical
Output 3 Output Optical
Output 4 Output Optical
Output 5 Output Optical
Output 6 Output Optical
Output 7 Output Optical
Output 8 Output Optical
Name and description Default value Default unit Units Value range
Bandwidth3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
[0,+INF[
Insertion lossInsertion loss of the demux
0 dB — [0,+INF[
DepthMaximum attenuation value for the filter
100 dB — [0,+INF[
Filter typeInternal filter type
Bessel — — Rectangle, Gaussian, Bessel
Filter orderOrder of the function when using Gaussian or Bessel filter type
2 — — [1,1000]
525
WDM DEMUX 1X8
Channels
Ripple
Name and description Default value Default unit Units Value range
Frequency[0]Filter center frequency for channel 0
193.1 THz Hz, THz, nm [30,3e5]
Frequency[1]Filter center frequency for channel 1
193.2 THz Hz, THz, nm [30,3e5]
Frequency[2]Filter center frequency for channel 2
193.3 THz Hz, THz, nm [30,3e5]
Frequency[3]Filter center frequency for channel 3
193.4 THz Hz, THz, nm [30,3e5]
Frequency[4]Filter center frequency for channel 4
193.5 THz Hz, THz, nm [30,3e5]
Frequency[5]Filter center frequency for channel 5
193.6 THz Hz, THz, nm [30,3e5]
Frequency[6]Filter center frequency for channel 6
193.7 THz Hz, THz, nm [30,3e5]
Frequency[7]Filter center frequency for channel 7
193.8 THz Hz, THz, nm [30,3e5]
Name and description Default value Units Value range
Ripple[0]Additional loss of the filter for channel 0
0 dB ]-INF,+INF[
Ripple[1] Additional loss of the filter for channel 1
0 dB ]-INF,+INF[
Ripple[2]Additional loss of the filter for channel 2
0 dB ]-INF,+INF[
Ripple[3]Additional loss of the filter for channel 3
0 dB ]-INF,+INF[
Ripple[4]Additional loss of the filter for channel 4
0 dB ]-INF,+INF[
Ripple[5]Additional loss of the filter for channel 5
0 dB ]-INF,+INF[
Ripple[6]Additional loss of the filter for channel 6
0 dB ]-INF,+INF[
Ripple[7]Additional loss of the filter for channel 7
0 dB ]-INF,+INF[
526
WDM DEMUX 1X8
Simulation
Noise
Technical background
The input signal is split into eight signals that are filtered by an optical filter. The optical filter can be a Rectangle, Gaussian, or Bessel optical filter. The subsystem is illustrated in Figure 1.
Figure 1 Demultiplexer subsystem
Name and description Default value Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
ResampleDetermines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rateNew output signal sample rate
128 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value Units Value range
Noise thresholdMinimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
527
WDM DEMUX 1X8
Defining crosstalk
The level of crosstalk for both MUX and DEMUX components, is defined by bandwidth, ripple, and depth of the filter. These 3 factors will determine how much power, from neighboring channels, will act as crosstalk terms when calculating the performance of a specific channel. The most important parameter is depth, as it will play the most significant role in determining the power levels of the neighboring channels.
528
WDM DEMUX
WDM DemuxDemultiplexes a user-defined number of WDM signal channels.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output 1 Output Optical
Output 2 Output Optical
Output 3 Output Optical
Output 4 Output Optical
Output 5 Output Optical
Output 6 Output Optical
Output 7 Output Optical
Output 8 Output Optical
Name and description Default value Default unit Units Value range
Number of output ports 8 — — [2, 1000]
Bandwidth3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
[0,+INF[
Insertion lossInsertion loss of the demux
0 dB — [0,+INF[
DepthMaximum attenuation value for the filter
100 dB — [0,+INF[
Filter typeInternal filter type
Bessel — — Rectangle, Gaussian, Bessel
Filter orderOrder of the function when using Gaussian or Bessel filter type
2 — — [1,1000]
529
WDM DEMUX
Channels
Ripple
Name and description Default value Default unit Units Value range
Frequency[0]Filter center frequency for channel 0
193.1 THz Hz, THz, nm [30,3e5]
Frequency[1]Filter center frequency for channel 1
193.2 THz Hz, THz, nm [30,3e5]
Frequency[2]Filter center frequency for channel 2
193.3 THz Hz, THz, nm [30,3e5]
Frequency[3]Filter center frequency for channel 3
193.4 THz Hz, THz, nm [30,3e5]
Frequency[4]Filter center frequency for channel 4
193.5 THz Hz, THz, nm [30,3e5]
Frequency[5]Filter center frequency for channel 5
193.6 THz Hz, THz, nm [30,3e5]
Frequency[6]Filter center frequency for channel 6
193.7 THz Hz, THz, nm [30,3e5]
Frequency[7]Filter center frequency for channel 7
193.8 THz Hz, THz, nm [30,3e5]
Name and description Default value Units Value range
Ripple[0]Additional loss of the filter for channel 0
0 dB ]-INF,+INF[
Ripple[1] Additional loss of the filter for channel 1
0 dB ]-INF,+INF[
Ripple[2]Additional loss of the filter for channel 2
0 dB ]-INF,+INF[
Ripple[3]Additional loss of the filter for channel 3
0 dB ]-INF,+INF[
Ripple[4]Additional loss of the filter for channel 4
0 dB ]-INF,+INF[
Ripple[5]Additional loss of the filter for channel 5
0 dB ]-INF,+INF[
Ripple[6]Additional loss of the filter for channel 6
0 dB ]-INF,+INF[
Ripple[7]Additional loss of the filter for channel 7
0 dB ]-INF,+INF[
530
WDM DEMUX
Simulation
Noise
Technical background
The input signal is split into N signals, where N is the number of output ports. The Signals are filtered by an optical filter. The optical filter can be a Rectangle, Gaussian, or Bessel optical filter. The subsystem is illustrated in Figure 1.
Figure 1 Demultiplexer subsystem
Name and description Default value Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
ResampleDetermines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rateNew output signal sample rate
128 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value Units Value range
Noise thresholdMinimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
531
WDM DEMUX
Defining crosstalk
The level of crosstalk for both MUX and DEMUX components, is defined by bandwidth, ripple, and depth of the filter. These 3 factors will determine how much power, from neighboring channels, will act as crosstalk terms when calculating the performance of a specific channel. The most important parameter is depth, as it will play the most significant role in determining the power levels of the neighboring channels.
532
WDM DEMUX ES
WDM Demux ESDemultiplexes a user-defined number of WDM signal channels. The center frequencies of the internal filters are equally spaced (ES).
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output 1 Output Optical
Output 2 Output Optical
Output 3 Output Optical
Output 4 Output Optical
Output 5 Output Optical
Output 6 Output Optical
Output 7 Output Optical
Output 8 Output Optical
Name and description Default value Default unit Units Value range
Number of output ports 8 — — [2, 1000]
FrequencyCenter frequency of the first filter
193.1 THz, Hz, nm [30,+INF[
Frequency spacingFrequency spacing between adjacent filters
100 GHz, THz, Hz, nm
]-INF,+INF[
Bandwidth3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
[0,+INF[
Insertion lossInsertion loss of the demux
0 dB — [0,+INF[
DepthMaximum attenuation value for the filter
100 dB — [0,+INF[
533
WDM DEMUX ES
Simulation
Noise
Technical Background
The WDM Demux ES is equivalent to the conventional WDM Demux component. However, the WDM Demux ES is easier to set up for WDM systems, since it requires only the filter center frequency and the spacing.
Filter typeInternal filter type
Bessel — — Rectangle, Gaussian, Bessel
Filter orderOrder of the function when using Gaussian or Bessel filter type
2 — — [1,1000]
Name and description Default value Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
ResampleDetermines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rateNew output signal sample rate
128 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value Units Value range
Noise thresholdMinimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
Name and description Default value Default unit Units Value range
534
IDEAL DEMUX
Ideal DemuxDemultiplexes a user-defined number of output WDM signal channels. This model is equivalent to an ideal splitter, since there is no power splitting and filtering.
Ports
Parameters
Main
Technical background
The input signal is duplicated and attenuated. The subsystem is illustrated in Figure 1.
Figure 1 Subsystem — duplicated and attenuated input signal
Name and description Port type Signal type
Input Input Optical
Output 1 Output Optical
Output 2 Output Optical
Name and description Default value Units Value range
Number of output ports 2 — [2, 1000]
Insertion lossInsertion loss of the demux
0 dB [0,+INF[
535
WDM MUX 2X1
WDM Mux 2x1Multiplexes two WDM signal channels.
Ports
Parameters
Main
Channels
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Output Output Optical
Name and description Default value Default unit Units Value range
Bandwidth3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
[0,+INF[
Insertion lossInsertion loss of the demux
0 dB — [0,+INF[
Depth Maximum attenuation value for the filter
100 dB — [0,+INF[
Filter typeInternal filter type
Bessel — — Rectangle, Gaussian, Bessel
Filter orderOrder of the function when using Gaussian or Bessel filter type
2 — — [1,1000]
Name and description Default value Default unit Units Value range
Frequency[0]Filter center frequency for channel 0
193.1 THz Hz, THz, nm [30,3e5]
Frequency[1]Filter center frequency for channel 1
193.2 THz Hz, THz, nm [30,3e5]
536
WDM MUX 2X1
Ripple
Simulation
Noise
Name and description Default value Units Value range
Ripple[0]Additional loss of the filter for channel 0
0 dB ]-INF,+INF[
Ripple[1] Additional loss of the filter for channel 1
0 dB ]-INF,+INF[
Name and description Default value Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
ResampleDetermines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rateNew output signal sample rate
128 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value Units Value range
Noise thresholdMinimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
537
WDM MUX 2X1
Technical backgroundThe two input signals are filtered by an optical filter and are combined in one signal. The optical filter can be a Rectangle, Gaussian, or Bessel optical filter. The subsystem is illustrated in Figure 1.
Figure 1 Multiplexer subsystem
Defining crosstalk
The level of crosstalk for both MUX and DEMUX components, is defined by bandwidth, ripple, and depth of the filter. These 3 factors will determine how much power, from neighboring channels, will act as crosstalk terms when calculating the performance of a specific channel. The most important parameter is depth, as it will play the most significant role in determining the power levels of the neighboring channels.
538
WDM MUX 4X1
WDM Mux 4x1Multiplexes four WDM signal channels.
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Input 3 Input Optical
Input 4 Input Optical
Output Output Optical
Name and description Default value Default unit Units Value range
Bandwidth3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
[0,+INF[
Insertion lossInsertion loss of the demux
0 dB — [0,+INF[
DepthMaximum attenuation value for the filter
100 dB — [0,+INF[
Filter typeInternal filter type
Bessel — — Rectangle, Gaussian, Bessel
Filter orderOrder of the function when using Gaussian or Bessel filter type
2 — — [1,1000]
539
WDM MUX 4X1
Channels
Ripple
Simulation
Noise
Name and description Default value Default unit Units Value range
Frequency[0]Filter center frequency for channel 0
193.1 THz Hz, THz, nm [30,3e5]
Frequency[1]Filter center frequency for channel 1
193.2 THz Hz, THz, nm [30,3e5]
Frequency[2]Filter center frequency for channel 2
193.3 THz Hz, THz, nm [30,3e5]
Frequency[3]Filter center frequency for channel 3
193.4 THz Hz, THz, nm [30,3e5]
Name and description Default value Units Value range
Ripple[0]Additional loss of the filter for channel 0
0 dB ]-INF,+INF[
Ripple[1] Additional loss of the filter for channel 1
0 dB ]-INF,+INF[
Ripple[2]Additional loss of the filter for channel 2
0 dB ]-INF,+INF[
Ripple[3]Additional loss of the filter for channel 3
0 dB ]-INF,+INF[
Name and description Default value Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
ResampleDetermines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rateNew output signal sample rate
128 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value Units Value range
Noise thresholdMinimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
540
WDM MUX 4X1
Technical backgroundThe four input signals are filtered by an optical filter and are combined in one signal. The optical filter can be a Rectangle, Gaussian, or Bessel optical filter. The subsystem is illustrated in Figure 1.
Figure 1 Multiplexer subsystem
Defining crosstalk
The level of crosstalk for both MUX and DEMUX components, is defined by bandwidth, ripple, and depth of the filter. These 3 factors will determine how much power, from neighboring channels, will act as crosstalk terms when calculating the performance of a specific channel. The most important parameter is depth, as it will play the most significant role in determining the power levels of the neighboring channels.
541
WDM MUX 4X1
Notes:
542
WDM MUX 8X1
WDM Mux 8x1Multiplexes eight WDM signal channels.
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Input 3 Input Optical
Input 4 Input Optical
Input 5 Input Optical
Input 6 Input Optical
Input 7 Input Optical
Input 8 Input Optical
Output Output Optical
Name and description Default value Default unit Units Value range
Bandwidth3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
[0,+INF[
Insertion lossInsertion loss of the demux
0 dB — [0,+INF[
DepthMaximum attenuation value for the filter
100 dB — [0,+INF[
Filter typeInternal filter type
Bessel — — Rectangle, Gaussian, Bessel
Filter orderOrder of the function when using Gaussian or Bessel filter type
2 — — [1,1000]
543
WDM MUX 8X1
Channels
Ripple
Name and description Default value Default unit Units Value range
Frequency[0]Filter center frequency for channel 0
193.1 THz Hz, THz, nm [30,3e5]
Frequency[1]Filter center frequency for channel 1
193.2 THz Hz, THz, nm [30,3e5]
Frequency[2]Filter center frequency for channel 2
193.3 THz Hz, THz, nm [30,3e5]
Frequency[3]Filter center frequency for channel 3
193.4 THz Hz, THz, nm [30,3e5]
Frequency[4]Filter center frequency for channel 4
193.5 THz Hz, THz, nm [30,3e5]
Frequency[5]Filter center frequency for channel 5
193.6 THz Hz, THz, nm [30,3e5]
Frequency[6]Filter center frequency for channel 6
193.7 THz Hz, THz, nm [30,3e5]
Frequency[7]Filter center frequency for channel 7
193.8 THz Hz, THz, nm [30,3e5]
Name and description Default value Units Value range
Ripple[0]Additional loss of the filter for channel 0
0 dB ]-INF,+INF[
Ripple[1] Additional loss of the filter for channel 1
0 dB ]-INF,+INF[
Ripple[2]Additional loss of the filter for channel 2
0 dB ]-INF,+INF[
Ripple[3]Additional loss of the filter for channel 3
0 dB ]-INF,+INF[
Ripple[4]Additional loss of the filter for channel 4
0 dB ]-INF,+INF[
Ripple[5]Additional loss of the filter for channel 5
0 dB ]-INF,+INF[
Ripple[6]Additional loss of the filter for channel 6
0 dB ]-INF,+INF[
Ripple[7]Additional loss of the filter for channel 7
0 dB ]-INF,+INF[
544
WDM MUX 8X1
Simulation
Noise
Technical background
The eight input signals are filtered by an optical filter and are combined in one signal. The optical filter can be a Rectangle, Gaussian, or Bessel optical filter. The subsystem is illustrated in Figure 1.
Figure 1 Multiplexer subsystem
Name and description Default value Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
ResampleDetermines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rateNew output signal sample rate
128 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value Units Value range
Noise thresholdMinimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
545
WDM MUX 8X1
Defining crosstalk
The level of crosstalk for both MUX and DEMUX components, is defined by bandwidth, ripple, and depth of the filter. These 3 factors will determine how much power, from neighboring channels, will act as crosstalk terms when calculating the performance of a specific channel. The most important parameter is depth, as it will play the most significant role in determining the power levels of the neighboring channels.
546
WDM MUX
WDM MuxMultiplexes a user-defined number of input WDM signal channels.
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Input 3 Input Optical
Input 4 Input Optical
Input 5 Input Optical
Input 6 Input Optical
Input 7 Input Optical
Input 8 Input Optical
Output Output Optical
Name and description Default value Default unit Units Value range
Number of input ports 8 — — [2,1000]
Bandwidth3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
[0,+INF[
Insertion lossInsertion loss of the demux
0 dB — [0,+INF[
DepthMaximum attenuation value for the filter
100 dB — [0,+INF[
Filter typeInternal filter type
Bessel — — Rectangle, Gaussian, Bessel
Filter orderOrder of the function when using Gaussian or Bessel filter type
2 — — [1,1000]
547
WDM MUX
Channels
Ripple
Name and description Default value Default unit Units Value range
Frequency[0]Filter center frequency for channel 0
193.1 THz Hz, THz, nm [30,3e5]
Frequency[1]Filter center frequency for channel 1
193.2 THz Hz, THz, nm [30,3e5]
Frequency[2]Filter center frequency for channel 2
193.3 THz Hz, THz, nm [30,3e5]
Frequency[3]Filter center frequency for channel 3
193.4 THz Hz, THz, nm [30,3e5]
Frequency[4]Filter center frequency for channel 4
193.5 THz Hz, THz, nm [30,3e5]
Frequency[5]Filter center frequency for channel 5
193.6 THz Hz, THz, nm [30,3e5]
Frequency[6]Filter center frequency for channel 6
193.7 THz Hz, THz, nm [30,3e5]
Frequency[7]Filter center frequency for channel 7
193.8 THz Hz, THz, nm [30,3e5]
Name and description Default value Units Value range
Ripple[0]Additional loss of the filter for channel 0
0 dB ]-INF,+INF[
Ripple[1] Additional loss of the filter for channel 1
0 dB ]-INF,+INF[
Ripple[2]Additional loss of the filter for channel 2
0 dB ]-INF,+INF[
Ripple[3]Additional loss of the filter for channel 3
0 dB ]-INF,+INF[
Ripple[4]Additional loss of the filter for channel 4
0 dB ]-INF,+INF[
Ripple[5]Additional loss of the filter for channel 5
0 dB ]-INF,+INF[
Ripple[6]Additional loss of the filter for hannel 6
0 dB ]-INF,+INF[
Ripple[7]Additional loss of the filter for channel 7
0 dB ]-INF,+INF[
548
WDM MUX
Simulation
Noise
Technical background
The input signals are filtered by an optical filter and combined in one signal. The optical filter can be a Rectangle, Gaussian, or Bessel optical filter. The subsystem is illustrated in Figure 1.
Figure 1 Multiplexer subsystem
Name and description Default value Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
ResampleDetermines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rateNew output signal sample rate
128 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value Units Value range
Noise thresholdMinimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
549
WDM MUX
Defining crosstalk
The level of crosstalk for both MUX and DEMUX components, is defined by bandwidth, ripple, and depth of the filter. These 3 factors will determine how much power, from neighboring channels, will act as crosstalk terms when calculating the performance of a specific channel. The most important parameter is depth, as it will play the most significant role in determining the power levels of the neighboring channels.
550
WDM MUX ES
WDM Mux ESThis component multiplexes a user-defined number of WDM signal channels. The center frequencies of the internal filters are equally spaced (ES).
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Input 3 Input Optical
Input 4 Input Optical
Input 5 Input Optical
Input 6 Input Optical
Input 7 Input Optical
Input 8 Input Optical
Output Output Optical
Name and description Default value Default unit Units Value range
Number of input ports 8 — — [2,1000]
FrequencyCenter frequency of the first filter
193.1 — THz, HZ, nm [30,+INF[
Frequency spacingFrequency spacing between adjacent filters
100 — GHz, THz, Hz, nm
]-INF,+INF[
Bandwidth3 dB filter bandwidth
10 GHz Hz, GHz, THz, nm
[0,+INF[
Insertion lossInsertion loss of the demux
0 dB — [0,+INF[
DepthMaximum attenuation value for the filter
100 dB — [0,+INF[
551
WDM MUX ES
Simulation
Noise
Technical Background
The WDM Mux ES is equivalent to the conventional WDM Mux component. However, the WDM Mux ES is easier to set up for WDM systems, since it only requires the filter center frequency and the spacing.
Filter typeInternal filter type
Bessel — — Rectangle, Gaussian, Bessel
Filter orderOrder of the function when using Gaussian or Bessel filter type
2 — — [1,1000]
Name and description Default value Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
ResampleDetermines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rateNew output signal sample rate
128 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value Units Value range
Noise thresholdMinimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
Name and description Default value Default unit Units Value range
552
IDEAL MUX
Ideal MuxMultiplexes a user-defined number of input WDM signal channels. This model is equivalent to an ideal adder, since there is no power splitting and filtering.
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Output Output Optical
Name and description Default value Units Value range
Number of input ports 2 — [2,1000]
LossInsertion loss of the demux
0 dB [0,+INF[
553
IDEAL MUX
Technical backgroundThe input signals are added and attenuated. The subsystem is illustrated in Figure 1.
Figure 1 Ideal Multiplexer subsystem
554
Network Library
This section contains information on the following network components.
Optical Switches
• Dynamic Y Select Nx1 Measured• Dynamic Y Switch 1xN Measured• Dynamic Y Switch 1xN• Dynamic Y Select Nx1• Dynamic Space Switch Matrix NxM Measured• Dynamic Space Switch Matrix NxM• Optical Switch• Digital Optical Switch• Optical Y Switch• Optical Y Select• Ideal Switch 2x2• Ideal Y Switch• Ideal Y Select• Ideal Y Switch 1x4• Ideal Y Select 4x1• Ideal Y Switch 1x8• Ideal Y Select 8x1• Ideal Y Select Nx1• Ideal Y Switch 1xN
555
Frequency Conversion
• Ideal Frequency Converter
556
DYNAMIC Y SELECT NX1 MEASURED
Dynamic Y Select Nx1 MeasuredY select with a user-defined mapping table for different switching events.
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Input 3 Input Optical
Input 4 Input Optical
Input 5 Input Optical
Input 6 Input Optical
Input 7 Input Optical
Input 8 Input Optical
Output Output Optical
Name and description Default value Default unit Units Value range
Number of input ports 8 — — [2, 1000]
Time constantSwitching time constant
50 ns s, ms, ns [0,+INF[
Switching event timeTime instant when the switching event occurs
50 ns s, ms, ns [0,+INF[
Repeat eventsDetermines if the events will be repeated for each event time
False — — True, False
Mapping table filenameFilename with the measured data
Table.dat — — —
557
DYNAMIC Y SELECT NX1 MEASURED
Technical background
Static solution
The switch model allows for the selection of the number of input ports N.
For the input ports i = 1…N, you can select the complex values of a mapping table:
where
If the light electric field complex amplitude entering the input port number 'i' is Ei, then the electric field complex amplitude at the output port due to Ei is:
(1)
When all input ports of the switch are used, the output complex amplitude at the output port is:
(2)
This sum includes all different wavelength contributions.
i = 1
i = 2
i = 3
.
.
.
i = N
n1 j α1×+
n2 j α2×+
n3 j α3×+
nN j αN×+
j 1–( )=
EOutput EiInpute
j ni jαi+( )=
EOutput EiInpute
j ni jαi+( )
i 1=
N
∑=
558
DYNAMIC Y SELECT NX1 MEASURED
Transients
This type of switch is characterized by switching time with a time constant.
Mathematically, a switching event is a replacement of one mapping table, T1, with a different one, T2.
To a first order approximation, the change from to resembles a charging process of a linear capacitor through a linear resistor. It has an exponential time behavior, with a time constant . The parameter time constant is universal and is shared by all transient events.
For a switching event that takes place at time t0, the real part of a mapping matrix element will change as:
(3)
t0 is the parameter Switching event time.
The parameter Repeat events allows you to generate multiple switching events. For example, changing the map table from 1 to 2 and vice versa.
File format
The file format for the data with the map table is:
where the first index is the input port (row) and the second index is the table number (1 or 2).
Assuming a component with 3 input ports, and transient from port 1 to 3:
n1,1 n1,2
n2,1 n2,2
.
.
nN,1 nN,2
0 0 0 10
0 10 0 10
0 10 0 0
ni j αi×+{ }T1 ni j αi×+{ }T2
τ τ
ni t( ) ni T1t t0–( ) τ⁄–( ) ni T2
1 t t0–( ) τ⁄–( )exp–{ }×+exp×=
α1 1, α1 2,
α2 1, α2 2,
αN 1, αN 2,
559
DYNAMIC Y SWITCH 1XN MEASURED
Dynamic Y Switch 1xN MeasuredY switch with user-defined mapping table for different switching events.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output 1 Output Optical
Output 2 Output Optical
Output 3 Output Optical
Output 4 Output Optical
Output 5 Output Optical
Output 6 Output Optical
Output 7 Output Optical
Output 8 Output Optical
Name and description Default value Default unit Units Value range
Number of output ports 8 — — [2, 1000]
Time constantSwitching time constant
50 ns s, ms, ns [0,+INF[
Switching event timeTime instant when the switching event occurs
50 ns s, ms, ns [0,+INF[
Repeat eventsDetermines if the events will be repeated for each event time
False — — True, False
Mapping table filenameFilename with the measured data
Table.dat — — —
560
DYNAMIC Y SWITCH 1XN MEASURED
Technical background
Static solution
The switch model allows for the selection of the number of output ports N.
For the output ports i = 1…N, you can select the complex values of a mapping table:
where
If the light electric field complex amplitude at the output port number 'i' is Ei, calculated from the electric field complex amplitude at the input port, Ei is:
(1)
Transients
This type of switch is characterized by switching time with a time constant.
Mathematically, a switching event is a replacement of one mapping table, T1, with a different one, T2.
To a first order approximation, the change from to resembles a charging process of a linear capacitor through a linear resistor. It has an exponential time behavior, with a time constant . The parameter time constant is universal and is shared by all transient events.
For a switching event that takes place at time t0, the real part of a mapping matrix element will change as:
(2)
t0 is the parameter Switching event time.
i = 1
i = 2
i = 3
.
.
.
i = N
n1 j α1×+
n2 j α2×+
n3 j α3×+
nN j αN×+
j 1–( )=
EOutput EiInpute
j ni jαi+( )=
ni j αi×+{ }T1 ni j αi×+{ }T2
τ τ
ni t( ) ni T1t t0–( ) τ⁄–( ) ni T2
1 t t0–( ) τ⁄–( )exp–{ }×+exp×=
561
DYNAMIC Y SWITCH 1XN MEASURED
The parameter Repeat events allows you to generate multiple switching events. For example, changing the map table from 1 to 2 and vice versa.
File format
The file format for the data with the map table is:
where the first index is the output port (row) and the second index is the table number (1 or 2).
Assuming a component with 3 output ports, and transient from port 3 to 1:
n1,1 n1,2
n2,1 n2,2
.
.
nN,1 nN,2
0 0 0 10
0 10 0 10
0 10 0 0
α1 1, α1 2,
α2 1, α2 2,
αN 1, αN 2,
562
DYNAMIC Y SWITCH 1XN
Dynamic Y Switch 1xNY switch that allows you to control the different values for attenuation and phase values with transient effects when switching from different input ports.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output 1 Output Optical
Output 2 Output Optical
Name and description Default value Default unit Unit Value range
Number of input ports 2 — — [2, 1000]
Port before eventPort number to use before the event
1 — — [1, 1000]
Port after eventPort number to use after the event
2 — — [1, 1000]
Switching event timeTime instant when the switching event occurs
50 ns s, ms, ns [0,+INF[
Repeat eventsDetermines if the events will be repeated for each event time
False — — True, False
Time constantSwitching time constant
50 ns s, ms, ns [0,+INF[
563
DYNAMIC Y SWITCH 1XN
Table
Technical background
Static solution
The switch model allows for the selection of the number of input ports N.
For the input ports i = 1…N, you can select the complex values of a mapping table:
where
If the light electric field complex amplitude entering the input port number 'i' is Ei, then the electric field complex amplitude at the output port due to Ei is:
(1)
Name and description Default value Units Value range
Real coeff. at selected portReal coeff. equivalent to the phase at the selected port
1e-006 — ]-INF,+INF[
Imag coeff. at selected portImag coeff. equivalent to the attenuation at the selected port
1 — ]-INF,+INF[
Real coeff. at other portsReal coeff. equivalent to the phase at other ports
1e-006 — ]-INF,+INF[
Imag coeff. at other portsImag coeff. equivalent to the attenuation at other ports
1e-006 — ]-INF,+INF[
i = 1
i = 2
i = 3
.
.
.
i = N
n1 j α1×+
n2 j α2×+
n3 j α3×+
nN j αN×+
j 1–( )=
EOutput EiInpute
j ni jαi+( )=
564
DYNAMIC Y SWITCH 1XN
When all input ports of the switch are used, the output complex amplitude at the output port is:
(2)
This sum includes all different wavelength contributions.
Transients
This type of switch is characterized by switching time with a time constant.
Mathematically, a switching event is a replacement of one mapping table, T1, with a different one, T2.
To a first order approximation, the change from to resembles a charging process of a linear capacitor through a linear resistor. It has an exponential time behavior, with a time constant . The parameter time constant is universal and is shared by all transient events.
For a switching event that takes place at time t0, the real part of a mapping matrix element will change as:
(3)
t0 is the parameter Switching event time.
The parameter Repeat events allows you to generate multiple switching events. For example, changing the map table from 1 to 2 and vice versa.
Mapping table
The mapping table is generated based on the values for the selected and unselected ports. You can select the values of the real and imag coefficients for the selected port and for the unselected ports. The models assumes that all unselected ports have the same phase and attenuation. For arbitrary values for these coefficients, use the equivalent measured component.
EOutput EiInpute
j ni jαi+( )
i 1=
N
∑=
ni j αi×+{ }T1 ni j αi×+{ }T2
τ τ
ni t( ) ni T1t t0–( ) τ⁄–( ) ni T2
1 t t0–( ) τ⁄–( )exp–{ }×+exp×=
565
DYNAMIC Y SWITCH 1XN
Notes:
566
DYNAMIC Y SELECT NX1
Dynamic Y Select Nx1Y select that allows you to control the different values for attenuation and phase values with transient effects when switching from different output ports.
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Output Output Optical
Name and description Default value Default unit Units Value range
Number of input ports 2 — — [2, 1000]
Port before eventPort number to use before the event
1 — — [1, 1000]
Port after eventPort number to use after the event
2 — — [1, 1000]
Switching event timeTime instant when the switching event occurs
50 ns s, ms, ns [0,+INF[
Repeat eventsDetermines if the events will be repeated for each event time
False — — True, False
Time constantSwitching time constant
50 ns s, ms, ns [0,+INF[
567
DYNAMIC Y SELECT NX1
Table
Technical background
Static solution
The switch model allows for the selection of the number of output ports N.
For the input ports i = 1…N, you can select the complex values of a mapping table:
where
If the light electric field complex amplitude at the output port number 'i' is Ei, calculated from the electric field complex amplitude at the input port, Ei is:
(1)
Name and description Default value Units Value range
Real coeff. at selected portReal coeff. equivalent to the phase at the selected port
1e-006 — ]-INF,+INF[
Imag coeff. at selected portImag coeff. equivalent to the attenuation at the selected port
1 — ]-INF,+INF[
Real coeff. at other portsReal coeff. equivalent to the phase at other ports
1e-006 — ]-INF,+INF[
Imag coeff. at other portsImag coeff. equivalent to the attenuation at other ports
1e-006 — ]-INF,+INF[
i = 1
i = 2
i = 3
.
.
.
i = N
n1 j α1×+
n2 j α2×+
n3 j α3×+
nN j αN×+
j 1–( )=
EOutput EiInpute
j ni jαi+( )=
568
DYNAMIC Y SELECT NX1
Transients
This type of switch is characterized by switching time with a time constant.
Mathematically, a switching event is a replacement of one mapping table, T1, with a different one, T2.
To a first order approximation, the change from to resembles a charging process of a linear capacitor through a linear resistor. It has an exponential time behavior, with a time constant . The parameter time constant is universal and is shared by all transient events.
For a switching event that takes place at time t0, the real part of a mapping matrix element will change as:
(2)
t0 is the parameter Switching event time.
The parameter Repeat events allows you to generate multiple switching events. For example, changing the map table from 1 to 2 and vice versa.
Mapping table
The mapping table is generated based on the values for the selected and unselected ports. You can select the values of the real and imag coefficients for the selected port and for the unselected ports. The models assume that all unselected ports have the same phase and attenuation. For arbitrary values for these coefficients, use the equivalent measured component.
ni j αi×+{ }T1 ni j αi×+{ }T2
τ τ
ni t( ) ni T1t t0–( ) τ⁄–( ) ni T2
1 t t0–( ) τ⁄–( )exp–{ }×+exp×=
569
DYNAMIC Y SELECT NX1
Notes:
570
DYNAMIC SPACE SWITCH MATRIX NXM MEASURED
Dynamic Space Switch Matrix NxM MeasuredSpace switch matrix with a user-defined mapping table for different switching events.
Ports
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Input 3 Input Optical
Input 4 Input Optical
Input 5 Input Optical
Input 6 Input Optical
Input 7 Input Optical
Input 8 Input Optical
Output 1 Output Optical
Output 2 Output Optical
Output 3 Output Optical
Output 4 Output Optical
Output 5 Output Optical
Output 6 Output Optical
Output 7 Output Optical
Output 8 Output Optical
571
DYNAMIC SPACE SWITCH MATRIX NXM MEASURED
Parameters
Main
Name and description Default value Default unit Unit Value range
Number of input ports 8 — — [1, 1000]
Number of output ports 8 — — [1, 1000]
Time constantSwitching time constant
50 ns s, ms, ns [0,+INF[
Switching event timeTime instant when the switching event occurs
50 ns s, ms, ns [0,+INF[
Repeat eventsDetermines if the events will be repeated for each event time
False — — True, False
Mapping table filenameFilename with the measured data
Table.dat — — —
572
DYNAMIC SPACE SWITCH MATRIX NXM MEASURED
Technical background
Static solution
The switch model allows for the selection of the number of input ports N and output ports M.
For the input ports i = 1…N, you can select the complex values of a mapping table:
where
If the light electric field complex amplitude entering the input port number 'i' is Ei, then the electric field complex amplitude at the output port due to Ei is:
(1)
When all input ports of the switch are used, the output complex amplitude at each output port is:
(2)
This sum includes all different wavelength contributions.
i = 1
i = 2
i = 3
.
.
.
i = N
n1 j α1×+
n2 j α2×+
n3 j α3×+
nN j αN×+
j 1–( )=
EOutput EiInpute
j ni jαi+( )=
EOutput EiInpute
j ni jαi+( )
i 1=
N
∑=
573
DYNAMIC SPACE SWITCH MATRIX NXM MEASURED
Transients
This type of switch is characterized by switching time with a time constant.
Mathematically, a switching event is a replacement of one mapping table, T1, with a different one, T2.
To a first order approximation, the change from to resembles a charging process of a linear capacitor through a linear resistor. It has an exponential time behavior, with a time constant . The parameter time constant is universal and is shared by all transient events.
For a switching event that takes place at time t0, the real part of a mapping matrix element will change as:
(3)
t0 is the parameter Switching event time.
The parameter Repeat events allows you to generate multiple switching events. For example, changing the map table from 1 to 2 and vice versa.
File format
The file format for the data with the map table is:
where the first index is the input port (row), the second index is the table number (1 or 2), and the third index is the output port. This means that there is one row for each input port and 4 columns for each output port.
Assuming a component with 3 input and output ports, and transient from port 1 to 3:
n1,1 n1,2 ... n1,1,M n1,2,M
n2,1 n2,2 ... n2,1,M n2,2,M
..
..
nN,1 nN,2 ... nN,1,M nN,2,M
0 0 0 10 0 10 0 10 0 10 0 10
0 10 0 10 0 10 0 10 0 10 0 10
0 10 0 10 0 10 0 10 0 10 0 0
ni j αi×+{ }T1 ni j αi×+{ }T2
τ τ
ni t( ) ni T1t t0–( ) τ⁄–( ) ni T2
1 t t0–( ) τ⁄–( )exp–{ }×+exp×=
α1 1, α1 2, α1 1 M, , α1 2 M, ,
α2 1, α2 2, α2 1 M, , α2 2 M, ,
αN 1, αN 2, αN 1 M, , αN 2 M, ,
574
DYNAMIC SPACE SWITCH MATRIX NXM
Dynamic Space Switch Matrix NxMSpace switch matrix that allows you to control the different values for attenuation and phase values with transient effects when switching from different input and output ports.
Ports
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Input 3 Input Optical
Input 4 Input Optical
Input 5 Input Optical
Input 6 Input Optical
Input 7 Input Optical
Input 8 Input Optical
Output 1 Output Optical
Output 2 Output Optical
Output 3 Output Optical
Output 4 Output Optical
Output 5 Output Optical
Output 6 Output Optical
Output 7 Output Optical
Output 8 Output Optical
575
DYNAMIC SPACE SWITCH MATRIX NXM
Parameters
Main
Table
Name and description Default value Default unit Unit Value range
Number of input ports 8 — — [2, 1000]
Number of output ports 8 — — [2, 1000]
Input port before eventPort number to use before the event
1 — — [1, 1000]
Input port after eventPort number to use after the event
1 — — [1, 1000]
Output port before eventPort number to use before the event
2 — — [1, 1000]
Output port after eventPort number to use after the event
2 — — [1, 1000]
Switching event timeTime instant when the switching event occurs
50 ns s, ms, ns [0,+INF[
Repeat eventsDetermines if the events will be repeated for each event time
False — — True, False
Time constantSwitching time constant
50 ns s, ms, ns [0,+INF[
Name and description Default value Units Value range
Real coeff. at selected portReal coeff. equivalent to the phase at selected port
1e-006 — ]-INF,+INF[
Imag coeff. at selected portImag coeff. equivalent to the attenuation at selected port
1 — ]-INF,+INF[
Real coeff. at other portsReal coeff. equivalent to the phase at other ports
1e-006 — ]-INF,+INF[
Imag coeff. at other portsImag coeff. equivalent to the attenuation at other ports
1e-006 — ]-INF,+INF[
576
DYNAMIC SPACE SWITCH MATRIX NXM
Technical background
Static solution
The switch model allows for the selection of the number of input ports N and output ports M.
For the input ports i = 1…N, you can select the complex values of a mapping table:
where
If the light electric field complex amplitude entering the input port number 'i' is Ei, then the electric field complex amplitude at the output port due to Ei is:
(1)
When all input ports of the switch are used, the output complex amplitude at each output port is:
(2)
This sum includes all different wavelength contributions.
i = 1
i = 2
i = 3
.
.
.
i = N
n1 j α1×+
n2 j α2×+
n3 j α3×+
nN j αN×+
j 1–( )=
EOutput EiInpute
j ni jαi+( )=
EOutput EiInpute
j ni jαi+( )
i 1=
N
∑=
577
DYNAMIC SPACE SWITCH MATRIX NXM
Transients
This type of switch is characterized by switching time with a time constant.
Mathematically, a switching event is a replacement of one mapping table, T1, with a different one, T2.
To a first order approximation, the change from to resembles a charging process of a linear capacitor through a linear resistor. It has an exponential time behavior, with a time constant . The parameter time constant is universal and is shared by all transient events.
For a switching event that takes place at time t0, the real part of a mapping matrix element will change as:
(3)
t0 is the parameter Switching event time.
The parameter Repeat events allows you to generate multiple switching events. For example, changing the map table from 1 to 2 and vice versa.
Mapping table
The mapping table is generated based on the values for the selected and unselected ports. You can select the values of the real and imag coefficients for the selected port and for the unselected ports. The models assume that all unselected ports have the same phase and attenuation. For arbitrary values for these coefficients, use the equivalent measured component.
ni j αi×+{ }T1 ni j αi×+{ }T2
τ τ
ni t( ) ni T1t t0–( ) τ⁄–( ) ni T2
1 t t0–( ) τ⁄–( )exp–{ }×+exp×=
578
OPTICAL SWITCH
Optical SwitchSimulates a non-ideal switch 2x2.
Ports
Parameters
Main
Technical background
The optical switch routes the optical signals at input port 1 and 2 to the two output ports, according to the parameter phase shift described as follows:• If the phase shift is 0, then the optical signal at input 1 is passed to output 2 and the optical
signal at input 2 is passed to output 1 (see Figure 1). • If the phase shift is , then the optical signal at input 2 is passed to output 2 and the optical
signal at input 1 is passed to output 1 (Figure 1).
Name and description Port type Signal type
Input1 Input Optical
Input 2 Input Optical
Output 1 Output Optical
Output 2 Output Optical
Name and description Default value Default unit Value range
Phase shift Zero — Zero, pi
Additional loss 0 dB [0, 1e100]
π
579
OPTICAL SWITCH
Figure 1 Switch behavior
The following equations describe the switch behavior:
where E1in and E2in are the input signals at input port 1 and 2 respectively.
(4)
(5)
(6)
(7)
where the coupling coefficient, cc, is 0.5, is the phase shift parameter, and is the additional loss.
E1out
E2out
αm11
m21
⋅=m12
m22
E1in
E2in
⋅
m11 1 cc–( ) j φ⋅( ) cc–exp⋅=
m12 1 cc– j cc j φ⋅( ) 1+exp( )⋅ ⋅ ⋅=
m21 1 cc– j cc j φ⋅( ) 1+exp( )⋅ ⋅ ⋅=
m22 1 cc–( ) cc j φ⋅( )exp⋅–⋅=
φ α
580
DIGITAL OPTICAL SWITCH
Digital Optical SwitchSimulates a non-ideal switch 2x2 with a control signal.
Ports
Parameters
Main
Name and description Port type Signal type
Control Input Binary
Input1 Input Optical
Input 2 Input Optical
Output 1 Output Optical
Output 2 Output Optical
Name and description Default value Default unit Value range
Additional loss 0 dB [0, 1e100]
581
DIGITAL OPTICAL SWITCH
Technical backgroundThe digital optical switch routes the optical signals at input port 1 and 2 to the two output ports, according to the control signal described as follows:• If the control signal is 0, then the optical signal at input 1 is passed to output 1 and the
optical signal at input 2 is passed to output 2.• If the control signal is 1, then the optical signal at input 2 is passed to output 1 and the
optical signal at input 1 is passed to output 2.
The working behavior of this component is similar to the optical switch component. When the control signal is 0, internally the phase shift is set at , and when the control signal is 1, the phase shift is set at 0.
π
582
OPTICAL Y SWITCH
Optical Y SwitchSimulates a non-ideal optical switch 1x2.
Ports
Parameters
Main
Name and description Port type Signal type
Control Input Binary
Input Input Optical
Output 1 Output Optical
Output 2 Output Optical
Name and description Default value Default unit Value range
Insertion loss 0 dB [0, 1e100]
Crosstalk 1 30 dB [0, 1e100]
Crosstalk 2 30 dB [0, 1e100]
Phase shift 1 90 deg [-1e50, 1e50]
Phase shift 2 90 deg [-1e50, 1e50]
583
OPTICAL Y SWITCH
Technical backgroundThe digital optical 1x2 switch routes the input signal to one of two output ports, including crosstalk and phase shift between the two input signals. The parameters responsible for crosstalk between the two output signals are crosstalk 1 and crosstalk 2. The phase shift is specified by phase shift 1 and phase shift 2.
This model has two modes of operation:• If the control is 0, then the optical signal at input is routed to output 1 (see Figure 1).• If the control is 1, then the optical signal at input is routed to output 2 (see Figure 1).
Figure 1 Switch behavior
584
OPTICAL Y SELECT
Optical Y SelectSimulates a non-ideal optical switch 2x1.
Ports
Parameters
Main
Name and description Port type Signal type
Control Input Binary
Input1 Input Optical
Input 2 Input Optical
Output Output Optical
Name and description Default value Default unit Value range
Insertion loss 0 dB [0, 1e100]
Crosstalk 1 30 dB [0, 1e100]
Crosstalk 2 30 dB [0, 1e100]
Phase shift 1 90 deg [-1e50, 1e50]
Phase shift 2 90 deg [-1e50, 1e50]
585
OPTICAL Y SELECT
Technical backgroundThe digital optical 2x1 switch selects one of the two input signals and the route to the output port, including crosstalk and phase shift between the two input signals. The parameters responsible for crosstalk between the input signals are crosstalk 1 and crosstalk 2. The phase shift is specified by phase shift 1 and phase shift 2.
This model has two modes of operation:• If the control is 0, then the optical signal at input 1 is passed to the output (see Figure 1).• If the control is 1, then the optical signal at input 2 is passed to the output (see Figure 1).
Figure 1 Switch behavior
586
IDEAL SWITCH 2X2
Ideal Switch 2x2Simulates an ideal switch 2x2.
Ports
Parameters
Simulation
Name and description Port type Signal type
Control Input Binary
Input1 Input Optical
Input 2 Input Optical
Output 1 Output Optical
Output 2 Output Optical
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
587
IDEAL SWITCH 2X2
Technical backgroundThe ideal optical 2x2-switch routes the optical signals at input port 1 and 2 to the two output ports according with the control signal.
The ideal 2x2 switch has two modes of operation:• If the control is 0, then the optical signal at input 1 is passed to output 1 and the optical
signal at input 2 is passed to output 2 (see Figure 1).• If the control is 1, then the optical signal at input 2 is passed to output 1 and the optical
signal at input 1 is passed to output 2 (see Figure 1).
Figure 1 Switch behavior
588
IDEAL Y SWITCH
Ideal Y SwitchSimulates an ideal optical 1x2 switch.
Ports
Parameters
Simulation
Name and description Port type Signal type
Control Input Binary
Input Input Optical
Output 1 Output Optical
Output 2 Output Optical
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
589
IDEAL Y SWITCH
Technical backgroundThe ideal optical 1x2 switch routes a signal in the input port to one of two output ports.
The ideal 2x1 switch has two modes of operation as follows:• If the control is 0, then the optical signal at input 1 is passed to output 1 (see Figure 1).• If the control is 1, then the optical signal at input 2 is passed to output 2 (see Figure 1).
Figure 1 Switch behavior
590
IDEAL Y SELECT
Ideal Y SelectSimulates an ideal optical select switch.
Ports
Parameters
Simulation
Name and description Port type Signal type
Control Input Binary
Input 1 Input Optical
Input 2 Input Optical
Output Output Optical
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
591
IDEAL Y SELECT
Technical backgroundThe ideal Y select switch has two modes of operation:• If the control is 0, then the optical signal at input 1 is passed to the output (see Figure 1).• If the control is 1, then the optical signal at input 2 is passed to the output (see Figure 1).
Figure 1 Switch behavior
592
IDEAL Y SWITCH 1X4
Ideal Y Switch 1x4Simulates an ideal optical 1x4 switch.
Ports
Parameters
Simulation
Name and description Port type Signal type
Control Input Binary
Input Input Optical
Output 1 Output Optical
Output 2 Output Optical
Output 3 Output Optical
Output 4 Output Optical
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
593
IDEAL Y SWITCH 1X4
Technical backgroundThe ideal optical 1x4 switch routes a signal in the input port to one of four output ports.
The ideal 1x4 switch has four states of operation, as follows:• If the control is 00, then the optical signal at input is passed to output 1 (see Figure 1).• If the control is 01, then the optical signal at input is passed to output 2 (see Figure 1).• If the control is 10, then the optical signal at input is passed to output 3 (see Figure 1).• If the control is 11, then the optical signal at input is passed to output 4 (see Figure 1).
Figure 1 Two possible working states of the 4x1 switch
594
IDEAL Y SELECT 4X1
Ideal Y Select 4x1Simulates an ideal optical switch 4x1.
Ports
Parameters
Simulation
Name and description Port type Signal type
Control Input Binary
Input 1 Input Optical
Input 2 Input Optical
Input 3 Input Optical
Input 4 Input Optical
Output Output Optical
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
595
IDEAL Y SELECT 4X1
Technical backgroundThe ideal Y select 4x1 switch has four states of operation:• If the control is 00, then the optical signal at input 1 is passed to out (see Figure 1).• If the control is 01, then the optical signal at input 2 is passed to out (see Figure 1).• If the control is 10, then the optical signal at input 3 is passed to out (see Figure 1).• If the control is 11, then the optical signal at input 4 is passed to out (see Figure 1).
Figure 1 Two possible working states of the 4x1 switch
596
IDEAL Y SWITCH 1X8
Ideal Y Switch 1x8Simulates an ideal optical 1x8 switch.
Ports
Parameters
Simulation
Name and description Port type Signal type
Control Input Binary
Input Input Optical
Output 1 Output Optical
Output 2 Output Optical
Output 3 Output Optical
Output 4 Output Optical
Output 5 Output Optical
Output 6 Output Optical
Output 7 Output Optical
Output 8 Output Optical
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
597
IDEAL Y SWITCH 1X8
Technical backgroundThe ideal optical 1x8-switch routes a signal in the input port to one of eight output ports (see Figure 1).
Figure 1 One possible working state of the 1x8 switch
Table 1 displays the switching states for the eight output ports.
Table 1 Switching states — output ports
Control Output 1 Output 2 Output 3 Output 4 Output 5 Output 6 Output 7 Output 8
000 X — — — — — — —
001 — X — — — — — —
010 — — X — — — — —
011 — — — X — — — —
100 — — — — X — — —
101 — — — — — X — —
110 — — — — — — X —
111 — — — — — — — X
598
IDEAL Y SELECT 8X1
Ideal Y Select 8x1Simulates an ideal optical switch 8x1.
Ports
Parameters
Simulation
Name and description Port type Signal type
Control Input Binary
Input 1 Input Optical
Input 2 Input Optical
Input 3 Input Optical
Input 4 Input Optical
Input 5 Input Optical
Input 6 Input Optical
Input 7 Input Optical
Input 8 Input Optical
Output Output Optical
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
599
IDEAL Y SELECT 8X1
Technical backgroundThe ideal optical 8x1-switch routes one of the 8 input signals to the output port.
Figure 1 One possible working state of the 8x1 switch
Table 2 displays the switching states for the eight input ports.
Table 2 Switching states — input ports
Control Input 1 Input 2 Input 3 Input 4 Input 5 Input 6 Input 7 Input 8
000 X — — — — — — —
001 — X — — — — — —
010 — — X — — — — —
011 — — — X — — — —
100 — — — — X — — —
101 — — — — — X — —
110 — — — — — — X —
111 — — — — — — — X
600
IDEAL Y SELECT NX1
Ideal Y Select Nx1Simulates an ideal optical switch with a variable number of input ports.
Ports
Parameters
Simulation
Name and description Port type Signal type
Control Input Binary
Input 1 Input Optical
Input 2 Input Optical
Output Output Optical
Name and description Default value Units Value range
Number of input ports 2 — [2, 1000]
EnabledDetermines whether or not the component is enabled
True — True, False
601
IDEAL Y SELECT NX1
Technical backgroundThe number of input ports for the Nx1 switch is given by the number of input ports parameter. The bit sequence length of control signals must be enough for the correct use of the switch. The minimum number of bits is:
where nb is the number of bits and Nin is the number of input ports.
The control signal specifies which input port will have the optical signal routed to the output port.
nb log2 Nin( )=
602
IDEAL Y SWITCH 1XN
Ideal Y Switch 1xNSimulates an ideal optical 1xN switch with a variable number of output ports.
Ports
Parameters
Simulation
Name and description Port type Signal type
Control Input Binary
Input Input Optical
Output 1 Output Optical
Output 2 Output Optical
Name and description Default value Units Value range
Number of output ports 2 — [2, 1000]
EnabledDetermines whether or not the component is enabled
True — True, False
603
IDEAL Y SWITCH 1XN
Technical backgroundThe control signal must be long enough for the correct use of the switch. The minimum number of bits is:
where nb is the number of bits and Nout is the number of output ports.
The control signal specifies which output port will have the optical signal roouted at the input port.
nb 2 Nout( )log=
604
IDEAL FREQUENCY CONVERTER
Ideal Frequency ConverterSimulates an ideal frequency converter.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Optical Input Optical
Optical Output Optical
Name and description Default value Default unit Value range
Frequency offset 100 GHz [-1e6, 1e6 ]
Shift band True — True, False
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
605
IDEAL FREQUENCY CONVERTER
Technical backgroundThe ideal frequency converter shifts the optical signal spectrum by the amount (frequency offset). There are two modes of operation:• If the shift band parameter is true, then the center frequency is changed and the complex
amplitude of the sampled eletrical field remains unchanged (see Figure 1).• If shift band parameter is false, a cyclic shift is performed (see Figure 1). The complex
amplitudes are changed according to:
For parameterized and noise bins signals, there is only one mode of operation — shift band true.
Figure 1 Ideal frequency converter behavior: (a) input signal, (b) output signal – shift band false and (c) output signal – shift band true
∆f
Eout t( ) Ein t( ) 2 π ∆f t⋅⋅ ⋅( )exp⋅=
606
Passives LibraryThis section contains information on the following passives.
Electrical• Electrical Signal Time Delay
Optical
• Optical Attenuator• Phase Shift• PMD Emulator• Time Delay
Couplers
• X Coupler• Pump Coupler Co-Propagating• Pump Coupler Counter-Propogating
Power Splitters
• Power Splitter 1x2• Power Splitter 1x4• Power Splitter 1x8• Power Splitter
Power Combiners
• Power Combiner 2x1• Power Combiner 4x1• Power Combiner 8x1• Power Combiner
607
Polarization
• Linear Polarizer• Circular Polarizer• Polarization Attenuator• Polarization Combiner• Polarization Controller• Polarization Rotator• Polarization Splitter
Isolators
• Isolator• Ideal Isolator
Circulators
• Circulator• Ideal Circulator
608
ELECTRICAL SIGNAL TIME DELAY
Electrical Signal Time Delay
Adds a time delay to the electrical signal input.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Units Value range
DelayDelay to apply to the signal input
0 s s, ms, ns [0,+INF[
Name and description Default value
Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
609
ELECTRICAL SIGNAL TIME DELAY
Notes:
610
OPTICAL ATTENUATOR
Optical Attenuator
Attenuates the optical signal power.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value Default unit Value range
AttenuationPower attenuation
0 dB [0,+INF[
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
611
OPTICAL ATTENUATOR
Technical backgroundThe signal input electrical field for both polarizations is attenuated as:
(1)
where α is the power attenuation.
EOutX Y, t( ) EInX Y,t( )10
α–20-------
=
612
PHASE SHIFT
Phase Shift
Adds a time phase advance/delay to the optical signal input.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value Units Value range
Phase shiftPhase shift to apply to the signal
0 deg ]-INF,+INF[
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
613
PHASE SHIFT
Notes:
614
PMD EMULATOR
PMD Emulator
This component simulates the effects of first- and second-order PMD in a linear fiber.
Ports
Parameters
Main
Name and description Port type Signal type
Input1 Input Optical
Output1 Output Optical
Name and description Symbol Default value
Units Value range
Length
Fiber length
L 50 km ]0,+INF[
Attenuation
Fiber attenuation coefficient
0.2 dB/km [0,+INF[
Dispersion
Dispersion at the frequency reference
D 17 ps / (nm - km)
]-INF, +INF[
Dispersion slope
Slope of the dispersion at the frequency reference
S 0.075 ps / (nm2 - km)
]-INF, +INF[
Frequency reference
Frequency of reference for the specified parameters
f 193.1 THz ]-INF, +INF[
Differential group delay 71 ps [0, +INF[
Polarization chromatic dispersion 1.3 ps/GHz ]-INF, +INF[
Depolarization rate 2k 10.8 Deg/GHz ]-INF, +INF[
α
∆τ0
∆τ'
615
PMD EMULATOR
Simulation
Technical backgroundAs bit rates increase to 10 Gbps and 40 Gbps, Polarization Mode Dispersion (PMD) becomes one of the leading causes of signal degradation in data transmission. A physical phenomenon in optical fiber that is statistical in nature, PMD causes dispersion, or spreading of pulses in time and distance, causing adjacent signal pulses to overlap and produce bit errors. The PMD emulator component consists of the PMD channel transfer function considering the first (frequency independent) and second order (frequency dependent) PMD effects.
A linear dispersive fiber can be represented by a 2x2 transfer matrix of the form [1]:
where is the fiber attenuation, is the mean propagation constant, and is the unitary matrix that can be written as:
takes into account the rotation of the principal states of polarization (PSP):
where the coefficient k is defined by the depolarization rate .
The parameter s is the direction of one of the two orthogonal eigenvectors.
D takes into account the different propagation speeds on the two PSPs, with the expressions:
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
(1)
(2)
T ω( ) α– j β ω( )⋅–( ) z⋅( ) M ω( )⋅exp=
α β M
M ω( ) R 1– ω( ) D ω( ) R ω( )⋅⋅=
R
R ω( ) k ω⋅( ) k ω⋅( )sincosk ω⋅( ) k ω⋅( )cossin–
=
2k ∂s∂ω-------=
D ω( ) j ∆τ ω 2⁄⋅ ⋅( )exp 0 0 j– ∆τ ω 2⁄⋅ ⋅( )exp
=
616
PMD EMULATOR
In the second-order approximation the time difference between the two polarizations is given by:
Where is frequency independent differential group delay, and the differential group delay frequency dependency is represented by the depolarization rate .
∆τ ∆τ0 ∆τ'ω+=
∆τ0∆τ'
617
PMD EMULATOR
References:[1] Cristian Francia, Frank Bruyere, Denis Penninckx, and Michel Chbat. " PMD Second-Order
Effects on Pulse Propagation in Single-Model Optical Fibers". IEEE Photonics Technology Letters, December 1998.
[2] L. E. Nelson, R. M. Jopson, H. Kogelnik, and G. J. Foschini. "Measurement of Depolarization and Scaling Associated with Second Order Polarization Mode Dispersion in Optical Fibers". IEEE Photonics Technology Letters, December 1999.
618
TIME DELAY
Time Delay
Adds a time delay to the optical signal input.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value
Default unit Units Value range
DelayDelay to apply to the signal input
0 s s, ms, ns [0,+INF[
Name and description Default value
Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
619
TIME DELAY
Notes:
620
X COUPLER
X Coupler
Cross coupler for combining or splitting optical signals.
Ports
ParametersMain
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Output 1 Output Optical
Output 2 Output Optical
Name and description Default value Units Value range
Coupling coefficientCoupling factor from port 1 to port 2
0.5 — [0,1]
Additional lossLoss applied to the signal after coupling
0 dB [0,+INF[
621
X COUPLER
Technical backgroundThe transmission matrix for the cross:
(1)
where c is coupling coefficient and and α is the additional loss.
References
[1] Gerd Keiser, “Optical Fiber Communications,” Third Edition, McGraw-Hill, Higher Education, 2000.
E1OutX Y,
E2OutX Y,
α1 c– j c
j c 1 c– E1InX Y,
E2InX Y,
=
622
PUMP COUPLER CO-PROPAGATING
Pump Coupler Co-Propagating
Equivalent to a pump coupler subsystem where you can control the attenuation of the signal and pump independently.
Ports
Parameters
Main
Name and description Port type Signal type
Signal Input Input Optical
Pump Input Input Optical
Output Output Optical
Name and description Default value Units Value range
Signal attenuationSignal power attenuation
0 dB [0,+INF[
Pump attenuationPump power attenuation
0 dB [0,+INF[
623
PUMP COUPLER CO-PROPAGATING
Technical backgroundThe input signals are attenuated and combined. The subsystem is illustrated in Figure 1.
Figure 1 Pump coupler co-propogating subsystem
624
PUMP COUPLER COUNTER-PROPOGATING
Pump Coupler Counter-Propogating
Equivalent to a subsystem where you can control the attenuation of the signal and pump independently.
Ports
Parameters
Main
Name and description Port type Signal type
Signal Input Input Optical
Pump Input Input Optical
Pump Output Output Optical
Output Output Optical
Name and description Default value Units Value range
Signal attenuationSignal power attenuation
0 dB [0,+INF[
Pump attenuationPump power attenuation
0 dB [0,+INF[
625
PUMP COUPLER COUNTER-PROPOGATING
Technical backgroundThe input signals are attenuated independently. The subsystem is illustrated in Figure 1.
Figure 1 Pump coupler counter-propogating subsystem
626
POWER SPLITTER 1X2
Power Splitter 1x2
Ideal power splitter — splits an optical input signal into two ouput signals.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output 1 Output Optical
Output 2 Output Optical
Name and description Default value Units Value range
LossLoss applied to the signal after splitting
0 dB [0,+INF[
627
POWER SPLITTER 1X2
Technical backgroundThe signal output for each port is attenuated by:
(1)
where α is the power attenuation and N is the number of ouput ports (N=2).
EOutX Y, t( )EInX Y,
t( )10α–
20-------
N-------------------------------=
628
POWER SPLITTER 1X4
Power Splitter 1x4
Ideal power splitter — splits an optical input signal in four ouput signals.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output 1 Output Optical
Output 2 Output Optical
Output 3 Output Optical
Output 4 Output Optical
Name and description Default value Units Value range
LossLoss applied to the signal after splitting
0 dB [0,+INF[
629
POWER SPLITTER 1X4
Technical backgroundThe signal output for each port is attenuated by:
(1)
where α is the power attenuation and N is the number of ouput ports (N=4).
EOutX Y, t( )EInX Y,
t( )10α–
20-------
N-------------------------------=
630
POWER SPLITTER 1X8
Power Splitter 1x8
Ideal power splitter — splits an optical input signal in eight output signals.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output 1 Output Optical
Output 2 Output Optical
Output 3 Output Optical
Output 4 Output Optical
Output 5 Output Optical
Output 6 Output Optical
Output 7 Output Optical
Output 8 Output Optical
Name and description Default value Units Value range
LossLoss applied to the signal after splitting
0 dB [0,+INF[
631
POWER SPLITTER 1X8
Technical backgroundThe signal output for each port is attenuated by:
(1)
where α is the power attenuation and N is the number of ouput ports (N=8).
EOutX Y, t( )EInX Y,
t( )10α–
20-------
N-------------------------------=
632
POWER SPLITTER
Power Splitter
Ideal power splitter — splits an optical input signal into a user-defined number of ouput signals.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output 1 Output Optical
Output 2 Output Optical
Name and description Default value Units Value range
Number of output ports 2 — [2,1000]
LossLoss applied to the signal after splitting
0 dB [0,+INF[
633
POWER SPLITTER
Technical backgroundThe signal output for each port is attenuated by:
(1)
where α is the power attenuation and N is the number of ouput ports.
EOutX Y, t( )EInX Y,
t( )10α–
20-------
N-------------------------------=
634
POWER COMBINER 2X1
Power Combiner 2x1
Ideal power combiner — combines two optical input signals.
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Output Output Optical
Name and description Default value Units Value range
LossLoss applied to the signal after splitting
0 dB [0,+INF[
635
POWER COMBINER 2X1
Technical backgroundThe signal output for each port is attenuated by:
(1)
where α is the power attenuation and N is the number of input ports (N=2).
EOutX Y, t( ) 10α–
20-------
N----------- EIn NX Y,, t( )
1
N
∑=
636
POWER COMBINER 4X1
Power Combiner 4x1
Ideal power combiner — combines four optical input signals.
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Input 3 Input Optical
Input 4 Input Optical
Output Output Optical
Name and description Default value Units Value range
LossLoss applied to the signal after splitting
0 dB [0,+INF[
637
POWER COMBINER 4X1
Technical backgroundThe signal output for each port is attenuated by:
(1)
where α is the power attenuation and N is the number of input ports (N=4).
EOutX Y, t( ) 10α–
20-------
N----------- EIn NX Y,, t( )
1
N
∑=
638
POWER COMBINER 8X1
Power Combiner 8x1
Ideal power combiner — combines eigth optical input signals.
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Input 3 Input Optical
Input 4 Input Optical
Input 5 Input Optical
Input 6 Input Optical
Input 7 Input Optical
Input 8 Input Optical
Output Output Optical
Name and description Default value Units Value range
LossLoss applied to the signal after splitting
0 dB [0,+INF[
639
POWER COMBINER 8X1
Technical backgroundThe signal output for each port is attenuated by:
(1)
where α is the power attenuation and N is the number of input ports (N=8).
EOutX Y, t( ) 10α–
20-------
N----------- EIn NX Y,, t( )
1
N
∑=
640
POWER COMBINER
Power Combiner
Ideal power combiner — combines a user-defined number of input signals.
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Output Output Optical
Name and description Default value Units Value range
Number of input ports 2 — [2,1000]
LossLoss applied to the signal after splitting
0 dB [0,+INF[
641
POWER COMBINER
Technical backgroundThe signal output for each port is attenuated by:
(1)
where α is the power attenuation and N is the number of input ports.
EOutX Y, t( ) 10α–
20-------
N----------- EIn NX Y,, t( )
1
N
∑=
642
LINEAR POLARIZER
Linear Polarizer
Simulates an ideal linear polarizer.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value Units Value range
Device angle 0 deg [ 1e-50, 1e-50 ]
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
643
LINEAR POLARIZER
Technical backgroundThe ideal linear polarizer transmits the linear polarization component that coincides with the transmission axis of the polarizer (given by device angle). The orthogonal component removed.
The following Jones (1) and Mueller (2) matrices describe the polarization transfer function of this model with an arbitrary device angle :
(1)
(2)
The Jones matrix is used in sampled signals. The Mueller matrix is used for parameterized and noise bins signals.
θ
cos2 θ( )θ( ) θ( )sin⋅cos
θ( ) θ( )sin⋅cos
sin2 θ( )
12---
12θ( )cos2θ( )sin
0
2θ( )cos
cos2 2θ( )2θ( ) sin 2θ( )⋅cos
0
2θ( )sin2θ( ) 2θ( )sin⋅cos
sin2 2θ( )0
0000
644
CIRCULAR POLARIZER
Circular Polarizer
Simulates an ideal circular polarizer.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value Units Value range
Circular type Right — Left, Right
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
645
CIRCULAR POLARIZER
Technical backgroundThe ideal circular polarizer transmits the circular polarization component of the input signal. The input signal type coincides with the polarizer type (given by circular type). The orthogonal circular polarized component is removed.
The following Jones and Mueller matrices describe the model:
(1)
(2)
The Jones matrices are used in sampled signals. The Mueller matrices are used for parameterized and noise bins signals.
Right Left
Right Left
1 2⁄j 2⁄
j 2⁄–0
1 2⁄j 2⁄–
j 2⁄0
1 2⁄00
1 2⁄
0000
0000
1 2⁄00
1 2⁄
1 2⁄00
1 2⁄–
0000
0000
1 2⁄–00
1 2⁄
646
POLARIZATION ATTENUATOR
Polarization Attenuator
Simulates a polarization attenuator.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value Units Value range
Attenuation X 0 dB [0, 1e+050]
Attenuation Y 0 dB [0, 1e+050]
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
647
POLARIZATION ATTENUATOR
Technical backgroundThe polarization attenuator allows the attenuation of each polarization component by multiplication with constant values. The parameters attenuation x and attenuation y define the amount of attenuation the x polarization and the y polarization components will be multiplied by.
The following Jones and Mueller matrices describe the transmission of the signal:
(1)
(2)
The Jones matrix is used in sampled signals. The Mueller matrix is used for parameterized and noise bins signals.
10αx 20⁄–
0
0
10αy 20⁄–
12---
10αx 10⁄–
10αy 10⁄–
+
10αx 10⁄–
10αy 10⁄–
–00
10αx 10⁄–
10αy 10⁄–
–
10αx 10⁄–
10αy 10⁄–
+00
00
2 10⋅αx 20⁄–
10αy 20⁄–
⋅0
000
2 10⋅αx 20⁄–
10αy 20⁄–
⋅
⋅
648
POLARIZATION COMBINER
Polarization Combiner
Simulates a polarization combiner.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Output Output Optical
Name and description Default value Units Value range
Device angle 0 deg [-1e-50, +1e-50 ]
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
649
POLARIZATION COMBINER
Technical backgroundThis model combines the two input signals to one output port. The polarization combiner selects the appropriate polarization component of each signal at the input ports and adds the selected polarization components. Figure 1 shows how this model is implemented. There is a linear polarizer at each input port. The angle of each polarizer is given by device angle. An angle of 90° is added to the device angle of the polarizer at input port 2.
Figure 1 Polarizer Combiner
650
POLARIZATION CONTROLLER
Polarization Controller
Simulates a polarization controller.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value Units Value range
Azimuth 0 deg [ -90, 90 ]
Ellipticity 0 deg [ -45, 45 ]
Symmetry factor 0 — [ -1e100, 1e100 ]
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
651
POLARIZATION CONTROLLER
Technical backgroundThe polarization controller sets the input signal in an arbitrary polarization state. The azimuth and ellipticity parameters define the polarization state of the output signal. In this case, the output polarization is independent of the input signal polarization.
Considering Einx and Einy as the polarization components of the input signal, the output signal is:
(1)
where k is the power splitting ratio parameter and is the phase difference between the x and y components.
The splitting ratio is:
(2)
and the phase difference is
(3)
The x and y phase components are derived from:
(4)
where sf is the symmetry factor.
For sampled signals, Equation 1, Equation 2, and Equation 3 describe the output signal. The following Stokes representation describes parameterized and noise bins signals:
(5)
Eout t( )1 k– j δx t( )⋅( )exp⋅
k j δx t( )⋅( )exp⋅
Einx2 Einy
2+⋅=
δyx t( )
k 1 2 η⋅( ) 2 ε⋅( )cos⋅cos–( ) 2⁄=
δyx arc 2 ε⋅( )sin2 k 1 k–( )⋅⋅-----------------------------------
sin=
sfδx δinx–δy δiny–--------------------=
Sout Einx2 Einy
2+( )
12 ε⋅( ) 2 η⋅( )cos⋅cos2 ε⋅( ) 2 η⋅( )sin⋅cos
2 ε⋅( )sin
=
652
POLARIZATION ROTATOR
Polarization Rotator
Simulates a rotation of coordinate axes.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value Units Value range
Rotation angle 0 deg [ 1e-50, 1e-50 ]
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
653
POLARIZATION ROTATOR
Technical backgroundThe polarization rotator performs a rotation of the coordinate axes system. The parameter Device angle rotates the angle by counterclockwise.
The rotation is:
(1)
(2)
Based on Equation 1 and Equation 2, the corresponding Jones matrix is defined as:
(3)
The corresponding Mueller matrix is:
(4)
The Jones matrix is used in sampled signals. The Mueller matrix is used for parameterized and noise bins signals.
φ
xo x φ( ) y φ( )sin⋅+cos⋅=
yo x φ( ) y φ( )cos⋅+sin⋅–=
φ( )cosφ( )sin–
φ( )sinφ( )cos
1000
02 φ⋅( )cos2 φ⋅( )sin–
0
02 φ⋅( )sin2 φ⋅( )cos0
0001
654
POLARIZATION SPLITTER
Polarization Splitter
Simulates a polarization splitter.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Optical
Output 1 Output Optical
Output 2 Output Optical
Name and description Default value Units Value range
Device angle 0 deg [-1e-50, +1e-50 ]
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
655
POLARIZATION SPLITTER
Technical backgroundThis model splits the input signal to two output ports. The polarization splitter selects the appropriate polarization component of the signal at the input port and each polarization component for one of two output ports. Figure 1 shows how this model is implemented.
Figure 1 Polarizer Splitter
656
ISOLATOR
Isolator
Optical isolator. You can control insertion loss, return loss, and isolation.
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 (forward) Input Optical
Output 2 (forward) Output Optical
Input 2 (backward) Input Optical
Output 1 (backward) Output Optical
Name and description Default value Units Value range
Insertion lossAttenuation between Input 1 – Output 2
0 dB [0,+INF[
Return lossReturn loss between Input 1 – Output 1, and Input 2 – Output 2
60 dB [0,+INF[
IsolationIsolation between Input 2 – Output 1
60 dB [0,+INF[
657
ISOLATOR
Technical backgroundThe subsystem is illustrated in Figure 1.
Figure 1 Isolator subsystem
658
IDEAL ISOLATOR
Ideal Isolator
Ideal optical isolator. You can control insertion loss — there is no return loss or ideal isolation.
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 (forward) Input Optical
Output 1 (forward) Output Optical
Input 2 (backward) Input Optical
Name and description Default value Units Value range
Insertion lossAttenuation between Input 1 – Output 1
0 dB [0,+INF[
659
IDEAL ISOLATOR
Technical backgroundThe subsystem is illustrated in Figure 1.
Figure 1 Ideal Isolator subsystem
660
CIRCULATOR
Circulator
Optical circulator. You can control insertion loss, return loss, and isolation.
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 Input Optical
Output 2 Output Optical
Input 2 Input Optical
Output 3 Output Optical
Input 3 Input Optical
Output 1 Output Optical
Name and description Default value Units Value range
Insertion lossAttenuation between Input 1 – Output 2, Input 2 – Output 3, and Input 3 – Output 1
0 dB [0,+INF[
Return lossReturn loss between Input 1 – Output 1, Input 2 – Output 2, and Input 3 – Output 3
60 dB [0,+INF[
IsolationIsolation between Input 3 – Output 2, Input 1 – Output 3, and Input 2 – Output 1
60 dB [0,+INF[
661
CIRCULATOR
Technical backgroundThe subsystem is illustrated in Figure 1.
Figure 1 Circulator subsystem
662
IDEAL CIRCULATOR
Ideal Circulator
Ideal optical isolator. Yyou can control insertion loss — there is no return loss or ideal isolation.
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 Input Optical
Output 2 Output Optical
Input 2 Input Optical
Output 3 Output Optical
Input 3 Input Optical
Output 1 Output Optical
Name and description Default value Units Value range
Insertion lossAttenuation between Input 1 – Output 2, Input 2 – Output 3, and Input 3 – Output 1
0 dB [0,+INF[
663
IDEAL CIRCULATOR
Technical backgroundThe subsystem is illustrated in Figure 1.
Figure 1 Ideal Circulator subsystem
664
Signal Processing Library
This section contains information on the following signal processors.
Arithmetic
Electrical
• Electrical Gain• Electrical Adder• Electrical Subtractor• Electrical Multiplier• Electrical Bias• Electrical Norm• Electrical Differentiator• Electrical Integrator• Electrical Limiter
Optical
• Optical Gain• Optical Adder• Optical Subtractor• Optical Bias• Optical Multiplier
Tools
Optical
• Merge Optical Signal Bands• Convert to Parameterized• Convert to Noise Bins
665
Logic
Binary
• Binary NOT• Binary AND• Binary OR• Binary XOR• Binary NAND• Binary NOR• Binary XNOR• Binary Delay• Duobinary precoder
666
ELECTRICAL GAIN
Electrical GainIdeal gain element.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output = Input * Gain Output Electrical
Name and description Default value Units Value range
GainGain to apply to the signal port
1 — ]-INF,+INF[
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
667
ELECTRICAL ADDER
Electrical AdderAdds the input electrical signals.
Ports
Name and description Port type Signal type
Input 1 Input Electrical
Input 2 Input Electrical
Output = (Input 1) + (Input 2) Output Electrical
668
ELECTRICAL SUBTRACTOR
Electrical SubtractorSubtracts the input electrical signals.
Ports
Name and description Port type Signal type
Input 1 Input Electrical
Input 2 Input Electrical
Output = (Input 1) – (Input 2) Output Electrical
669
ELECTRICAL MULTIPLIER
Electrical MultiplierMultiplies the input electrical signals.
Ports
Name and description Port type Signal type
Input 1 Input Electrical
Input 2 Input Electrical
Output = (Input 1) * (Input 2) Output Electrical
670
ELECTRICAL BIAS
Electrical BiasAdds a constant value to the input signal.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output = Input + Bias Output Electrical
Name and description Default value Units Value range
BiasConstant value to add to the input signal
0 — ]-INF,+INF[
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
671
ELECTRICAL NORM
Electrical NormCalculates the equivalent power value of the electrical signal.
Ports
Parameters
Simulation
Name and description Port type Signal type
Input Input Electrical
Output = Input * Input Output Electrical
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
672
ELECTRICAL DIFFERENTIATOR
Electrical DifferentiatorCalculates the time derivative of the input signal. It can be used in frequency demodulators.
Ports
Parameters
Simulation
Technical Background
This component calculates the derivative of the input electrical signal according to:
, where is the input electrical signal.
Name and description Port type Signal type
Input Input Electrical
Output = d(Input) / dt Output Electrical
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
vout t( )dvin t( )
dt----------------= vin
673
ELECTRICAL INTEGRATOR
Electrical IntegratorCalculates the time integral of the input signal. It can be used in phase demodulators.
Ports
Parameters
Simulation
Technical Background
Calculates the integral of the input electrical signal according to:
, where is the input electrical signal.
Name and description Port type Signal type
Input Input Electrical
Output = Integ(Input) Output Electrical
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
vout t( ) vin t( ) td∫= vin
674
ELECTRICAL LIMITER
Electrical LimiterScales the minimum and maximum values of the input signal to user-defined minimum and maximum values.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value Units Value range
Minimum amplitudeThe minimum value of the signal output
0 a.u. ]-INF,+INF[
Maximum amplitudeThe maximum value of the signal output
1 a.u. ]-INF,+INF[
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
675
ELECTRICAL LIMITER
Technical BackgroundThis model estimates the minimum and maximum values of the input signal and calculates the scale and bias factor according to the user defined values. The output signal is scaled according to:
, where is the input electrical signal.
and are calculated according to:
where and are the maximum and minimum values for the signal input and output.
vout t( ) avin t( ) b+= vin
a b
aMinout Maxout–Minin Maxin–
----------------------------------------=
bMaxoutMinin MaxinMinout–
Minin Maxin–-----------------------------------------------------------------------=
Max Min
676
OPTICAL GAIN
Optical GainIdeal gain element.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Optical
Output = Input * Gain Output Optical
Name and description Default value Units Value range
GainGain to apply to the signal port
0 — ]-INF,+INF[
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
677
OPTICAL ADDER
Optical AdderAdds the input optical signals.
Ports
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Output = (Input 1) + (Input 2) Output Optical
678
OPTICAL SUBTRACTOR
Optical SubtractorSubtracts the input optical signals.
Ports
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Output = (Input 1) – (Input 2) Output Optical
679
OPTICAL BIAS
Optical BiasAdds a constant value to the input signal.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Optical
Output = Input + Bias Output Optical
Name and description Default value Units Value range
BiasConstant value to add to the input signal
0 — ]-INF,+INF[
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
680
OPTICAL MULTIPLIER
Optical MultiplierMultiplies the input optical signals.
Ports
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Output = (Input 1) * (Input 2) Output Optical
681
MERGE OPTICAL SIGNAL BANDS
Merge Optical Signal BandsMerges multiple sampled signals into one signal.
Ports
Parameters
Simulation
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
682
CONVERT TO PARAMETERIZED
Convert to ParameterizedThis component converts sampled signals and noise bins to parameterized signals.
Ports
Parameters
Main
Simulation
Technical Background
This component converts sampled signals and noise bins to parameterized signals. The user selects the type of signals to be converted by using the parameter Signal type. By default only sampled signals will be converted to parameterized signals.
Sampled signal channels are converted to parameterized in the frequency domain. The total power for each channel per polarization is translated to a parameterized signal. The same approach is used for noise bins, where the total power for each noise bin is translated to a parameterized signal.
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value Units Value range
Signal typeDefines the input signal type to be converted to parameterized signals
Sampled signals — Sampled signals, Noise bins, Sampled signals and Noise bins
Name and description Default value Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
683
CONVERT TO NOISE BINS
Convert to Noise BinsThis component converts sampled signals and parameterized signals to noise bins.
Ports
Parameters
Main
Simulation
Technical Background
This component converts sampled signals and parameterized signals to noise bins. The user selects the type of signals to be converted by using the parameter Signal type. By default only sampled signals will be converted to noise bins.
Sampled signals are first converted to parameterized signals. The total power for each channel per polarization is translated to a parameterized signal.
Parameterized signals are then converted to noise bins. The power spectral density depends on the noise bin bandwidth. If there is only one channel available, the bandwidth is 100 GHz. If more then one channel is available, the bandwidth is the frequency separation between adjacent channels.
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value Units Value range
Signal typeDefines the input signal type to be converted to noise bins
Sampled signals — Sampled signals, Parameterized signals, Sampled and Parameterized signals
Name and description Default value Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
684
BINARY NOT
Binary NOTLogic NOT operator.
Ports
Parameters
Simulation
Name and description Port type Signal type
Input Input Binary
Output Output Binary
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
685
BINARY AND
Binary ANDLogic AND operator.
Ports
Name and description Port type Signal type
Input 1 Input Binary
Input 2 Input Binary
Output = (Input 1) AND (Input 2) Output Binary
686
BINARY OR
Binary ORLogic OR operator
Ports
Name and description Port type Signal type
Input 1 Input Binary
Input 2 Input Binary
Output = (Input 1) OR (Input 2) Output Binary
687
BINARY XOR
Binary XORLogic XOR operator.
Ports
Name and description Port type Signal type
Input 1 Input Binary
Input 2 Input Binary
Output = (Input 1) XOR (Input 2) Output Binary
688
BINARY NAND
Binary NANDLogic NAND operator.
Ports
Name and description Port type Signal type
Input 1 Input Binary
Input 2 Input Binary
Output = (Input 1) NAND (Input 2) Output Binary
689
BINARY NOR
Binary NORLogic NOR operator.
Ports
Name and description Port type Signal type
Input 1 Input Binary
Input 2 Input Binary
Output = (Input 1) NOR (Input 2) Output Binary
690
BINARY XNOR
Binary XNORLogic XNOR operator.
Ports
Name and description Port type Signal type
Input 1 Input Binary
Input 2 Input Binary
Output = (Input 1) XNOR (Input 2) Output Binary
691
BINARY DELAY
Binary DelayAdds a time delay in number of bits to the binary signal input.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Binary
Output Output Binary
Name and description Default value Units Value range
DelayDelay to apply to the signal input
1 — [0, 1e+009]
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
692
DUOBINARY PRECODER
Duobinary precoderThis component simulates a precoder generally utilized in a duobinary modulation.
Ports
Parameters
Main
Simulation
Technical background
Normally, an optical duobinary system requires a precoder in order to avoid recursive decoding in the receiver, error propagation and reduce hardware complexity. The precoder is composed on an exclusive-or gate with a delayed feedback path. The precoding rule for this is:
where is the transmitted binary data sequence, is the precoded binary sequence, and represents the logic instruction exclusive-or “XOR”. Due to the use of the precoder in a
transmitter, decoding in the receiver is simple.
Figure 1 shows a diagram detailing the precoder. You can specify the number of bits delayed in the feedback path.
Name and description Port type Signal type
Input1 Input Binary
Output1 Output Binary
Name and description Default value Units Value range
DelayDelay to apply to the signal input
1 bits [1, +INF]
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
bk dk bk 1–⊕=
dk bk ⊕
693
DUOBINARY PRECODER
Figure 1 Duobinary precoder
694
Tools LibraryThis section contains information on the following tools.• Switch• Select• Loop Control• Ground• Buffer Selector• Fork 1xN• Binary Null• Optical Null• Electrical Null• Binary Delay• Optical Delay• Electrical Delay• Optical Ring Controller• Electrical Ring Controller• Duplicator• Limiter• Initializer• Save to file• Load from file• Command Line Application
695
Notes:
696
SWITCH
Switch
This component is a switch. The signal entering the input port will be send to one of the output ports.
Ports
Main
Name and description Port type Signal type
Input Input All types
Output 1 Output All types
Output 2 Output All types
Output 3 Output All types
Name and description Default value Default unit Units Value range
Number of output ports 4 — — [2, 1000]
SelectionSelects the signal output port
1 — — [1 - number of output ports]
697
SWITCH
Technical backgroundThe signal entering the input port will go to the selected output port. This component is used to sweep components. The user can define the signal path by changing the parameter Selection.
The following block diagram shows an example where 4 types of filters are used with a system:
In this project, the user can sweep the Selection parameter from the Switch and the Select components from 1 to 4. By changing these parameters, a different filter will be used for each sweep iteration.
698
SELECT
Select
This component is a select switch. One of the signals entering the input ports will be sent to the output port.
Ports
Main
Name and description Port type Signal type
Input 1 Input All types
Input 2 Input All types
Input 3 Input All types
Input 4 Input All types
Output Output All types
Name and description Default value Default unit Units Value range
Number of input ports 4 — — [2, 1000]
SelectionSelects the signal output port
1 — — [1 - number of output ports]
699
SELECT
Technical BackgroundOne of the signals entering the input ports will go to the output port. This component is used to sweep components. The user can define the input signal and the signal path by changing the parameter Selection.
The following block diagram shows an example where 4 types of filters are used with a system:
In this project, the user can sweep the Selection parameter from the Switch and the Select components from 1 to 4. By changing these parameters, a different filter will be used for each sweep iteration.
700
FORK 1X2
Fork 1x2
Copies the input signal into two output signals. This tool allows you to duplicate component output ports.
Ports
Name and description Port type Signal type
Input Input Any type
Output 1 Output Any type
Output 2 Output Any type
701
LOOP CONTROL
Loop Control
Allows you to build systems using loop structures.
Ports
Parameters
Main
Simulation
Technical backgroundThe loop topology starts at the Loop output port and terminates at the Loop input port. The signal enters the Input port and circulates in the loop N times, where N is defined by the parameter Number of Loops.
Name and description Port type Signal type
Input Input Any type
Loop Input Input Any type
Output Output Any type
Loop Output Output Any type
Name and description Default value Units Value range
Number of loops
Number of iterations in the loop
0 — [0,+INF[
Name and description Default value Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
702
GROUND
Ground
Ports
Name and description Port type Signal type
Input Input Any type
703
BUFFER SELECTOR
Buffer Selector
Allows you to select one of the signals from the input buffer.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Any type
Output Output Any type
Name and description Default value Default unit Value range
Selection
Index of the signal buffer
0 — [0,+INF[
Name and description Default value Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
Iterations
Maximum number of signals in the input buffer
Iterations — [1,1e9]
704
FORK 1XN
Fork 1xN
Copies the input signal into a user-defined number of ouptut signals. Allows you to duplicate component ouput ports.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Any type
Output 1 Output Any type
Output 2 Output Any type
Output 3 Output Any type
Output 4 Output Any type
Name and description Default value Default unit Value range
Number of output ports 4 — [2,1000]
705
BINARY NULL
Binary Null
Generates a zero-value binary signal.
Ports
Parameters
Simulation
Name and description Port type Signal type
Output Output Binary
Name and description Default value Units Value range
Iterations
Number of times to repeat the calculation
Iterations — [1,1e9]
706
OPTICAL NULL
Optical Null
Generates a zero-value optical signal.
Ports
Parameters
Simulation
Name and description Port type Signal type
Output Output Optical
Name and description Default value Units Value range
Iterations
Number of times to repeat the calculation
Iterations — [1, 1e+009]
707
ELECTRICAL NULL
Electrical Null
Generates a zero-value electrical signal.
Ports
Parameters
Simulation
Name and description Port type Signal type
Output Output Electrical
Name and description Default value Units Value range
Iterations
Number of times to repeat the calculation
Iterations — [1,1e9]
708
BINARY DELAY
Binary Delay
Generates binary signal delays. The delay is added by sending a NULL signal to the output port.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Binary
Output Output Binary
Name and description Default value Units Value range
Delay
Number of delay signals
1 — [0,+INF[
Name and description Default value Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
709
OPTICAL DELAY
Optical Delay
Generates optical signal delays. The delay is added by sending NULL signals to the output port.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value Units Value range
Delay
Number of delay signals
1 — [0,+INF[
Name and description Default value Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
710
ELECTRICAL DELAY
Electrical Delay
Generates electrical signal delays. The delay is added by sending NULL signals to the output port.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value Units Value range
Delay
Number of delay signals
1 — [0,+INF[
Name and description Default value Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
711
ELECTRICAL DELAY
Notes:
712
OPTICAL RING CONTROLLER
Optical Ring Controller
This component allows the user to build systems using ring structures with optical signals.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value Units Value range
Number of loops
Number of iterations in the loop
0 — [0, 1e+009]
Name and description Default value Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
713
OPTICAL RING CONTROLLER
Technical backgroundThe signal enters the Input port and circulates through the ring N times, where N is defined by the parameter Number of Loops. The ring is initialized by a null optical signal.
The block diagram of this component is:
714
ELECTRICAL RING CONTROLLER
Electrical Ring Controller
This component allows the user to build systems using ring structures with electrical signals.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value Units Value range
Number of loops
Number of iterations in the loop
0 — [0, 1e+009]
Name and description Default value Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
715
ELECTRICAL RING CONTROLLER
Technical backgroundThe signal enters the Input port and circulates through the ring N times, where N is defined by the parameter Number of Loops. The ring is initialized by a null electrical signal.
The block diagram of this component is:
716
ELECTRICAL RING CONTROLLER
Duplicator
Ports
Simulation
Name and description Port type Signal type
Input Input Binary
Output Output Binary
Name and description Default value Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
Iterations
Number of times to repeat the calculation
Iterations — [1,1e9]
717
ELECTRICAL RING CONTROLLER
Notes:
718
LIMITER
Limiter
This component controls the number of signals passing from the input to the output port. It can be used as a ring controller module.
Ports
Parameters
Main
Simulation
(same as delays, parameter ‘enable only)
Name and description Port type Signal type
Input Input All types
Output Output All types
Name and description Default value Units Value range
Number of loops
Number of iterations in the loop ring
1 — [0,+INF[
Name and description Default value Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
719
LIMITER
Technical BackgroundThis component counts the number of signals passing from the input to the output port. It will interrupt the signal propagation when the number of signals is equal to the parameter Number of loops.
The Limiter is used for ring controlling, since a signal can enter the input port and circulate through the ring the number of times dictated by the parameter Number of loops.
720
INITIALIZER
Initializer
This component is a select switch. The signal entering the first input port is sent to the output a user-defined number of times.
Ports
Parameters
Main
Name and description Port type Signal type
Input 1 Input All types
Input 2 Input All types
Output Output All types
Name and description Default value Units Value range
Number of signals
Number of signals from the first input port to be sent to the output port
1 — [0,+INF[
721
INITIALIZER
Technical BackgroundThe signal entering the first input port goes to the output port times, where is defined by the parameter Number of signals. After that, signals from the second input port go to the output port.
The Initializer is used to initialize ring structures, as it allows the user to specify the initial signal to circulate in the ring.
The block diagram below shows an optical ring controller using the Initializer component instead of the Optical Delay tool.
N N
722
INITIALIZER
Save to file
Saves the input signal to a file.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Binary
Name and description Default value Default unit Value range
Save signal mode
Select if you want to save all signals, only the first signal, or the last signal from the signal buffer
All signals — First signal, All signals, Last signal
Filename
Filename for the saved data
— — —
723
LOAD FROM FILE
Load from file
Loads the input signal from a file.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Output Output Binary
Name and description Default value Units Value range
Filename
Filename to load the data
Signal.ods — —
Number of signals to skip
Number of signal to skip when loading a file with multiple signals
0 — [0, 1e+009]
Name and description Default value Units Value range
Iterations
Number of times to repeat the calculation
Iterations — [1, 1e+009]
724
COMMAND LINE APPLICATION
Command Line Application
This component can create a process with user defined command line parameters. It can be used to call any Windows application. It requires a signal at the input port to trigger the calculation.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Any type
Output Output Any type
Name and description Default value Units Value range
Application
The name of the program to be called
Command line arguments
List of command line arguments available
Name and description Default value Units Value range
Enabled
Determines whether or not the component is enabled
True — True, False
725
COMMAND LINE APPLICATION
Technical BackgroundThis component allows the user to run another program or application during the simulation process. Command Line Application will run the application with the user defined command line arguments. The component only runs if there is a signal of any type in the input port. After closing the application the component will generate a trigger signal at the output. The trigger signal will be the same signal at the input port.
The component will only finish the calculation when the application is closed, this means that if you run Notepad, for example, only when you close notepad the calculation of other components will continue.
Typically this component is used for cosimulation with EDA tools, together with triggered load and save modules from the EDA cosimulation library (see Figure 1 and Figure 2).
Figure 1 Cosimulation using command line application
726
COMMAND LINE APPLICATION
Figure 2 Command line arguments for the application
727
COMMAND LINE APPLICATION
Notes:
728
Optiwave Software Tools
This section contains information on the following Optiwave software tools.
• OptiAmplifier• IFO_Gratings• WDM_Phasar Demux 1xN• WDM_Phasar Mux Nx1• OptiBPM Component NxM
729
Notes:
730
OPTIAMPLIFIER
OptiAmplifierOptiSystem can call Optiwave’s OptiAmplifier software to design optical fiber amplifiers and lasers.
Since the amplifier performance depends on the input signal, OptiSystem calls the OptiAmplifier engine to simulate the amplifer (see Figure 1).
Figure 1 OptiAmplifier
731
OPTIAMPLIFIER
Ports
Parameters
Main
Polarization
Simulation
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description Default value Units Value range
OptiAmplifier ProjectFilename with the OptiAmplifier project
— — —
Show project after calculationDetermines if the amplifier layout will appear after the calculation ends
False — True, False
Name and description Default value Units Value range
Polarization filterDetermines the polarization filter type
None — None, Polarization X, Polarization Y
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
732
OPTIAMPLIFIER
Noise
Random numbers
Technical background
From the OptiAmplifier icon, you can create a new project file, open an existing project file, show the layout of the current project, or access the component properties and parameters (see Figure 2).
Figure 2 OptiAmplifier open menu
You can enter component parameters in the Properties dialog box (see Figure 3).
Name and description Default value Units Value range
Noise thresholdMinimum value for adaptation of noise bins
–100 dB ]-INF,0[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB [0,+INF]
Convert noise binsDetermines if the generated noise bins are incorporated into the signal
Convert noise bins
— True, False
Name and description Default value Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
733
OPTIAMPLIFIER
Figure 3 OptiAmplifier component properties dialog box
A new OptiAmplifier file opens in OptiAmplifier Main Layout. You can use OptiAmplifier to design the amplifier (see Figure 4).
734
OPTIAMPLIFIER
Figure 4 OptiAmplifier software
OptiAmplifier receives signals from OptiSystem using the input and output ports. OptiAmplifier calculates the layout and sends the output signal back to OptiSystem (see Figure 5).
735
OPTIAMPLIFIER
Figure 5 OptiAmplifier and OptiSystem integration
You can close OptiAmplifier and open it later by selecting Open Layout from the OptiAmplifier Component dialog box. You can also load an existing OptiAmplifier project by selecting Open OptiAmplifier File from the OptiAmplifier component dialog box (see Figure 6).
736
OPTIAMPLIFIER
Figure 6 Loading OptiAmplifier files
737
OPTIAMPLIFIER
Notes:
738
IFO_GRATINGS
IFO_GratingsLoads Optiwave’s IFO_Gratings complex spectrum files. IFO_Gratings is an Integrated and Fiber Optical Gratings Design Software which can export the results to OptiSystem. This component can also be used to load measured data from files.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Optical
Transmission Output Optical
Reflection Output Optical
Name and description Default value Default unit Units Value range
User-defined frequency Determines whether you can define the filter center frequency or use the value from the measurements
False — — True, False
Frequency User-defined filter center frequency
193.1 THz Hz, THz, nm [0,+INF[
FBG filename FBG.txt — — —
Name and description Default value Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
ResampleDetermines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rateNew output signal sample rate
500 GHz Hz, GHz, THz ]0,+INF[
739
IFO_GRATINGS
Noise
Graphs
Name and description Default value Units Value range
Noise thresholdMinimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
Name and description X Title Y Title
Filter reflection - real part Frequency (Hz) Amplitude (a.u.)
Filter reflection - imag part Frequency (Hz) Amplitude (a.u.)
Filter transmission - real part Frequency (Hz) Amplitude (a.u.)
Filter transmission - imag part Frequency (Hz) Amplitude (a.u.)
740
IFO_GRATINGS
Technical backgroundThe input file is formatted containing three items per line — the wavelngth in microns, a complex value transmission, and a complex value for the reflection.
1.5465000 -0.95054476 0.31058130 0.0019538914 0.00030748692
1.5465047 -0.83933357 -0.54361247 -0.00053900650 0.0020880603
1.5465093 -0.10532500 -0.99443599 -0.0017730023 -0.00074527952
1.5465140 0.70683493- 0.70737604 0.0012775158 -0.0013700226
1.5465187 0.99451620 0.10456029 0.0012534218 0.0017631583
1.5465233 0.54426584 0.83891013 -0.0018252456 0.0010779574
1.5465280 -0.30982698 0.95079110 -0.00049861026- 0.0018114039
.
.
.
The parameter User defined frequency determines if you can enter the center frequency. This means that the filter data is shifted from the grating center frequency to the user center frequency that you define in the parameter Frequency.
This file can be generated by IFO_Grating using the Export Complex Spectrum tool (see Figure 1).
741
IFO_GRATINGS
Figure 1 Exporting results from IFO_Grating to OptiSystem
742
WDM_PHASAR DEMUX 1XN
WDM_Phasar Demux 1xNLoads Optiwave’s WDM_Phasar PIW files. WDM_Phasar is Phased Array WDM Device Design Software which can export the results to OptiSystem. This components can also be used to load measured data from files.
Ports
Parameters
Main
Simulation
Noise
Name and description Port type Signal type
Input Input Optical
Output 1 Output Optical
Output 2 Output Optical
Name and description Default value Units Value range
Number of output ports 2 — [2,1000]
FilenameFilename with the .piw data
WDM_Phasar.piw — —
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
Name and description Default value Units Value range
Noise thresholdMinimum value for adaptation of noise bins
-100 dB ]-INF,+INF[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
743
WDM_PHASAR DEMUX 1XN
Graphs
Technical background
The PIW file contains the file header, number of wavelength points, and number of wavelength channels.
BCF2DMC
121 6
[wl ][ -4.564250E+001] [ -3.258100E+001] [ -1.954000E+001] [ -6.511500E+000] [ 6.510500E+000] [ 1.953900E+001] [ 3.258000E+001] [ 4.564150E+001]
1.546000E+000 9.689700E-005 8.340647E-005 7.325889E-006 5.303238E-005 3.161631E-005 7.236055E-005
1.546075E+000 1.293506E-004 8.015659E-005 2.596500E-005 1.780735E-005 4.972572E-005 2.968608E-005
1.546150E+000 1.690047E-004 7.332815E-005 3.134233E-005 1.449511E-005 4.502246E-005 3.533981E-006
1.546225E+000 1.238766E-004 7.758708E-005 9.527608E-006 2.024385E-005 1.532031E-005 3.790632E-006
1.546300E+000 6.985230E-005 7.710248E-005 1.613273E-006 1.720816E-005 4.933527E-007 1.170849E-005
OptiSystem skips the first four lines of the file. The resulting file is:
1.546000E+000 9.689700E-005 8.340647E-005 7.325889E-006 5.303238E-005 3.161631E-005 7.236055E-005
1.546075E+000 1.293506E-004 8.015659E-005 2.596500E-005 1.780735E-005 4.972572E-005 2.968608E-005
1.546150E+000 1.690047E-004 7.332815E-005 3.134233E-005 1.449511E-005 4.502246E-005 3.533981E-006
1.546225E+000 1.238766E-004 7.758708E-005 9.527608E-006 2.024385E-005 1.532031E-005 3.790632E-006
1.546300E+000 6.985230E-005 7.710248E-005 1.613273E-006 1.720816E-005 4.933527E-007 1.170849E-005
The first column is the transmission wavelength in microns. The other columns are the transmission power for each channel. OptiSystem recognizes the number of columns and associates each one to an internal filter and an ouput port.
Name and description X Title Y Title
Filter transmission Frequency (Hz) Amplitude (a.u.)
744
WDM_PHASAR MUX NX1
WDM_Phasar Mux Nx1Loads Optiwave’s WDM_Phasar PIW files. WDM_Phasar is Phased Array WDM Device Design Software which can export the results to OptiSystem. This component can also be used to load measured data from files.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Output Output Optical
Name and description Default value Units Value range
Number of input portsDetermines whether or not the component is enabled
2 — [2,1000]
FilenameFilename with the .piw data
WDM_Phasar.piw — —
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
745
WDM_PHASAR MUX NX1
Noise
Graphs
Technical background
The PIW file contains the file header, number of wavelength points, and number of wavelength channels.
BCF2DMC
121 6
[wl ][ -4.564250E+001] [ -3.258100E+001] [ -1.954000E+001] [ -6.511500E+000] [ 6.510500E+000] [ 1.953900E+001] [ 3.258000E+001] [ 4.564150E+001]
1.546000E+000 9.689700E-005 8.340647E-005 7.325889E-006 5.303238E-005 3.161631E-005 7.236055E-005
1.546075E+000 1.293506E-004 8.015659E-005 2.596500E-005 1.780735E-005 4.972572E-005 2.968608E-005
1.546150E+000 1.690047E-004 7.332815E-005 3.134233E-005 1.449511E-005 4.502246E-005 3.533981E-006
1.546225E+000 1.238766E-004 7.758708E-005 9.527608E-006 2.024385E-005 1.532031E-005 3.790632E-006
1.546300E+000 6.985230E-005 7.710248E-005 1.613273E-006 1.720816E-005 4.933527E-007 1.170849E-005
OptiSystem skips the first four lines of the file. The resulting file is:
1.546000E+000 9.689700E-005 8.340647E-005 7.325889E-006 5.303238E-005 3.161631E-005 7.236055E-005
1.546075E+000 1.293506E-004 8.015659E-005 2.596500E-005 1.780735E-005 4.972572E-005 2.968608E-005
1.546150E+000 1.690047E-004 7.332815E-005 3.134233E-005 1.449511E-005 4.502246E-005 3.533981E-006
1.546225E+000 1.238766E-004 7.758708E-005 9.527608E-006 2.024385E-005 1.532031E-005 3.790632E-006
1.546300E+000 6.985230E-005 7.710248E-005 1.613273E-006 1.720816E-005 4.933527E-007 1.170849E-005
.
.
.
The first column is the transmission wavelength in microns. The other columns are the transmission power for each channel. OptiSystem recognizes the number of columns and associates each one to an internal filter and an ouput port.
Name and description Default value Units Value range
Noise thresholdMinimum value for adaptation of noise bins
–100 dB ]-INF,+INF[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB ]-INF,+INF[
Name and description X Title Y Title
Filter transmission Frequency (Hz) Amplitude (a.u.)
746
OPTIBPM COMPONENT NXM
OptiBPM Component NxM
Description
This component loads Optiwave's OptiBPM 's' files. OptiBPM is a software suite for the design of a variety of integrated and fiber optic guided problems, which can export the results to OptiSystem. This component can also be used to load measured data from files.
Ports
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Input 3 Input Optical
Input 4 Input Optical
Input 5 Input Optical
Input 6 Input Optical
Input 7 Input Optical
Input 8 Input Optical
Output 1 Output Optical
Output 2 Output Optical
Output 3 Output Optical
Output 4 Output Optical
Output 5 Output Optical
Output 6 Output Optical
Output 7 Output Optical
Output 8 Output Optical
747
OPTIBPM COMPONENT NXM
Parameters
Main
Enhanced
Simulation
Noise
Name and description Default value Units Value range
File formatDefines the format of the file with the ‘s’ data.
Real Imag — Real Imag, Amplitude Phase
Filename(s)Filename with the ‘s’ data
OptiBPM.s — —
Vertical flipDefines whether or not the vertical flip is enabled.
False — True, False
Name and description Default value Units Value range
Central wavelength approximationDefines whether or not the central wavelength approximation is enabled.
False — True, False
LengthWaveguide length
100 ]0,+INF[
Reference index (real)Real part of the complex reference index.
1 — ]0,+INF[
Reference index (imag)Imaginary part of the complex reference index.
0 — ]-INF,+INF[
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
Name and description Default value Units Value range
Noise thresholdMinimum value for adaptation of noise bins.
–100 dB ]-INF,+INF[
Noise dynamicThreshold ratio for adaptation of noise bins.
3 dB ]-INF,+INF[
µm
748
OPTIBPM COMPONENT NXM
Technical BackgroundThe first line of the 's' file contains the number of inputs and outputs, the consecutive lines have the wavelength in microns and the complex values of the amplitude transmission between each input x output port. The parameter File format defines whether the complex values are defined by the real and imaginary parts, or amplitude and phase.
Ninputs Noutputs
l(1) S11(1) S12(1) … S1M(1) S21(1) S22(1) S2M(1) … SN1(1) SN2(1) … SNM(1)
(2) S11(2) S12(2) … S1M(2) S21(2) S22(2) S2M(2) … SN1(2) SN2(2) … SNM(2)
.
.
.
(L) S11(L) S12(L) … S1M(L) S21(L) S22(L) S2M(L) … SN1(L) SN2(L) … SNM(L)
Where Sij(k) is a complex number, i is the input port index, j is the output port index and k is the row index. The complex number is represented by two real numbers: real and imaginary.
The total number of elements in each row is the number of inputs times the number of outputs times 2 (real/amplitude and imaginary/phase parts) plus one (wavelength).
Example with 2 inputs and 2 outputs:
Example with 1 input and 2 outputs:
λ
λ
λ
749
OPTIBPM COMPONENT NXM
Example with 3 inputs and 1 output:
Central wavelength approximation
The approximation uses the following expression:
where is the central wavelength, is the reference index and L is the length.
The simulation was done with only one wavelength, which is considered to be the central one.
S'11 λ( ) S11 λ0( ) j2πn0L 1λ0-----
1λ---
–exp⋅=
λ0 n0
750
MATLAB Library
This section contains information on the following MATLAB components.
• MATLAB Filter Component• MATLAB Optical Filter Component• MATLAB Component
751
MATLAB LIBRARY
Notes:
752
MATLAB FILTER COMPONENT
MATLAB Filter ComponentSimulates an electrical filter using MATLAB.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description
Default value Default unit
Units Value range
Convert units True — — True, False
FrequencyFilter center frequency
0 GHz Hz, MHz, GHz
[30,+INF[
BandwidthFilter bandwidth
3.5 GHz Hz, MHz, GHz
[0,+INF[
Run commandMATLAB command to execute during the calculation
Order = Factor =(( Frequency - CenterFrequency )/( Bandwidth / 2.0 ) ).^(2.0 * Order)TransferFunction =exp( -0.5 * 0.693147180559945309417 * Factor )
— — —
753
MATLAB FILTER COMPONENT
MATLAB
Simulation
Name and description Default value Units Value range
MATLAB search pathPath to add to the MATLAB search path
— — —
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
754
MATLAB FILTER COMPONENT
Technical backgroundWhen the MATLAB filter component is active, it opens the MATLAB program. The MATLAB filter component performs a co-simulation with the MATLAB.
At the beginning of the simulation, the MATLAB adds the path (defined by the matlab search path parameter) to the MATLAB search path. This is where you put the created MATLAB files that will be used in the simulation.
Next, OptiSystem puts the following frequencies into the MATLAB workspace:• Vector Frequency with whole frequencies of the electrical signal spectrum• Variable CenterFrequency with center frequency of the MATLAB filter defined by the
Frequency parameter• Variable Bandwidth with the 3 dB bandwidth of filter defined by Bandwidth parameter
(see Figure 1).
Figure 1 MATLAB workspace in OptiSystem
OptiSystem executes the command defined by the Run command in MATLAB. This parameter can contain a command, a file name, or a sequence of commands, such as the default run command.
755
MATLAB FILTER COMPONENT
Note: Your program must be able to handle the frequency vector, center frequency, and 3 dB frequency bandwidth to successfully perform the transfer function of the electrical filter (see Figure 2).
Figure 2 MATLAB workspace after generation of the transfer function for OptiSystem
756
MATLAB OPTICAL FILTER COMPONENT
MATLAB Optical Filter ComponentSimulates an optical filter using MATLAB.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Optical
Output Output Optical
Name and description
Default value Default unit
Units Value range
FrequencyFilter center frequency
193.1 THz Hz THz nm
[30,+INF[
BandwidthFilter bandwidth
10 GHz Hz GHz THz nm
[0,+INF[
Run commandMATLAB command to execute during the calculation
Order = Factor =(( Frequency - CenterFrequency )/( Bandwidth / 2.0 ) ).^(2.0 * Order)TransferFunction =exp( -0.5 * 0.693147180559945309417 * Factor )
— — —
757
MATLAB OPTICAL FILTER COMPONENT
MATLAB
Simulation
Noise
Name and description Default value Units Value range
MATLAB search pathPath to add to the MATLAB search path
— — —
Name and description Default value Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
ResampleDetermines if the filter will down sample the signal bandwidth to the filter sample rate
False — — True, False
Sample rateNew output signal sample rate
1000 GHz Hz, GHz, THz ]0,+INF[
Name and description Default value Default unit Units Value range
Noise thresholdMinimum value for adaptation of noise bins
–100 dB — ]-INF,+INF[
Noise dynamicThreshold ratio for adaptation of noise bins
3 dB — ]-INF,+INF[
Noise calculation bandwidthCalculation bandwidth, outside of this range calculation is replaced by the attenuation
0.5 THz Hz, GHz, THz, nm
]0,+INF[
758
MATLAB OPTICAL FILTER COMPONENT
Technical backgroundWhen the MATLAB optical filter component is active, it opens the MATLAB program. The MATLAB optical filter component performs a co-simulation with the MATLAB.
At the beginning of the simulation, the MATLAB adds the path (defined by the matlab search path parameter) to the MATLAB search path. This is where you put the created MATLAB files that will be used in the simulation.
Next, OptiSystem puts the following frequencies into the MATLAB workspace:• Vector Frequency with whole frequencies of the electrical signal spectrum• Variable CenterFrequency with center frequency of the filter defined by the Frequency
parameter• Variable Bandwidth with the 3 dB bandwidth of filter defined by Bandwidth parameter (see
Figure 1).
Figure 1 MATLAB workspace in OptiSystem
OptiSystem executes the command defined by the Run command in MATLAB. This parameter can contain a command, a file name, or a sequence of commands, such as the default run command.
759
MATLAB OPTICAL FILTER COMPONENT
Note: Your program must be able to handle the frequency vector, center frequency, and 3 dB frequency bandwidth to successfully perform the transfer function of the optical filter (see Figure 2).
Figure 2 MATLAB workspace after generation of the transfer function for OptiSystem
760
MATLAB COMPONENT
MATLAB ComponentEnables the utilization of components created in MATLAB.
Ports
Parameters
Main
Simulation
Input
Name and description Port type Signal type
Input 1 Input Optical
Output 1 Output Optical
Name and description Default value Units Value range
Load MATLABDefines whether MATLAB should be loaded before the calculation starts and kept open after the simulation is completed.
False — True or False
Run commandMATLAB command to execute during calculation
OutputPort1 = InputPort1
— —
MATLAB search pathPath to add to the MATLAB search path
— — —
Sampled signal domainSignal domain when transferring signal to MATLAB
Frequency — Frequency, Time
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
Name and description Default value Units Value range
Number of input portsSpecify the number of input ports
1 — [1, 50]
761
MATLAB COMPONENT
Output
User parameters
Simulation
Random numbers
Signal type (Input 1)Specify signal type for Input Port 1)* Optical signal = 0, Electrical signal = 1, Binary signal = 2
0* — [0, 2]*
Name and description Default value Units Value range
Number of input portsSpecify the number of output ports
1 — [1, 50]
Signal type (Output 1)Specify signal type for Output Port 1)* Optical signal = 0, Electrical signal = 1, Binary signal = 2
0* — [0, 2]*
Name and description Default value Units Value range
Number of parametersSpecify the number of user parameters
1 — [1, 50]
Parameter0Specify the value of the parameter
0 — [-1e+100, 1e+100]
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
Name and description Default value Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
Name and description Default value Units Value range
762
MATLAB COMPONENT
Technical backgroundBy selecting Load MATLAB, the MATLAB software is loaded before the calculation starts. It will stay open after the calculation is complete. Use this option when you want to display graphs from MATLAB. By default, MATLAB is loaded and closed during the calculations.
In this model, you define the number of input ports and output ports and the signal type (optical, electrical, or binary) of each port. For each input port, OptiSystem assembles a structure with the signal and puts this structure into the MATLAB workspace.
Optical signal
For an optical signal at InputPort1, the following structure is launched in the workspace:
Structure 1.0
The field Channel is a double array containing the wavelengths of each channel at InputPort1. As the optical signal can be presented in three formats (sampled, parameterized, and noise bins), the structure for the optical signal contains fields for each format. Figure 1 shows examples of optical signals launched in the workspace.
Figure 1 Examples of optical signals launched in the MATLAB workspace
InputPort1
TypeSignal Optical
Sampled [ struct ]
Parameterized [ struct ]
Noise [ struct ]
Channels [ channels array ]
763
MATLAB COMPONENT
The field Sampled indicates if the input signal at InputPort1 has optical sampled signals. The structure is defined by:
Structure 1.1
If Signal contains an electrical field, it can be a vector 1XN (one polarization component) or a matrix 2XN (two polarization components) of complex numbers. N is the number of samples in the signal. Figure 2 shows examples of structures for the sampled signal.
Figure 2 Structures of optical sampled signals in the MATLAB workspace
The field CentralFrequency indicates the central frequency of the frequency window for the signal. Depending on the parameter Sampled domain, the sampled signal will be in the time or frequency domain. The default value of the Sampled domain parameter is frequency domain. Figure 3 shows an example of a signal in time domain.
Figure 3 Structure of optical sampled signal (time domain) in the MATLAB workspace
The field Parameterized in Structure 1.0 indicates if the InputPort1 signal has optical parameterized signals. The structure is defined by:
Structure 1.2
The field Power indicates the total power of each parameterized signal in the input port.
InputPort1.Sampled
Signal [ Ex; Ey ]
CentralFrequency Central frequency
Frequency | Time [ frequency array ] | [ time array ]
InputPort1.Parameterized
Power [ power ]
Frequency [ frequency ]
SplittingRatio [ sr ]
Phase [ phase ]
764
MATLAB COMPONENT
SplittingRatio gives the ratio between the power of the polarization components and the total power. Phase shows the phase difference between the x and y components. The Frequency field indicates the frequency of each parameterized channel. Figure 4 shows two examples of a parameterized signal structure.
Figure 4 Structure of optical parameterized signals in the MATLAB workspace
The field Noise in Structure 1.0 indicates if the InputPort1 signal has optical noise bins. The structure is defined by:
Structure 1.3
The optical noise structure represents a set of noise bins. The field Power contains a vector or matrix with the power of each noise bin for each polarization state. The LowerFrequency and UpperFrequency fields define the range of each noise bin. The central frequency of each noise bin can be defined as:
CentralFrequency = (InputPort1.Noise.UpperFrequency + InputPort1.Noise.LowerFrequency)/2
The frequency slot of each noise bin can be defined as:
FrequencySlot = InputPort1.Noise.UpperFrequency - InputPort1.Noise.LowerFrequency
Figure 5 shows an example of optical noise structure.
Figure 5 Structure of an optical noise signal in the MATLAB workspace
InputPort1.Noise
Power [ powerX, powerY ]
LowerFrequency [ lowfrequency ]
UpperFrequency [ upfrequency ]
Phase [ phase ]
765
MATLAB COMPONENT
Electrical signalThe structure for electrical signals is simpler than for optical signals. For an electrical signal at InputPort1, the following structure is launched in the workspace:
Structure 2.0
This signal has two other structures inside, one for the signal (Sampled) and the other for noise (Noise). Figure 6 shows an example of an electrical signal launched in the workspace.
Figure 6 Structure of an electrical sampled signal in the MATLAB workspace
The field Sampled indicates if the InputPort1 signal has electrical sampled signals. It is defined by:
Structure 2.1
As with the optical sampled signal, the user can select the domain (time domain or frequency domain) of the electrical sampled signal through the parameter Sampled domain. Figure 7 shows two examples of electrical signals.
Figure 7 Structures of an electrical sampled signal in the MATLAB workspace
InputPort1
TypeSignal Electrical
Sampled [ struct ]
Noise [ struct ]
InputPort1.Sampled
Signal [ E ]
Frequency | Time Frequency | time
766
MATLAB COMPONENT
The field Noise in Structure 2.0 indicates if the InputPort1 signal has electrical noise. The structure is defined by:
Structure 2.2
The structure found in Structure 2.2 is equal to the sampled signal and has the same time domain options. Figure 8 shows two examples of noise signals in different signal domains.
Figure 8 Structures of an electrical noise signal in the MATLAB workspace
InputPort1.Noise
Signal [ E ]
Frequency | Time Frequency | time
767
MATLAB COMPONENT
Binary signalsThe structure for a Binary signal is characterized by the bit sequence and the bit rate. For a binary signal at InputPort1, the following structure is launched in the workspace:
Structure 3.0
Figure 9 is an example of a binary structure.
Figure 9 Structure of a binary signal in the MATLAB workspace
After OptiSystem puts the input signals in the MATLAB workspace, OptiSystem executes the command defined by the Run command parameter in MATLAB. This parameter can contain a command, a file name, or a sequence of commands.
Note: Your program must be able to handle the structures for each input port to successfully obtain the output signals. For each output port, you must create a structure according to the signal type.
For an optical signal to the OutputPort1:
Structure 4.0
The field Sampled in Structure 4.0 is defined by a structure similar to Structure 1.1.
The field Parameterized in Structure 4.0 is similar to Structure 1.2, and the field Noise in Structure 4.0 is similar to Structure 1.3.
InputPort1
TypeSignal Binary
Sequence [ Sequence of bits ]
BitRate bitrate
OutputPort1
TypeSignal Optical
Sampled [ struct ]
Parameterized [ struct ]
Noise [ struct ]
768
MATLAB COMPONENT
For an electrical signal to OutputPort1:
Structure 5.0
The field Sampled in Structure 5.0 is similar to Structure 2.1.
For a binary signal to OutputPort1, the structure is similar to Structure 3.0.
OptiSystem loads the output signal for the appropriate output port and continues the simulation.
Example
Designing an optical amplitude modulator
To design an optical amplitude modulator using a MATLAB component, the component has to be able to handle an optical and electrical signal input to generate an optical signal output. The input and output tab parameters are shown in Figure 10.
Figure 10 Input and Output parameters
As we use some MATLAB files to model the amplitude modulator, all files are located in the ‘c:\temp’ folder, and the parameter Matlab search path has to point to it (see Figure 11).
The file that contains the program utilized by OptiSystem is AmplitudeModulatorComponent, and is specified by the parameter Run command. Because this example modulates an optical signal in time, the parameter Sampled domain is set to Time (see Figure 11).
OutputPort1
TypeSignal Electrical
Sampled [ struct ]
769
MATLAB COMPONENT
Figure 11 MATLAB component Main tab for amplitude modulator model
The equation describing the behaviour of this model is similiar to that found in the Amplitude modulator - Transmitters library. An amplitude modulator parameter Modulation index is necessary to make the MATLAB model work in a manner similiar to the original amplitude modulator. Parameter0 on the User Parameters tab is defined as our Modulation index (see Figure 12).
Figure 12 MATLAB component User Parameters tab for amplitude modulator model
With the parameters of the MATLAB components already defined, the MATLAB code that handles the OptiSystem signals must be generated. In accordance with the Run command parameter, the file AmplitudeModulatorComponent is executed (the code can be seen in Figure 13).
The functions of this file are to:• count the number of sampled signals• count the number of parameterized signals• count the number of noise signals• call the corresponding routine to calculate the output signals for each existing signal
(sample, parameterized, and noise)• verify the other polarization component, in the case of sampled signals
This example shows how generic code can be made to handle all the possibilities of the OptiSystem signals. Users have to be aware of all these possibilities.
770
MATLAB COMPONENT
Figure 13 Code of the AmplitudeModulatorComponent file
The following MATLAB files are used to handle different kinds of signals:• Figure 14 is for optical sampled signals• Figure 15 is for parameterized signals• Figure 16 is for noise bin signals
771
MATLAB COMPONENT
Figure 14 Optical sampled signals
Figure 15 Parameterized signals
Figure 16 Noise bin signals
772
MATLAB COMPONENT
The system shown in Figure 17 demonstrates how this component works. The MATLAB component modulates the two optical signals in accordance with the electrical modulation signal. One of the optical signals is parameterized, and the other is sampled. Both have noise bins. The modulation index (Parameter0) is defined as 1.
Figure 17 Amplitude modulator system
773
MATLAB COMPONENT
Notes:
774
EDA Cosimulation Library
This section contains information on the following EDA Cosimulation components.
• Save ADS File• Load ADS File• Save Spice Stimulus File• Load Spice CSDF File• Triggered Save Spice Stimulus File• Triggered Load Spice CSDF File
775
EDA COSIMULATION LIBRARY
Notes:
776
SAVE ADS FILE
Save ADS FileThis component can save files in the 'TIM' format. The .tim and files are signal data files in Agilent EEsoft ADS, MDIF format. They contain time-domain waveform data for defining the signals associated with certain sources.
Ports
Parameters
Main
Random numbers
Name and description Port type Signal type
Input Input Electrical
Name and description Default value Units Value range
Output dataThe signal type to save to the file
Signal and noise SignalSignal and NoiseNoise
File typeType of file to be saved
TIM MDIF
Filename (.tim)File name with the electrical signal in time domain with TIM format
Signal_2.tim
Reference resistanceThe resistance to be added to the output file
50 Ohm [0,+INF[
Name and description Default value Units Value range
Generate random seedDetermines the interpolation algorithm for the measured data
YES Yes, No
Random seed indexUser-defined seed index for signal generation
0 — [0,4999]
777
SAVE ADS FILE
Technical backgroundThe .tim files are signal data files in Agilent EEsoft ADS, MDIF format. They contain time-domain waveform data for defining the signals associated with certain sources.
The general .tim file format is:
An exclamation point (!) at the beginning of a line makes it a comment line. Characters following the ! are ignored by the program. The TIMEDATA data block is required. The option line format is the following:
# T ( [ SEC / MSEC / USEC / NSEC / PSEC ] V/MV R xx )
where
The Format line is: % t v
where
By design of the program, the syntax t and v in the Format line are completely arbitrary. These values can be whatever you prefer. For example, an option line such as: % time voltage.
# = Delimiter that tells the program you are specifying these parameters
T = Time
SEC / MSEC / USEC / NSEC / PSEC
= Your choice of Seconds, Milliseconds, Microseconds, Nanoseconds, or Picoseconds
V/MV = Your choice of Volts or Millivolts
R = Reference resistance, default is 50.0
xx = User-specified value for reference resistance
% = Delimiter that tells the program you are specifying
t = time
v = voltage
778
LOAD ADS FILE
Load ADS FileThis component can load files in the 'TIM' format. The .tim and files are signal data files in Agilent EEsoft ADS, MDIF format. They contain time-domain waveform data for defining the signals associated with certain sources.
Ports
Parameters
Main
Numerical
Name and description Port type Signal type
Output Output Electrical
Name and description Default value Units Value range
File typeType of file to be loaded
TIM MDIF
Filename (.tim)File name with the electrical signal in time domain with TIM format
Signal.tim
Reload fileDefines whether the component should reload the signal for each run.
no — True, false
Name and description Default value Units Value range
InterpolationDetermines the interpolation algorithm for the measured data
Linear — Linear, Cubic
779
LOAD ADS FILE
Simulation
The .tim and files are signal data files in Agilent EEsoft ADS, MDIF format. They contain time-domain waveform data for defining the signals associated with certain sources.
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
IterationsNumber of times to repeat the calculation
Iterations — —
Sample rateOutput signal sample rate
Hz Hz, GHz, THz
780
LOAD ADS FILE
The general .tim file format is:
he ! are ignored by the program. The TIMEDATA data block is required. The option line format is the following:
# T ( [ SEC / MSEC / USEC / NSEC / PSEC ] V/MV R xx )
where
The Format line is the following: % t v
where
By design of the program, the syntax t and v in the Format line are completely arbitrary. These values can be whatever you prefer. For example, an option line such as:
% time voltage
# = Delimiter that tells the program you are specifying these parameters
T = Time
SEC / MSEC / USEC / NSEC / PSEC
= Your choice of Seconds, Milliseconds, Microseconds, Nanoseconds, or Picoseconds
V/MV = Your choice of Volts or Millivolts
R = Reference resistance, default is 50.0
xx = User-specified value for reference resistance
% = Delimiter that tells the program you are specifying
t = time
v = voltage
781
LOAD ADS FILE
Notes:
782
SAVE SPICE STIMULUS FILE
Save Spice Stimulus FileThis component can save ASCII files in a user define format. By default the file has the PSpice Stimulus data format .stl. The .stl files are signal data files used in PSpice. They contain time-domain waveform data, based on a piece-wise linear algorithm, for defining the signals associated with certain sources and nodes.
Ports
Parameters
Main
File format
Name and description Port type Signal type
Input Input Electrical
Name and description Default value Units Value range
Output dataThe signal type to save to the file
Signal and noise SignalSignal and noiseNoise
Filename (.stl)File name with the electrical signal in time domain
Signal.stl
Name and description Default value Units Value range
File commentCharacter string for comments in the file
*
File beginCharacter string to be added to the first line of the file
.STIMULUS SIGNAL PWL
File endCharacter string to be added to the last line of the file
783
SAVE SPICE STIMULUS FILE
Random numbers
Technical Background
This component can save the data in a user defined file format. The parameters in the File format tab define the additional format information to be added to the signal data.
The general file format is:
COMMENT Written by OptiSystem 3.0
COMMENT EDA Cosimulation Library
COMMENT Save Spice Stimulus File Component
BEGIN
LINE BEGIN time1 DELIMITER amplitude1 LINE END
LINE BEGIN time2 DELIMITER amplitude2 LINE END
LINE BEGIN time… DELIMITER amplitude… LINE END
…
END
File line beginCharacter string to be added to the beginning of each line of data
+(
File line endCharacter string to be added to the end of each line
)
File delimiterCharacter string to be used in each line of data, to separate multiple values
,
Name and description Default value Units Value range
Generate random seedDetermines the interpolation algorithm for the measured data
YES Yes, No
Random seed indexUser-defined seed index for signal generation
0 — [0,4999]
Name and description Default value Units Value range
784
SAVE SPICE STIMULUS FILE
By default, the signal will be saved using the .stl format, e.g. after a source:
* Written by OptiSystem 3.0
* EDA Cosimulation Library
* Save Spice Stimulus File Component
.STIMULUS SIGNAL PWL
+ (0,1)
+ (6.25e-012, 1)
+ (1.25e-011, 1)
+ (1.875e-011, 1)
+ (2.5e-011, 1)
+ (3.125e-011, 1)
+ (5.119375e-008, 1)
In this case, the parameter Comment is "*", the Begin is ".STIMULUS SIGNAL PWL", the Line Begin is "+(", the Delimiter is ",", the Line End is ")", there is no format for the End, and the value is "".
Typically this component is used after an electrical pulse generator in the transmitter stage, or after the photodetectors, in the receiver stage. The electrical signals are exported to a file and processed by a circuit simulator such as PSpice.
Figure 1 Exporting data using Save Spice Stimulus File
785
SAVE SPICE STIMULUS FILE
Figure 2 Formatting the file using Stimulus format
After the simulation, a text file ‘NRZ.stl’ is generated by OptiSystem. Figure 3 shows the file data using the Stimulus format.
786
SAVE SPICE STIMULUS FILE
Figure 3 NRZ.stl STIMULUS file
The signal can be loaded into a Stimulus editor, and then compared with the original signal from OptiSystem. Figure 4 shows the same signals in OptiSystem and in the Stimulus editor:
Figure 4 OptiSystem and Stimulus editor signals
787
SAVE SPICE STIMULUS FILE
Notes:
788
LOAD SPICE CSDF FILE
Load Spice CSDF FileThis component can load Common Simulation Data Format (CSDF) files from EDA tools that can export PROBE results into CSDF file format. The .csd files are signal data files exported from circuit simulators such as PSpice.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Output Output Electrical
Name and description Default value Units Value range
Node nameName of the circuit node. The signal at this node will be extracted from the file.
V (0)
Filename (.stl)File name with the data signal in time domain with CDSF format
Signal.csd
Reload fileDefines whether the component should reload the signal for each run
no — True, false
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
IterationsNumber of times to repeat the calculation
Iterations — —
Sample rateOutput signal sample rate
Hz Hz, GHz, THz
789
LOAD SPICE CSDF FILE
Technical BackgroundThe .csd files are signal data files exported from circuit simulators such as PSpice. They are used for post-processing and waveform analysis. They contain time-domain waveform data for defining the signals associated with certain nodes in the circuit. Usually the data is voltage, current, or digital levels (1 or 0).
Circuit simulators can export PROBE data using CSDF option. In the following example, a RLC filter is used to filter a 2.5 GB/s signal. The simulation circuit file and the result is displayed in Figure 1 and Figure 2.
Figure 1 Spice circuit file will generate the PROBE data using CSDF option
790
LOAD SPICE CSDF FILE
Figure 2 Simulation results after filtering a NRZ signal using a RLC filter
The following figure (Figure 3) shows OptiSystem loading the file using Load Spice CSDF File component, after the simulation the results will be displayed in the Oscilloscope Visualizer (Figure 4).
Figure 3 OptiSystem project that loads a .csd file
791
LOAD SPICE CSDF FILE
Figure 4 Signal from circuit simulator in OptiSystem visualizer
792
TRIGGERED SAVE SPICE STIMULUS FILE
Triggered Save Spice Stimulus FileThis component has the same engine as the Save Spice Stimulus File component. It will copy the input signal to the output signal. The output port can be connected to other component to be used as a signal trigger.
Ports
Parameters
Main
File format
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value Units Value range
Output dataThe signal type to save to the file
Signal and noise SignalSignal and noiseNoise
Filename (.stl)File name with the electrical signal in time domain
Signal.stl
Name and description Default value Units Value range
File commentCharacter string for comments in the file
*
File beginCharacter string to be added to the first line of the file
.STIMULUS SIGNAL PWL
File endCharacter string to be added to the last line of the file
793
TRIGGERED SAVE SPICE STIMULUS FILE
Random numbers
Technical Background
Refer to the Technical Background of the Save Spice Stimulus File component for additional information. Additionally this component can generate a signal trigger after saving the signal. It can be used together with the Command Line Application component, from the Tools component library. This module can save the signal into a file, then triggers the command line component to open another application that can load the saved file.
Typically this component is used for cosimulation with EDA tools, together with triggered load component from the EDA cosimulation library. Figure 1 shows one example of application, the file will be saved with a 2.5 GB/s signal, the file format is Spice PWL, with a source named Vsupply. The file name will be NRZ25.stl, and it will be loaded as a voltage source into the circuit simulation (Figure 2).
The file data after the simulation is presented in Figure 3. After saving the file a signal trigger will be send to the Command Line Application component, that will perform its own calculation.
File line beginCharacter string to be added to the beginning of each line of data
+(
File line endCharacter string to be added to the end of each line
)
File delimiterCharacter string to be used in each line of data, to separate multiple values
,
Name and description Default value Units Value range
Generate random seedDetermines the interpolation algorithm for the measured data
YES Yes, No
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
Name and description Default value Units Value range
794
TRIGGERED SAVE SPICE STIMULUS FILE
Figure 1 Cosimulation using Triggered Save Spice Stimulus File component
Figure 2 Triggered Save Spice Stimulus file parameter for the file header
795
TRIGGERED SAVE SPICE STIMULUS FILE
Figure 3 NRZ25.stl file generated from OptiSystem
796
TRIGGERED LOAD SPICE CSDF FILE
Triggered Load Spice CSDF FileThis component has the same engine as the Load Spice CSDF File component. It will run only if there is a signal at the input port. The signal can be off any type and it will work as a trigger.
Ports
Parameters
Main
File format
Name and description Port type Signal type
Output Output Electrical
Name and description Default value Units Value range
Output dataThe signal type to save to the file
Signal and noise SignalSignal and noiseNoise
Filename (.stl)File name with the electrical signal in time domain
Signal.stl
Name and description Default value Units Value range
File commentCharacter string for comments in the file
*
File beginCharacter string to be added to the first line of the file
.STIMULUS SIGNAL PWL
File endCharacter string to be added to the last line of the file
797
TRIGGERED LOAD SPICE CSDF FILE
Simulation
Technical Background
Refer to the Technical Background of the Load Spice CSDF File component for additional information. Additionally, this component can generate a signal trigger after loading the signal. It can be used together with the Command Line Application component, from the Tools component library. This module can load the simulation results into OptiSystem after receiving a signal trigger at the input port.
Typically this component is used for cosimulation with EDA tools, together with triggered save component from the EDA cosimulation library. Figure 1 shows one example of application, the file will be saved with a 2.5 GB/s signal, the file format is Spice PWL, with a source named Vsupply. The file name will be NRZ25.stl, and it will be loaded as a voltage source into the circuit simulation (Figure 2).
The Command Line Application component will call the application, in this case, PSpice, that will perform the simulation and generate a .csd file. This component will load the signal at node V(2) into OptiSystem.
File line beginCharacter string to be added to the beginning of each line of data
+(
File line endCharacter string to be added to the end of each line
)
File delimiterCharacter string to be used in each line of data, to separate multiple values
,
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
Sample rateOutput signal sample rate
Hz Hz, GHz, THz
Name and description Default value Units Value range
798
TRIGGERED LOAD SPICE CSDF FILE
Figure 1 Cosimulation using Triggered Load Spice CSDF file component
Figure 2 Triggered Load Spice CSDF file parameters: selected CSDF file data
799
TRIGGERED LOAD SPICE CSDF FILE
Notes:
800
Cable Access Library
This section contains information on the following Cable Access components:
Carrier generators
• Carrier Generator• Carrier Generator Measured
Transmitters
Modulators
• Electrical Amplitude Modulator (AM)• Electrical Frequency Modulator (FM)• Electrical Phase Modulator• Quadrature Modulator• PAM Modulator• QAM Modulator• PSK Modulator• DPSK Modulator• OQPSK Modulator• MSK Modulator• FSK Modulator• CPFSK Modulator
Pulse generators
• M-ary Pulse Generator• PAM Pulse Generator• QAM Pulse Generator• PSK Pulse Generator• DPSK Pulse Generator
801
CABLE ACCESS LIBRARY
• OQPSK Pulse Generator• MSK Pulse Generator
Sequence generators
• PAM Sequence Generator• QAM Sequence Generator• PSK Sequence Generator• DPSK Sequence Generator
Receivers
Demodulators
• Electrical Amplitude Demodulator• Electrical Phase Demodulator• Electrical Frequency Demodulator• Quadrature Demodulator
Decoders
• PAM Sequence Decoder• QAM Sequence Decoder• PSK Sequence Decoder• DPSK Sequence Decoder
Detectors
• M-ary Threshold Detector
802
CARRIER GENERATOR
Carrier Generator
This component generates a user-defined number of carriers. The output is a sum of sinusoidal electrical signals with constant amplitude. The phase can be constant or random.
Ports
Parameters
Main
Name and description Port type Signal type
Output Output Electrical
Name and description Default value Units Value range
Number of channelsNumber of output signal carriers
2 — [1,+INF[
FrequencyFrequency of the first carrier
50 Hz, MHz, GHz
[0,+INF[
Frequency spacingSpacing between adjacent carriers
3.5 Hz, MHz, GHz
[0,+INF[
AmplitudeOutput signal amplitude of each carrier
1 a.u. ]-INF,+INF[
BiasDC bias
0 a.u. ]-INF,+INF[
Random phaseDefines whether the phase of the output carriers will be random or user defined
Yes — True, false
PhaseConstant phase
0 deg ]-INF,+INF[
803
CARRIER GENERATOR
Simulation
Random numbers
Technical backgroundThis component generates a sum of sinusoidal carriers with the same zero peak amplitude according to:
, where is the signal for each carrier, is the parameter,
Number of channels and Vbias is the parameter Bias.
Each carrier is defined by:
, where is the frequency of each carrier.
The phase can be defined as random, or user-defined. The user-defined phase is the same for all the carriers.
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
IterationsNumber of times to repeat the calculation
Iterations — — [1,+INF[
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
Name and description Default value
Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
vout vi t( ) vbias+i 1=
N
∑= vi N
vi A 2πft φi+( )sin= fi
804
CARRIER GENERATOR MEASURED
Carrier Generator Measured
This component loads a file with the list of frequency, amplitude and phase of each carrier, and generates a sum of sinusoidal electrical signals.
Ports
Parameters
Main
Name and description Port type Signal type
Output Output Electrical
Name and description Default value Units Value range
Frequency amplitude phase (Hz a.u. deg)Table with the carrier data
50e6 1 0
58e6 1 0
Hz, a.u., deg
Amplitude and phase file nameFile name with the list of carriers.
1 Hz, MHz, GHz
[0,+INF[
Frequency spacingSpacing between adjacent carriers
8 Hz, MHz, GHz
0,+INF[
BiasDC bias
0 a.u. ]-INF,+INF[
805
CARRIER GENERATOR MEASURED
Simulation
Technical backgroundThis component generates a sum of sinusoidal carriers according to:
, where is the signal for each carrier, is the number of channels,
and Vbias is the parameter Bias.
Each carrier is defined by:
, where are the amplitude, frequency and phase of each carrier.
The user can provide the measurements in the parameter Frequency amplitude phase (Hz a.u. deg); alternatively the measurements can be loaded from a file using the parameter Amplitude and phase file name. The amplitude and phase curves must be provided in the file containing three columns, where the first one refers to the frequency specified in [Hz] units; the second one gives the amplitude curve in [a.u.] units, and the last one gives the phase in [deg] units.
As an example of input file we have:
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
IterationsNumber of times to repeat the calculation
Iterations — — [1,+INF[
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
vout vi t( ) vbias+i 1=
N
∑= vi N
vi A 2πfit φi+( )sin= Ai, fi, and φl
806
ELECTRICAL AMPLITUDE MODULATOR (AM)
Electrical Amplitude Modulator (AM)
Ports
Parameters
Main
Frequency [Hz] Amplitude [a.u.] Phase [deg]
50e6 1.00 0.00
58e6 1.00 0.00
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Value range
Frequency
Frequency of the input signal carrier
50 MHz, Hz, GHz, Thz
[0,+INF[
BiasDC Offset of the pulse
1 a.u. ]-INF,+INF[
Gain
Linear gain to be applied to the signal input
1 ]-INF,+INF[
PhasePhase of the input signal carrier
0 deg,rad ]-INF,+INF[
807
ELECTRICAL AMPLITUDE MODULATOR (AM)
Simulation
Technical BackgroundThe Electrical Amplitude Modulator implements an analog amplitude modulator. The output signal is modulated according to:
where is the input electrical signal, is the parameter gain, is the bias, is the carrier frequency, and is the phase of the carrier.
Figure 1 shows the block diagram of this component.
Figure 1 Electrical Amplitude Modulator block diagram
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
vout t( ) Gvin t( ) 2πfct φc+( ) b+cos=
vin G b fcφc
808
ELECTRICAL FREQUENCY MODULATOR (FM)
Electrical Frequency Modulator (FM)
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Value range
Frequency
Frequency of the input signal carrier
50 MHz, Hz, GHz, Thz
[0,+INF[
AmplitudePeak-to-peak amplitude of the pulse
1 a.u. ]-INF,+INF[
BiasDC Offset of the pulse
1 a.u. ]-INF,+INF[
PhasePhase of the input signal carrier
0 deg,rad ]-INF,+INF[
Modulation constantFrequency change relative to the input signal amplitude
1 Hz, kHz, Mhz, GHz
]-INF,+INF[
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
809
ELECTRICAL FREQUENCY MODULATOR (FM)
Technical BackgroundThe Electrical Frequency Modulator implements an analog frequency modulator. The output signal is modulated according to:
where is the input electrical signal, is the modulation constant, is the parameter amplitude, is the bias, is the carrier frequency, and is the phase of the carrier.
vout t( ) A 2( πfct 2π m vin t( )∫ dt φc )++ b+cos=
vin m Ab fc φc
810
ELECTRICAL PHASE MODULATOR
Electrical Phase Modulator
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Default unit Value range
Frequency
Frequency of the input signal carrier
50 MHz, Hz, GHz, Thz
[0,+INF[
AmplitudePeak-to-peak amplitude of the pulse
1 a.u. ]-INF,+INF[
BiasDC Offset of the pulse
1 a.u. ]-INF,+INF[
PhasePhase of the input signal carrier
0 deg,rad ]-INF,+INF[
Modulation constantPhase change relative to the input signal amplitude
1 deg, rad ]-INF,+INF[
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
811
ELECTRICAL PHASE MODULATOR
Technical BackgroundThe Electrical Phase Modulator implements an analog phase modulator. The output signal is modulated according to:
where is the input electrical signal, is the modulation constant, is the parameter amplitude, is the bias, is the carrier frequency, and is the phase of the carrier.
vout t( ) A 2πfct mvin t( ) φ+ c+( ) b+cos=
vin M Ab fc φc
812
QUADRATURE MODULATOR
Quadrature Modulator
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input-I Input Electrical
Input-Q Input Electrical
Output Output Electrical
Name and description Default value
Default unit Value range
Frequency
Frequency of the input signal carrier
50 MHz, Hz, GHz, Thz
[0,+INF[
BiasDC Offset of the pulse
1 a.u. ]-INF,+INF[
GainLinear gain to be applied to the signal input
1 ]-INF,+INF[
PhasePhase of the input signal carrier
0 deg,rad ]-INF,+INF[
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
813
QUADRATURE MODULATOR
Technical BackgroundThe Quadrature Modulator implements a quadrature analog amplitude modulator. The output signal is modulated according to:
where and are the input electrical signals, is the parameter gain, is the bias, is the carrier frequency, and is the phase of the carrier.
Figure 1 shows the block diagram of this component.
Figure 1 Quadrature Modulator block diagram
Reference:[1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y.,
(1987).
vout t( ) G I t( ) 2πfct φc+( ) Q t( ) 2πfct φc+( )sin–cos[ ] b+=
I Q G bfc φc
814
PAM MODULATOR
PAM Modulator
Encodes and modulates binary signal to an electrical signal using pulse amplitude modulation (PAM).
Ports
Parameters
Main
Name and description Port type Signal type
Bit Sequence Input Binary
Output Output Electrical
Name and description Default value
Default unit Value range
Frequency
Frequency of the input signal carrier
50 MHz, Hz, GHz, Thz
[0,+INF[
Amplitude 1 a.u. ]-INF,+INF[
BiasDC Offset of the pulse
1 a.u. ]-INF,+INF[
PhasePhase of the input signal carrier
0 deg,rad ]-INF,+INF[
Bits per symbolNumber of bits per symbol used in the coding
2 [0,100]
Duty cycleDuration of the high level bit
0.5 bit [0,1]
Position 0 bit
Gray codeDefines whether or not to use Gray code
False True, False
815
PAM MODULATOR
Simulation
Technical BackgroundThe PAM Modulator implements a PAM modulator [1].
Figure 1 shows a block diagram of the component.
Figure 1 PAM Modulator block diagram
Reference:[1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y.,
(1987).
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
816
QAM MODULATOR
QAM Modulator
Encodes and modulates a binary signal to an electrical signal using quadrature amplitude modulation (QAM).
Ports
Parameters
Main
Name and description Port type Signal type
Bit Sequence Input Binary
Output Output Electrical
Name and description Default value
Default unit Value range
Frequency
Frequency of the input signal carrier
50 MHz, Hz, GHz, Thz
[0,+INF[
Amplitude
BiasDC Offset of the pulse
0 a.u. ]-INF,+INF[
PhasePhase of the input signal carrier
0 deg,rad ]-INF,+INF[
Bits per symbolNumber of bits per symbol used in the coding
2 [0,100]
Duty cycleDuration of the high level bit
0.5 bit [0,1]
Position 0 bit
Gray codeDefines whether or not to use Gray code
False True, False
817
QAM MODULATOR
Simulation
Technical BackgroundThe QAM Modulator implements a QAM Modulator [1].
Figure 1 shows a block diagram of this component.
Figure 1 QAM Modulator block diagram
Reference:[1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y.,
(1987).
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
818
PSK MODULATOR
PSK Modulator
Encodes and modulates a binary signal to an electrical signal using phase shift keying modulation (PSK).
Ports
Parameters
Main
Name and description Port type Signal type
Bit Sequence Input Binary
Output Output Electrical
Name and description Default value
Default unit Value range
Frequency
Frequency of the input signal carrier
50 MHz, Hz, GHz, Thz
[0,+INF[
Amplitude
BiasDC Offset of the pulse
0 a.u. ]-INF,+INF[
PhasePhase of the input signal carrier
0 deg,rad ]-INF,+INF[
Bits per symbolNumber of bits per symbol used in the coding
2 [0,100]
Phase offsetDefines whether to use Gray coding or not
45 deg, rad ]-INF,+INF[
Gray codeDefines whether or not to use Gray code
False True, False
819
PSK MODULATOR
Simulation
Technical BackgroundThe PSK Modulator implements a PSK modulator [1].
Figure 1 shows a block diagram of this component.
Figure 1 PSK Modulator block diagram
Reference:[1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y.,
(1987).
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
820
DPSK MODULATOR
DPSK Modulator
Encodes and modulates a binary signal to an electrical signal using differential phase shift keying modulation (DPSK).
Ports
Parameters
Main
Name and description Port type Signal type
Bit Sequence Input Binary
Output Output Electrical
Name and description Default value
Default unit Value range
Frequency
Frequency of the input signal carrier
50 MHz, Hz, GHz, Thz
[0,+INF[
Amplitude
BiasDC Offset of the pulse
0 a.u. ]-INF,+INF[
PhasePhase of the input signal carrier
0 deg,rad ]-INF,+INF[
Bits per symbolNumber of bits per symbol used in the coding
2 [0,100]
Phase offsetDefines whether to use Gray coding or not
45 deg, rad ]-INF,+INF[
Gray codeDefines whether or not to use Gray code
False True, False
821
DPSK MODULATOR
Simulation
Technical BackgroundThe DPSK Modulator implements a DPSK modulator [1].
Figure 1 shows a block diagram of this component.
Figure 1 DPSK Modulator block diagram
Reference:[1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y.,
(1987).
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
822
OQPSK MODULATOR
OQPSK Modulator
Encodes and modulates a binary signal to an electrical signal using offset quadrature phase shift keying modulation (OQPSK).
Ports
Parameters
Main
Name and description Port type Signal type
Bit Sequence Input Binary
Output Output Electrical
Name and description Default value
Default unit Value range
Frequency
Frequency of the input signal carrier
50 MHz, Hz, GHz, Thz
[0,+INF[
Amplitude
BiasDC Offset of the pulse
0 a.u. ]-INF,+INF[
PhasePhase of the input signal carrier
0 deg,rad ]-INF,+INF[
Phase offsetDefines whether to use Gray coding or not
45 deg, rad ]-INF,+INF[
Gray codeDefines whether or not to use Gray code
False True, False
823
OQPSK MODULATOR
Simulation
Technical BackgroundThe OQPSK Modulator implements an OQDPSK modulator [1].
Figure 1 shows a block diagram of this component.
Figure 1 OQPSK Modulator block diagram
Reference:[1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y.,
(1987).
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
824
MSK MODULATOR
MSK Modulator
Encodes and modulates a binary signal to an electrical signal using minimum shift keying modulation (MSK).
Ports
Parameters
Main
Name and description Port type Signal type
Bit Sequence Input Binary
Output Output Electrical
Name and description Default value
Default unit Value range
Frequency
Frequency of the input signal carrier
50 MHz, Hz, GHz, Thz
[0,+INF[
Amplitude
BiasDC Offset of the pulse
0 a.u. ]-INF,+INF[
PhasePhase of the input signal carrier
0 deg,rad ]-INF,+INF[
Phase offsetDefines whether to use Gray coding or not
45 deg, rad ]-INF,+INF[
Gray codeDefines whether or not to use Gray code
False True, False
825
MSK MODULATOR
Simulation
Technical BackgroundThe MSK Modulator implements a MSK modulator [1].
Figure 1 shows a block diagram of this component.
Figure 1 MSK Modulator block diagram
Reference:[1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y.,
(1987).
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
826
FSK MODULATOR
FSK Modulator
Encodes and modulates a binary signal to an electrical signal using frquency shift keying modulation (FSK).
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Binary
Output Output Electrical
Name and description Default value
Default unit Value range
Frequency
Frequency of the input signal carrier
50 MHz, Hz, GHz, Thz
[0,+INF[
Amplitude
BiasDC Offset of the pulse
0 a.u. ]-INF,+INF[
PhasePhase of the input signal carrier
0 deg,rad ]-INF,+INF[
Bits per symbolNumber of bits per symbol used in the coding
2 [0,100]
Frequency separationFrequency separation between symbols
1 Hz, MHz, GHz, THz
[0,+INF[
Gray codeDefines whether or not to use Gray code
False True, False
827
FSK MODULATOR
Simulation
Technical BackgroundThe FSK Modulator implements a FSK modulator [1].
When transmitting information, we can vary the frequency of a signal according to the source symbols. The frequency values takes information from the set of amplitudes [1]:
where is the frequency separation, is the number of possible sequences of binary digits, calculated according to:
where is the number of bits per symbol.
where is the parameter amplitude, is the bias, is the carrier frequency, and is the phase of the carrier.
Reference:[1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y.,
(1987).
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
ai fs 2i 1– M–( ) i, 1 2 ...M, ,= =
fs M
M 2h=
h
vout t( ) A 2πfct 2πai φc+ +( ) b+cos=
A b fcφc
828
CPFSK MODULATOR
CPFSK Modulator
Encodes and modulates a binary signal to an electrical signal using continuous phase frequency shift keying modulation (CPFSK).
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Binary
Output Output Electrical
Name and description Default value
Default unit Value range
Frequency
Frequency of the input signal carrier
50 MHz, Hz, GHz, Thz
[0,+INF[
Amplitude
BiasDC Offset of the pulse
0 a.u. ]-INF,+INF[
PhasePhase of the input signal carrier
0 deg,rad ]-INF,+INF[
Bits per symbolNumber of bits per symbol used in the coding
2 [0,100]
Frequency separationFrequency separation between symbols
1 Hz, MHz, GHz, THz
[0,+INF[
Gray codeDefines whether or not to use Gray code
False True, False
829
CPFSK MODULATOR
Simulation
Technical BackgroundThe CPFSK Modulator implements a CPFSK modulator [].
When transmitting information, we can vary the frequency of a signal according to the source symbols. The frequency values takes information from the set of amplitudes []:
where is the frequency separation, is the number of possible sequences of binary digits, calculated according to:
where is the number of bits per symbol.
where is the parameter amplitude, is the bias, is the carrier frequency, and is the phase of the carrier.
In this model, because the phase transitions are constant, a single oscillator with a modulated frequency modulated is used. The absence of abrupt phase transitions results in a narrower spectrum.
Reference:Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987)
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
ai fs 2i 1– M–( ) i, 1 2 ...M, ,= =
fs M
M 2h=
h
vout t( ) A 2πfct 2πai φc+ +( ) b+cos=
A b fcφc
830
M-ARY PULSE GENERATOR
M-ary Pulse Generator
Generates multilevel pulses according to the M-ary signal input.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input Input M-ary
Output Output Electrical
Name and description Default value
Units Value range
GainLinear gain to be applied to the signal input
0 ]-INF,+INF[
BiasDC Offset of the pulse
1 a.u. ]-INF,+INF[
Duty cycleDuration of the high level bit
1 bit [0,1]
Position 0 bit
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
831
M-ARY PULSE GENERATOR
Technical BackgroundThis model generates pulses according to:
where is the input M-ary signal, is the linear gain, and is the parameter Bias.
is the bit period, is the duty cycle, and is the pulse position.
vout t( )b 0 t t1<≤,
avin t( ) b t1 t t1 tc+<≤,+b t1 tc t T<≤+,
=
vin a b
T tc t1
832
PAM PULSE GENERATOR
PAM Pulse Generator
Generates a M-ary electrical signal from binary signals using pulse amplitude modulation (PAM).
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Bit sequence Input Binary
PAM Pulses Output Electrical
Name and description Default value
Units Value range
Bits per symbolNumber of bits per symbol used in the coding
2 [0,100]
Duty cycleDuration of the high level bit
0.5 bit [0,1]
Position 0 bit
Gray codeDefines whether or not to use Gray code
False True, False
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
833
PAM PULSE GENERATOR
Technical BackgroundWhen transmitting information, we can vary the amplitude of a signal according to the source symbols. The amplitude values are taken from the set of amplitudes [1]:
where is the number of possible sequences of binary digits, calculated according to:
where is the number of bits per symbol.
Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit.
This model generates pulses according to:
where is the amplitude of the signal , is the bit period, is the duty cycle, and is the pulse position.
Figure 1 shows the block diagram of this component.
Figure 1 PAM Pulse Generator block diagram
Reference:
[1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987).
ai 2i 1– M–( ) i, 1 2 ...M, ,= =
M
M 2h=
h
vk out–
0 0 t t1<≤,
ak t1 t t1 tc+<≤,
0 t1 tc+ t T<≤,
=
ak k T tct1
834
QAM PULSE GENERATOR
QAM Pulse Generator
Generates two parallel M-ary electrical signals from binary signals using quadrature amplitude modulation (QAM).
Ports
Parameters
Main
Name and description Port type Signal type
Bit sequence Input Binary
Output - I Output Electrical
Output - Q Output Electrical
Name and description Default value
Units Value range
Bits per symbolNumber of bits per symbol used in the coding
2 [0,100]
Duty cycleDuration of the high level bit
0.5 bit [0,1]
Position 0 bit
Gray codeDefines whether or not to use Gray code
False True, False
835
QAM PULSE GENERATOR
Simulation
Technical BackgroundWith the QAM sequence generator, the bit sequence is split into two parallel subsequences, each transmitted in two quadrature carriers when building a QAM modulator. This is done by using a serial to parallel converter.
When transmitting information, we can vary the amplitude of a signal according to the source symbols.
For each output port, the value of the amplitude takes value from the set of amplitudes [1]
where is the number of possible sequence of binary digits, calculated according to:
where is the number of bits per symbol. The equivalent QAM set is given by the square of .
This means:
If , , then we have a 4-QAM. If , , then we have a 16-QAM.
If , , then we have a 64-QAM. If , , then we have a 256-QAM.
Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit.
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
a1 2i 1– M–( ) i, 1 2 ..., M, ,= =
M
M 2h 2⁄=
hM
h 2= M 2= h 4= M 4=
h 6= M 8= h 8= M 16=
836
QAM PULSE GENERATOR
This model generates pulses according to:
where is the amplitude of the signal , is the bit period, is the duty cycle, and is the pulse position.
Figure 1 represents the block diagram of this component.
Figure 1 QAM Pulse Generator block diagram
vk out– t( )0 0 t t1<≤,
ak t1 t t1 tc+<≤,
0 t1 tc+ t T<≤,
=
ak k T tct1
837
QAM PULSE GENERATOR
Reference:
[1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987).
838
PSK PULSE GENERATOR
PSK Pulse Generator
Generates two parallel M-ary electrical signals from binary signals using phase shift keying modulation (PSK).
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Bit sequence Input Binary
Output - I Output Electrical
Output - Q Output Electrical
Name and description Default value
Units Value range
Bits per symbolNumber of bits per symbol used in the coding
2 [0,100]
Phase offsetInitial phase offset
45 deg, rad ]-INF,+INF[
Gray codeDefines whether or not to use Gray code
False True, False
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
839
PSK PULSE GENERATOR
Technical BackgroundWhen transmitting information, we can vary the phase of a signal according to the source symbols. The phase values are taken from the set of angles [1]:
where is the number of possible sequence of binary digits, calculated according to:
where is the number of bits per symbol, and is the phase offset. The in-phase and the quadrature-channel will have amplitudes according to:
Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit.
This model generates pulses according to:
where and are the amplitudes of the output signals and is the bit period.
Figure 1 shows the block diagram of this component.
Figure 1 PSK Pulse Generator block diagram
Reference:
[1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987).
ϕi2πM------ i 1–( ) φ+
i, 1 2 ...M, ,= =
M
M 2h=
h φ
Ii ϕi( ) i,cos 1 2 ...M, ,= =
Qi ϕi( ) i,sin 1 2 ...M, ,= =
Ik out– t( ) Ik 0 t T<≤,=
Qk out– t( ) Qk 0 t T<≤,=
Ik Qk k T
840
DPSK PULSE GENERATOR
DPSK Pulse Generator
Generates two parallel M-ary electrical signals from binary signals using differential phase shift keying modulation (DPSK).
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Bit sequence Input Binary
Output - I Output Electrical
Output - Q Output Electrical
Name and description Default value
Units Value range
Bits per symbolNumber of bits per symbol used in the coding
2 [0,100]
Phase offsetInitial phase offset
45 deg, rad ]-INF,+INF[
Gray codeDefines whether or not to use Gray code
False True, False
Name and description Default value
Default units
Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
841
DPSK PULSE GENERATOR
Technical BackgroundWhen transmitting information, we can vary the phase of a signal according to the source symbols. The phase values are taken from the set of angles [1], [2]:
where is the phase value for the current symbol, and is the phase value for the previous symbol. is the number of possible sequence of binary digits, calculated according to:
where is the number of bits per symbol, and is the phase offset. The in-phase and the quadrature-channel will have amplitudes according to:
This model generates pulses according to:
where and are the amplitudes of the output signals and is the bit period.
Figure 1 shows the block diagram of this component.
Figure 1 DPSK Pulse Generator block diagram
Reference:
[1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987).
[2] Pawula, R.F., “On M-ary DPSK Transmission Over Terrestrial and Satellite Channels”, IEEE Trans. on Commun. COM-32, 752-761, (July 1984).
ϕki ϕk 1–2πM------ i 1–( ) φ+
+ i, 1 2 ...M, ,= =
ϕki ϕk 1–M
M 2h=
h φ
Iki ϕki( ) i,cos 1 2 ...M, ,= =
Qki ϕki( ) i,sin 1 2 ...M, ,= =
Ik out– t( ) Ik 0 t T<≤,=
Qk out– t( ) Qk 0 t T<≤,=
Ik Qk k T
842
OQPSK PULSE GENERATOR
OQPSK Pulse Generator
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Bit sequence Input Binary
Output - I Output Electrical
Output - Q Output Electrical
Name and description Default value Units Value range
Phase offsetInitial phase offset
45 deg, rad ]-INF,+INF[
Gray codeDefines whether or not to use Gray code
False True, False
Name and description Default value Default units Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
843
OQPSK PULSE GENERATOR
Technical BackgroundWhen transmitting information, we can vary the phase of a signal according to the source symbols. The phase values take the values in the set of angles [1]:
where is the number of possible sequence of binary digits, when using quadrature phase shift keying (QPSK), this number is equal to 4, and is the phase offset. A reduction of the signal fluctuations is possible by delaying the Q channel by one bit period. The bit period is calculated from the input binary signal.
The in-phase and the quadrature-channel will have amplitudes according to:
Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit.
This model generates pulses according to:
where is the amplitude of the signal , is the bit period, and is the input bit period.
Figure 1 shows the block diagram of this component.
Figure 1 OQPSK Pulse Generator block diagram
Reference:
[1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987).
ϕi2πM------ i 1–( ) φ+
i, 1 2 ...M, ,= =
Mφ
Ii ϕi( ) i,cos 1 2 ...M, ,= =
Qi ϕi( ) i,sin 1 2 ...M, ,= =
Ik out– t( ) Ik 0 t T<≤,=
Qk out– t( ) Qk Ts t T Ts+<≤,=
k I T Ts
844
MSK PULSE GENERATOR
MSK Pulse GeneratorGenerates two parallel M-ary symbol sequences from binary signals using minimum shift keying modulation (MSK).
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Bit sequence Input Binary
Output - I Output Electrical
Output - Q Output Electrical
Name and description Default value Units Value range
Phase offsetInitial phase offset
45 deg, rad ]-INF,+INF[
Gray codeDefines whether or not to use Gray code
False True, False
Name and description Default value Default units Unit Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
Sample rateFrequency simulation window
Sample rate Hz Hz, GHz, THz ]0,+INF[
845
MSK PULSE GENERATOR
Technical BackgroundWhen transmitting information, we can vary the phase of a signal according to the source symbols. The phase values take the values in the set of angles [1]:
where is the number of possible sequence of binary digits, when using quadrature phase shift keying (QPSK), this number is equal to 4, and is the phase offset. A reduction of the signal fluctuations is possible by delaying the Q channel by one bit period. The bit period is calculated from the input binary signal. The MSK is a special case of OQPSK in which a sinusoidal pulse replaces the rectangular waveform.
The in-phase and the quadrature-channel will have amplitudes according to:
Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit.
This model generates pulses according to:
where is the amplitude of the signal , is the bit period, and is the input bit period.
Figure 1 shows the block diagram of this component.
ϕi2πM------ i 1–( ) φ+
i, 1 2 ...M, ,= =
Mφ
Ii ϕi( ) i,cos 1 2 ...M, ,= =
Qi ϕi( ) i,sin 1 2 ...M, ,= =
Ik out– t( ) Ikπt
2Ts---------
sin 0 t T<≤,=
Qk out– t( ) Qkπt
2Ts---------
cos Ts t T Ts+<≤,=
k I T Ts
846
MSK PULSE GENERATOR
Figure 1 MSK Pulse Generator block diagram
847
MSK PULSE GENERATOR
Reference:[1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987).
848
PAM SEQUENCE GENERATOR
PAM Sequence Generator
Generates a M-ary symbol sequence from binary signals using pulse amplitude modulation (PAM).
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Bit sequence Input Binary
PAM sequence Output M-ary
Name and description Default value Units Value range
Bits per symbolNumber of bits per symbol used in the coding
2 [0,100]
Gray codeDefines whether to use Gray coding or not
False True, False
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
849
PAM SEQUENCE GENERATOR
Technical BackgroundWhen transmitting information, we can vary the amplitude of a signal according to the source symbols. The value of the amplitude takes value from the set of amplitudes [1]:
where is the number of possible sequence of binary digits, calculated according to:
where is the number of bits per symbol.
If bits per symbol ( ) equals 2, is equal to 8, and values of and will be:
If bits per symbol ( ) equals 3, is equal to 8, and values of and will be:
Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit.
Bit sequence i ai
00 1 -3
01 2 -1
10 3 1
11 4 3
Bit sequence i ai
000 1 -7
001 2 -5
010 3 -3
011 4 -1
100 5 1
101 6 3
110 7 5
111 8 7
a1 2i 1– M–( ) i, 1 2 ..., M, ,= =
M
M 2h=
h
h M a i
h M a i
850
PAM SEQUENCE GENERATOR
In the case of bits per symbol ( ) equals 3, is equal to 8, with Gray code, and the values of will be:
Bit sequence ai
000 -7
001 -5
101 -3
100 -1
110 1
111 3
011 5
010 7
h Ma
851
PAM SEQUENCE GENERATOR
Reference:
[1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987).
852
QAM SEQUENCE GENERATOR
QAM Sequence Generator
Generates two parallel M-ary symbol sequences from binary signals using quadrature amplitude modulation (QAM).
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Bit sequence Input Binary
Output - I Output M-ary
Output - Q Output M-ary
Name and description Default value Units Value range
Bits per symbolNumber of bits per symbol used in the coding
2 Hz, THz, nm [0,100]
Gray codeDefines whether to use Gray coding or not
False True, False
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
853
QAM SEQUENCE GENERATOR
Technical BackgroundWith the QAM sequence generator, the bit sequence is split into two parallel subsequences, each can be transmitted in two quadrature carriers when building a QAM modulator. This is achieved by using a serial to parallel converter.
When transmitting information, we can vary the amplitude of a signal according to the source symbols.
For each output port, the amplitude takes one of the values from the set of amplitudes [1]:
where is the number of possible sequence of binary digits, calculated according to:
where is the number of bits per symbol. The equivalent QAM set is given by the square of .
This means:
If , , then we have a 4-QAM. If , , then we have a 16-QAM.
If , , then we have a 64-QAM. If , , then we have a 256-QAM.
If bits per symbol ( ) are equal to 4, we have a 16-QAM that requires 2 consecutive bits from the input sequence for each subsequence:
Sequence Subsequence I/i a Subsequence Q / i
a
0000 00 / 1 -3 00 / 1 -3
0001 00 / 1 -3 01 / 2 -1
0010 00 / 1 -3 10 / 3 1
0011 00 / 1 -3 11 / 4 3
0100 01 / 2 -1 00 / 1 -3
0101 01 / 2 -1 01 / 2 -1
0110 01 / 2 -1 10 / 3 1
0111 01 / 2 -1 11 / 4 3
1000 10 / 3 1 00 / 1 -3
1001 10 / 3 1 01 / 2 -1
1010 10 / 3 1 10 / 3 1
a1 2i 1– M–( ) i, 1 2 ..., M, ,= =
M
M 2h 2⁄=
hM
h 2= M 2= h 4= M 4=
h 6= M 8= h 8= M 16=
h
854
QAM SEQUENCE GENERATOR
Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit.
1011 10 / 3 1 11 / 4 3
1100 11 / 4 3 00 / 1 -3
1101 11 / 4 3 01 / 2 -1
1110 11 / 4 3 10 / 3 1
1111 11 / 4 3 11 / 4 3
Sequence Subsequence I/i a Subsequence Q / i
a
855
QAM SEQUENCE GENERATOR
Reference:
[1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987).
856
PSK SEQUENCE GENERATOR
PSK Sequence Generator
Generates two parallel M-ary symbol sequences from binary signals using phase shift keying modulation (PSK).
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Bit sequence Input Binary
Output - I Output M-ary
Output - Q Output M-ary
Name and description Default value Units Value range
Bits per symbolNumber of bits per symbol used in the coding
2 [0,100]
Phase offsetInitial phase offset
45 deg, rad ]-INF, +INF[
Gray codeDefines whether or not to use Gray code
False True, False
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
857
PSK SEQUENCE GENERATOR
Technical BackgroundWhen transmitting information, we can vary the phase of a signal according to the source symbols. The phase values are taken from the set of angles [1]:
where is the number of possible sequence of binary digits, calculated according to:
where is the number of bits per symbol, and is the phase offset. The in-phase and the quadrature-channel will have amplitudes according to:
Assuming , if bits per symbol ( ) equals 2, equals 4, the values of and will be:
Assuming , if bits per symbol ( ) equals 3, equals 8, the values of and will be:
Bit sequence I Q
00 1 0
01 0 1
10 -1 0
11 0 -1
Bit sequence I Q
000 1 0
001
010 0 1
ϕi2πM------ i 1–( ) φ+
i, 1 2 ...M, ,= =
M
M 2h=
h φ
Ii ϕi( ) i,cos 1 2 ...M, ,= =
Qi ϕi( ) i,sin 1 2 ...M, ,= =
φ 0= h M IQ
φ 0= h M IQ
22
------- 22
-------
858
PSK SEQUENCE GENERATOR
Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit.
011
100 -1 0
101
110 0 -1
111
Bit sequence I Q
22
-------– 22
-------
22
-------– 22
-------–
22
------- 22
-------–
859
PSK SEQUENCE GENERATOR
Reference:
[1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987).
860
DPSK SEQUENCE GENERATOR
DPSK Sequence Generator
Generates two parallel M-ary symbol sequences from binary signals using differential phase shift keying modulation (DPSK).
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Bit sequence Input Binary
Output - I Output M-ary
Output - Q Output M-ary
Name and description Default value Units Value range
Bits per symbolNumber of bits per symbol used in the coding
2 [0,100]
Phase offsetInitial phase offset
45 deg, rad ]-INF, +INF[
Gray codeDefines whether to use Gray coding or not
False True, False
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
861
DPSK SEQUENCE GENERATOR
Technical BackgroundWhen transmitting information, we can vary the phase of a signal according to the source symbols. The phase values are taken from the set of angles [1], [2]:
where is the phase value for the current symbol, and is phase value for the previous symbol. is the number of possible sequence of binary digits, calculated according to:
where is the number of bits per symbol, and is the phase offset. The in-phase and the quadrature-channel will have amplitudes according to:
Assuming , if bits per symbol ( ) equals 2, equals 4, the values of and will be:
Assuming , if bits per symbol ( ) equals 3, equals 8, the values of and will be:
k Bit sequence I Q
0 00 1 0
1 01 0 1
2 10 -1 0
3 11 0 -1
k Bit sequence I Q
0 000 1 0
1 001
ϕki ϕk 1–2πM------ i 1–( ) φ+
+ i, 1 2 ...M, ,= =
ϕki ϕk 1–M
M 2h=
h φ
Iki ϕki( ) i,cos 1 2 ...M, ,= =
Qki ϕki( ) i,sin 1 2 ...M, ,= =
φ 0= h M IQ
φ 0= h M IQ
22
------- 22
-------
862
DPSK SEQUENCE GENERATOR
Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit.
2 010 0 1
3 011
4 100 -1 0
5 101
6 110 0 -1
7 111
k Bit sequence I Q
22
-------– 22
-------
22
-------– 22
-------–
22
------- 22
-------–
863
DPSK SEQUENCE GENERATOR
Reference:
[1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987).
[2] Pawula, R.F., “On M-ary DPSK Transmission Over Terrestrial and Satellite Channels”, IEEE Trans. on Commun. COM-32, 752-761, (July 1984).
864
ELECTRICAL AMPLITUDE DEMODULATOR
Electrical Amplitude Demodulator
A coherent amplitude demodulator.
Ports
Parameters
Main
Low Pass Filter
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Units Value range
FrequencyFrequency of the input signal carriert
50 MHz, Hz, GHz, Thz [0,+INF[
PhasePhase of the input signal carrier
0 deg, rad ]-INF,+INF[
GainLinear gain to be applied to the signal input
1 ]-INF,+INF[
Name and description Default value
Units Value range
Cut off frequency3 dB cut off frequency of the filter
50 MHz, Hz, GHz, Thz [0,+INF[
Filter typeInternal filter type
Cosine Roll Off
Rectangular, Cosine Roll Off, Squared Cosine Roll Off
Roll Off factor 0.2 [0.1]
865
ELECTRICAL AMPLITUDE DEMODULATOR
Simulation
Technical BackgroundThe component implements an analog demodulator for amplitude-modulated signals. The output signal is demodulated according to:
,
where is the input electrical signal, is the parameter gain, is the carrier frequency,
is the phase of the carrier, and is the time response of the low pass filter.
The filter type is described according to filter components in the Electrical Filters library:
• rectangle• cosine roll off• squared cosine roll off
Figure 1 shows a block diagram of this component.
Figure 1 Electrical amplitude demodulator block diagram
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
vout t( ) Gvin t( ) 2πfct φc+( )cos[ ]∗hlow t( )=
vin G fc
φc hlow
866
ELECTRICAL PHASE DEMODULATOR
Electrical Phase Demodulator
A coherent phase demodulator.
Ports
Parameters
Main
Low Pass Filter
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Units Value range
FrequencyFrequency of the input signal carriert
50 MHz, Hz, GHz, Thz [0,+INF[
PhasePhase of the input signal carrier
0 deg, rad ]-INF,+INF[
Peak to peak amplitudePeak to peak output signal
1 ]-INF,+INF[
Name and description Default value
Units Value range
Cut off frequency3 dB cut off frequency of the filter
50 MHz, Hz, GHz, Thz [0,+INF[
Filter typeInternal filter type
Cosine Roll Off
Rectangular, Cosine Roll Off, Squared Cosine Roll Off
Roll Off factor 0.2 [0.1]
867
ELECTRICAL PHASE DEMODULATOR
Simulation
Technical BackgroundThis component implements an analog demodulator for phase-modulated signals. The output signal is demodulated using a frequency discriminator followed by an integrator according to:
where is the input electrical signal, is the carrier frequency, is the phase of the carrier, and is the time response of the low pass filter. The signal is then scaled to the user-defined peak-to-peak amplitude.
The filter type is described according to filter components in the Electrical Filters library:• rectangle• cosine roll off• squared cosine roll off
Figure 1 shows a block diagram of this component.
Figure 1 Electrical phase demodulator block diagram
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
vd t( ) ddt-----vin t( )=
v t( ) vd∫ t( ) td=
vout t( ) v t( ) 2πfct φc+( )cos[ ]∗hlow t( )=
vin fc φchlow
868
ELECTRICAL FREQUENCY DEMODULATOR
Electrical Frequency Demodulator
Frequency demodulator based on a frequency discriminator.
Ports
Parameters
Main
Low Pass Filter
Name and description Port type Signal type
Input Input Electrical
Output Output Electrical
Name and description Default value
Units Value range
FrequencyFrequency of the input signal carriert
50 MHz, Hz, GHz, Thz [0,+INF[
PhasePhase of the input signal carrier
0 deg, rad ]-INF,+INF[
Peak to peak amplitude
Peak to peak output signal
1 ]-INF,+INF[
Name and description Default value
Units Value range
Cut off frequency3 dB cut off frequency of the filter
50 MHz, Hz, GHz, Thz [0,+INF[
Filter typeInternal filter type
Cosine Roll Off
Rectangular, Cosine Roll Off, Squared Cosine Roll Off
Roll Off factor 0.2 [0.1]
869
ELECTRICAL FREQUENCY DEMODULATOR
Simulation
Technical BackgroundThis component implements an analog demodulator for frequency-modulated signals. The output signal is demodulated using a frequency discriminator according to:
.
where is the input electrical signal, is the carrier frequency, is the phase of the
carrier, and is the time response of the low pass filter. The signal is then scaled to the user-defined peak-to-peak amplitude.
The filter type is described according to filter components in the Electric Filters library:• rectangle• cosine roll off• squared cosine roll off
Figure 1 shows a block diagram of this component.
Figure 1 Electrical frequency demodulator block diagram
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
vd t( ) ddt-----vin t( )=
vout t( ) vd t( ) 2πfct φc+( )cos[ ]∗hlow t( )=
vin fc φc
hlow
870
QUADRATURE DEMODULATOR
Quadrature Demodulator
A coherent amplitude demodulator for quadrature components (I and Q).
Ports
Parameters
Main
Low Pass Filter
Name and description Port type Signal type
Input Input Electrical
Output-I Output Electrical
Output-Q Output Electrical
Name and description Default value
Units Value range
FrequencyFrequency of the input signal carriert
50 MHz, Hz, GHz, Thz [0,+INF[
PhasePhase of the input signal carrier
0 deg, rad ]-INF,+INF[
GainLinear gain to be applied to the signal input
1 ]-INF,+INF[
Name and description Default value
Units Value range
Cut off frequency3 dB cut off frequency of the filter
50 MHz, Hz, GHz, Thz [0,+INF[
Filter typeInternal filter type
Cosine Roll Off
Rectangular, Cosine Roll Off, Squared Cosine Roll Off
Roll Off factor 0.2 [0.1]
871
QUADRATURE DEMODULATOR
Simulation
Technical BackgroundThis component implements an alalog demodulator using a carrier generator for Q and I quadrature components. The output signal is demodulated according to:
where is the input electrical signal, is the parameter gain, is the carrier frequency,
is the phase of the carrier, and is the time response of the low pass filter.
The filter type is described according to filter components in the Electric Filters library:• rectangle• cosine roll off• squared cosine roll off
Figure 1 shows a block diagram of this component.
Figure 1 Quadrature demodulator block diagram
Name and description Default value Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
vI t( ) Gvin t( ) 2πfct φc+( )cos[ ]∗hlow t( )=
vQ t( ) G– vin t( ) 2πfct φc+( )sin[ ]∗hlow t( )=
vin G fc
φc hlow
872
PAM SEQUENCE DECODER
PAM Sequence Decoder
Decodes a PAM M-ary symbol sequence to a binary signal.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
PAM sequence Input M-ary
Bit sequence Output Binary
Name and description Default value Units Value range
Bits per symbolNumber of bits per symbol used in the coding
2 [0,100]
Gray codeDefines whether or not to use Gray code
False True, False
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
873
PAM SEQUENCE DECODER
Technical BackgroundWhen transmitting information, we can vary the amplitude of a signal according to the source symbols. The amplitude values are taken from the set of amplitudes [1]:
is the number of possible sequence of binary digits, calculated according to:
where is the number of bits per symbol. . The PAM decoder will calculate the value of for each amplitude of the signal :
and convert the values of to the equivalent binary sequence.
If bits per symbol ( ) equals 2, equals 4, the values of and will be:
If bits per symbol ( ) equals 3, equals 8, the values of and will be:
Bit sequence i ai
00 1 -3
01 2 -1
10 3 1
11 4 3
Bit sequence i ai
000 1 -7
001 2 -5
010 3 -3
011 4 -1
100 5 1
101 6 3
110 7 5
111 8 7
ai 2i 1– M–( ) i, 1 2 ...M, ,= =
MM 2h=
h φi k
i ak 1 M+ +( ) 2⁄= i
h M a i
h M a i
874
PAM SEQUENCE DECODER
Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit. In the case where bits per symbol ( ) equals 3, equals 8, with Gray code, the values of will be:
Bit sequence ai
000 -7
001 -5
101 -3
100 -1
110 1
111 3
011 5
010 7
hM a
875
PAM SEQUENCE DECODER
Reference:
[1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987).
876
QAM SEQUENCE DECODER
QAM Sequence Decoder
Decodes two parallel QAM M-ary symbol sequences to a binary signal.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input - I Input M-ary
Input - Q Input M-ary
Bit sequence Output Binary
Name and description Default value Units Value range
Bits per symbolNumber of bits per symbol used in the coding
2 [0,100]
Gray codeDefines whether or not to use Gray code
False True, False
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
877
QAM SEQUENCE DECODER
Technical BackgroundIn the QAM sequence decoder, the bit sequence is split into two parallel subsequences, each can be transmitted in two quadrature carriers when building a QAM modulator. This is achieved by using a serial to parallel converter.
When transmitting information, we can vary the amplitude of a signal according to the source symbols.
For each output port, the value of the amplitude takes value from the set of amplitudes [1]
where is the number of possible sequence of binary digits, calculated according to:
where is the number of bits per symbol. The equivalent QAM set is given by the square of .
This means:
If , , then we have a 4-QAM. If , , then we have a 16-QAM.
If , , then we have a 64-QAM. If , , then we have a 256-QAM.
The QAM decoder calculates the value of for the amplitude of each signal input :
and convert the values of to the equivalent binary sequence.
If bits per symbol ( ) equals 4, we have a 16-QAM that requires 2 consecutive bits from the input sequence for each subsequence:
Sequence Subsequence I/i a Subsequence Q / i
a
0000 00 / 1 -3 00 / 1 -3
0001 00 / 1 -3 01 / 2 -1
0010 00 / 1 -3 10 / 3 1
0011 00 / 1 -3 11 / 4 3
0100 01 / 2 -1 00 / 1 -3
0101 01 / 2 -1 01 / 2 -1
0110 01 / 2 -1 10 / 3 1
0111 01 / 2 -1 11 / 4 3
a1 2i 1– M–( ) i, 1 2 ..., M, ,= =
M
M 2h 2⁄=
hM
h 2= M 2= h 4= M 4=
h 6= M 8= h 8= M 16=
i k
i ak 1 M+ +( ) 2⁄=
i
h
878
QAM SEQUENCE DECODER
Using Gray code, adjacent signal amplitudes that correspond to binary sequences will differ by only one digit.
1000 10 / 3 1 00 / 1 -3
1001 10 / 3 1 01 / 2 -1
1010 10 / 3 1 10 / 3 1
1011 10 / 3 1 11 / 4 3
1100 11 / 4 3 00 / 1 -3
1101 11 / 4 3 01 / 2 -1
1110 11 / 4 3 10 / 3 1
1111 11 / 4 3 11 / 4 3
Sequence Subsequence I/i a Subsequence Q / i
a
879
QAM SEQUENCE DECODER
Reference:
[1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987).
880
PSK SEQUENCE DECODER
PSK Sequence Decoder
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input - I Input M-ary
Input - Q Input M-ary
Bit sequence Output Binary
Name and description Default value Units Value range
Bits per symbolNumber of bits per symbol used in the coding
2 [0,100]
Phase offsetInitial phase offset
45 deg, rad ]-INF, +INF[
Gray codeDefines whether or not to use Gray code
False True, False
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
881
PSK SEQUENCE DECODER
Technical BackgroundWhen transmitting information, we can vary the phase of a signal according to the source symbols. The phase values are taken from the set of angles [1]:
where is the number of possible sequence of binary digits, calculated according to:
where is the number of bits per symbol, and is the phase offset. The in-phase and the quadrature channel will have amplitudes according to:
The PSK decoder will calculate the value of for the phase of each signal input :
and convert the values of to the equivalent binary sequence.
Assuming , if bits per symbol ( ) equals 2, and , then the values for and will be:
Bit sequence I Q
00 1 0
01 0 1
10 -1 0
11 0 -1
ϕi2πM------ i 1–( ) φ+
i, 1 2 ...M, ,= =
M
M 2h=
h φ
Ii ϕi( ) i,cos 1 2 ...M, ,= =
Qi ϕi( ) i,sin 1 2 ...M, ,= =
i k
ϕk arc Qk Ik⁄( )tan=
iϕk ϕ–( )M
2π------------------------- 1+=
i
ϕ 0= h M 4=I Q
882
PSK SEQUENCE DECODER
Assuming , if bits per symbol ( ) equals 3, and , then the values for and will be
Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit.
Bit sequence I Q
000 1 0
001
010 0 1
011
100 -1 0
101
110 0 -1
111
ϕ 0= h M 8=I Q
22
------- 22
-------
22
-------– 22
-------
22
-------– 22
-------–
22
------- 22
-------–
883
PSK SEQUENCE DECODER
Reference:
[1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987).
884
DPSK SEQUENCE DECODER
DPSK Sequence Decoder
Decodes two parallel DPSK M-ary symbol sequences to binary signals.
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Input - I Input M-ary
Input - Q Input M-ary
Bit sequence Output Binary
Name and description Default value Units Value range
Bits per symbolNumber of bits per symbol used in the coding
2 [0,100]
Phase offsetInitial phase offset
45 deg, rad ]-INF, +INF[
Gray codeDefines whether or not to use Gray code
False True, False
Name and description Default value
Default unit Units Value range
EnabledDetermines whether or not the component is enabled
True — — True, False
885
DPSK SEQUENCE DECODER
Technical BackgroundWhen transmitting information, we can vary the phase of a signal according to the source symbols. The phase values are taken from the set of angles [1], [2]:
where is the phase value for the current symbol, and is phase value for the previous symbol.
is the number of possible sequence of binary digits, calculated according to:
where is the number of bits per symbol, and is the phase offset. The in-phase and the quadrature-channel will have amplitudes according to:
The DPSK decoder will calculate the value of from the phase difference between consecutive signals and :
Assuming , if bits per symbol ( ) equals 2, equals 4, the values of and will be:
k Bit sequence I Q
0 00 1 0
1 01 0 1
2 10 -1 0
3 11 0 -1
ϕki ϕk 1–2πM------ i 1–( ) φ+
+ i, 1 2 ...M, ,= =
ϕki ϕk 1–
M
M 2h=
h φ
Iki ϕki( ) i,cos 1 2 ...M, ,= =
Qki ϕki( ) i,sin 1 2 ...M, ,= =
ik k 1–
ϕk arc Qk Ik⁄( )tan=
iϕk ϕk 1–– φ–( )M
2π------------------------------------------- 1+=
φ 0= h M IQ
886
DPSK SEQUENCE DECODER
Assuming , if bits per symbol ( ) equals 3, equals 8, the values of and will be:
Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit.
k Bit sequence I Q
0 000 1 0
1 001
2 010 0 1
3 011
4 100 -1 0
5 101
6 110 0 -1
7 111
φ 0= h M IQ
22
------- 22
-------
22
-------– 22
-------
22
-------– 22
-------–
22
------- 22
-------–
887
DPSK SEQUENCE DECODER
Reference:
[1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987).
[2] Pawula, R.F., “On M-ary DPSK Transmission Over Terrestrial and Satellite Channels”, IEEE Trans. on Commun. COM-32, 752-761, (July 1984).
888
M-ARY THRESHOLD DETECTOR
M-ary Threshold Detector
Decodes multilevel pulses to a M-ary signal output.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Electrical
Output Output M-ary
Name and description Default value Default unit Units Value range
Reference bit rateReference bit rate to use for the decision instant calculation
Bit rate Bits/s Bits/s
MBits/s
GBits/s
[0,+INF[
Delay compensationDelay to apply to the signal input
0 s s, ms, ns ]-INF,+INF[
Threshold amplitudesList of threshold levels for decision
-5, -3.5, -1.5, 0
1.5, 3.5, 5
a.u. ]-INF,+INF[
Decision instantValue for the decision instant to use when recovering the bit sequence
0.5 Bit — [0,1]
Output amplitudesList of multilevel symbols for the output M-ary sequence
-7, -5, -3, -1, 1, 3, 5, 7
a.u. ]-INF,+INF[
889
M-ARY THRESHOLD DETECTOR
Simulation
Random numbers
Technical BackgroundThis model compares the electrical signal at a user-defined decision instant with a list of threshold levels. The comparison generates an index used to generate the output amplitude.
For example, if the signal input has a value of -3.3, the output level will be -3, since -3.3 is between -3.5 and -1.5.
The delay compensation parameter allows the user to compensate delay occurred during the signal propagation. The number of output levels must be greater than the number of threshold levels.
By selecting ‘parameter enable’ to false, the module will generate the levels at the decision instant without comparison and decision based on the output levels. This means the user can access the values at decision instant before the quantization.
Name and description Default value
Units Value range
EnabledDetermines whether or not the component is enabled
True — True, False
Name and description Default value
Units Value range
Generate random seedDetermines if the seed is automatically defined and unique
True — True, False
Random seed indexUser-defined seed index for noise generation
0 — [0,4999]
890
Visualizer LibraryThis book contains information on the following visualizers.
Optical
• Optical Spectrum Analyzer (OSA)• Optical Time Domain Visualizer (OTDV)• Optical Power Meter Visualizer• WDM Analyzer (WDMA)• Dual Port WDM Analyzer (DPWDMA)
Electrical
• Oscilloscope Visualizer• RF Spectrum Analyzer (RFSA)• Eye Diagram Analyzer• BER Analyzer• Electrical Power Meter• Electrical Carrier Analyzer (ECAN)• Electrical Constellation Visualizer
891
Notes:
892
OPTICAL SPECTRUM ANALYZER (OSA)
Optical Spectrum Analyzer (OSA)
Ports
Parameters
Resolution bandwidth
Graphs
Name and description Port type Signal type
Optical Input Optical
Name and description Default value
Default unit Value range
Resolution bandwidth
Determines whether or not the resolution filter is enabled
Off — On, Off
Filter type
Determines the type of resolution filter
Rectangle — Rectangle, Gaussian, Butterworth
Bandwidth
Resolution filter bandwidth
0.01 nm [0, 1e+100]
Name and description Default value
Default unit Value range
Power unit dBm — dBm, W
Minimum value –100 dBm [-1e+100, 1e+100]
Frequency unit m — m, Hz
Limit number of points True — True, False
Max. number of points 128000 — [100, 1e+008]
893
OPTICAL SPECTRUM ANALYZER (OSA)
Simulation
Graphs
Sampled signals
Parameterized signals
Noise bins
Name and description Default value
Default unit Value range
Enabled
Determines whether or not the component is enabled
True — True, False
Name and description X Title Y Title
Sampled signal spectrum Wavelength (m) Power (dBm)
Sampled signal spectrum X Wavelength (m) Power (dBm)
Sampled signal spectrum Y Wavelength (m) Power (dBm)
Name and description X Title Y Title
Parameterized signal spectrum Wavelength (m) Power (dBm)
Parameterized signal spectrum X Wavelength (m) Power (dBm)
Parameterized signal spectrum Y Wavelength (m) Power (dBm)
Name and description X Title Y Title
Noise bins signal spectrum Wavelength (m) Power (dBm)
Noise bins signal spectrum X Wavelength (m) Power (dBm)
Noise bins signal spectrum Y Wavelength (m) Power (dBm)
894
OPTICAL SPECTRUM ANALYZER (OSA)
Technical backgroundAfter you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser (see Figure 1), or by double-clicking a visualizer in the Main Layout.
Figure 1 Project browser
Access the Optical Spectrum Analyzer (OSA) parameters, graphs, and results from the simulation (see Figure 2).
Figure 2 OSA display
895
OPTICAL SPECTRUM ANALYZER (OSA)
Use the signal index to select the signal to display from the signal buffer.
Use the tabs on the left side of the graph to select the representation that you want to view (see Figure 3).• Signal• Noise• Signal + Noise• All
Figure 3 Multiple signal types display
Use the tabs at the bottom of the graph to access the optical signal polarization (see Figure 4).• Power: Total power• Power X: Power from polarization X• Power Y: Power from polarization Y
Figure 4 Signal polarization display
896
OPTICAL TIME DOMAIN VISUALIZER (OTDV)
Optical Time Domain Visualizer (OTDV)
Ports
Parameters
Graphs
Name and description Port type Signal type
Optical Input Optical
Name and description Default value
Default unit Units Value range
Time unit
Time unit for the horizontal axis
s — — s, bits
Reference bit rate
Reference bit rate to use when the time unit is Bit period
Bit rate Bits/s Bits/s
MBits/s
GBits/s
[0, 1e+012]
Phase unit
Phase unit for the vertical axis
deg — — deg, rad
Unwrap phase
Determines whether or not to remove the phase discontinuity
True — — True, False
Power unit
Power unit for the vertical axis
W — — W, dBm
Minimum value
Minimum value for power when using units in dBm
–100 dBm — [-1e+100, 1e+100]
Limit number of points
Determines if you can enter the maximum number of points to display
True — — True, False
897
OPTICAL TIME DOMAIN VISUALIZER (OTDV)
Downsampling
Simulation
Random numbers
Max. number of points
Maximum number of points displayed per graph
128,000 — — [100, 1e+008]
Name and description Default value
Default unit Default unit Value range
Centered at max power
Determines whether the internal filter will be centered at the maximum amplitude of the signal or if it will be user-defined
True — — True, False
Center frequency
User-defined center frequency for the internal filter
193.1 THz Hz, THz, nm [30,3e5]
Sample rate 5*(Sample rate) THz Hz, GHz, THz, nm
[1, 1e+100]
Name and description Default value
Default unit Value range
Enabled
Determines whether or not the component is enabled
True — True, False
Name and description Default value
Default unit Value range
Generate random seed
Determines if the seed is automatically defined and unique
True — True, False
Random seed index
User-defined seed index for noise generation
0 — [0,4999]
Name and description Default value
Default unit Units Value range
898
OPTICAL TIME DOMAIN VISUALIZER (OTDV)
Graphs
Signal
Noise
Signal + Noise
Name and description X Title Y Title
Signal power Time (s) Power (W)
Signal power X Time (s) Power (W)
Signal power Y Time (s) Power (W)
Signal phase X Time (s) Phase (deg)
Signal phase Y Time (s) Phase (deg)
Signal chirp X Time (s) Frequency (Hz)
Signal chirp Y Time (s) Frequency (Hz)
Name and description X Title Y Title
Noise power Time (s) Power (W)
Noise power X Time (s) Power (W)
Noise power Y Time (s) Power (W)
Noise phase X Time (s) Phase (deg)
Noise phase Y Time (s) Phase (deg)
Noise chirp X Time (s) Frequency (Hz)
Noise chirp Y Time (s) Frequency (Hz)
Name and description X Title Y Title
Signal + Noise power Time (s) Power (W)
Signal + Noise power X Time (s) Power (W)
Signal + Noise power Y Time (s) Power (W)
Signal + Noise phase X Time (s) Phase (deg)
Signal + Noise phase Y Time (s) Phase (deg)
Signal + Noise chirp X Time (s) Frequency (Hz)
Signal + Noise chirp Y Time (s) Frequency (Hz)
899
OPTICAL TIME DOMAIN VISUALIZER (OTDV)
Technical backgroundAfter you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser (see Figure 1), or by double-clicking a visualizer in the Main Layout.
Figure 1 Project browser
900
OPTICAL TIME DOMAIN VISUALIZER (OTDV)
The Optical Time Domain Visualizer (OTDV) is an Oscilloscope for optical signals. Access the OTDV parameters, graphs, and results from the simulation (see Figure 2).
Figure 2 OTDV display.
Use the signal index to select the signal to display from the signal buffer.
Use the tabs on the left side of the graph to select the representation that you want to view (see Figure 3).• Signal• Noise• Signal + Noise• All
Figure 3 Multiple signal types display
901
OPTICAL TIME DOMAIN VISUALIZER (OTDV)
Use the tabs at the bottom of the graph to access the optical signal polarization (see Figure 4).• Power: Total power• Power X: Power from polarization X• Power Y: Power from polarization Y
Figure 4 Signal polarization display
When you select Power X or Power Y, you can access the signal phase and chirp by selecting the Analysis option.
902
OPTICAL POWER METER VISUALIZER
Optical Power Meter Visualizer
Ports
Parameters
Main
Simulation
Results
Name and description Port type Signal type
Optical Input Optical
Name and description Default value
Default unit Value range
Minimum value
Minimum value for power when using units in dBm
–100 dBm [-1e+100, 1e+100]
Name and description Default value
Default unit Value range
Enabled
Determines whether or not the component is enabled
True — True, False
Name and description Unit
Total power dBm
Total power W
Signal power dBm
Signal power W
Sampled signal power dBm
Sampled signal power W
903
OPTICAL POWER METER VISUALIZER
Technical backgroundAfter you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser (see Figure 1), or by double-clicking a visualizer in the Main Layout.
Figure 1 Project browser
Access the Optical Power Meter Visualizer (OTDV) parameters, graphs, and results from the simulation (see Figure 2).
Figure 2 OPMV display
You can select the total signal power to display for each signal type. When you select the signal power, the result is the sum of the sampled and parameterized signals.
Parameterized signal power dBm
Parameterized signal power W
Noise power dBm
Noise power W
Name and description Unit
904
WDM ANALYZER (WDMA)
WDM Analyzer (WDMA)
Ports
Parameters
Main
Interpolation
Name and description Port type Signal type
Optical Input Optical
Name and description Default value
Default unit Value range
Resolution bandwidth
Determines whether or not the resolution filter is enabled
0.1 nm [0,+INF[
Minimum value
Minimum value for power when using units in dBm
–100 dBm ]INF,+INF[
Lower frequency limit
Defines the lower frequency limit for the calculatino bandwidth
185 Hz, THz, and nm
[30,+INF[
Upper frequency limit
Defines the upper frequency limit for the calculation bandwidth
200 Hz, THz, and nm
[30,+INF[
Name and description Default value
Default unit Value range
Noise interpolation
Determines if the noise will be estimated by using the signal
Auto — On, Off, Auto
Interpolation offset
Spacing between the signal maximum and the signal value used as noise value
0.5 nm [0,+INF[
905
WDM ANALYZER (WDMA)
Graphs
Simulation
Graphs
Results
Signal
Name and description Default value
Default unit Value range
Frequency unit
Frequency unit for the horizontal axis
nm — nm, m, Hz, THz
Name and description Default value
Default unit Value range
Enabled
Determines whether or not the component is enabled
True — True, False
Name and description X Title Y Title
Signal spectrum Wavelength (nm) Power (dBm)
Noise spectrum Wavelength (nm) Power (dBm)
Name and description Unit
Min. signal power dBm
Min. signal power W
Frequency at min. signal power Hz
Wavelength at min. signal power nm
Max. signal power dBm
Max. signal power W
Frequency at max. signal power Hz
Wavelength at max. signal power nm
Total signal power dBm
Total signal power W
Ratio max/min signal power dB
Ratio max/min signal power —
906
WDM ANALYZER (WDMA)
Noise
OSNR
Name and description Unit
Min. noise power dBm
Min. noise power W
Frequency at min. noise power Hz
Wavelength at min. noise power nm
Max. noise power dBm
Max. noise power W
Frequency at max. noise power Hz
Wavelength at max. noise power nm
Total noise power dBm
Total noise power W
Ratio max/min noise power dB
Ratio max/min noise power —
Name and description Unit
Min. OSNR dB
Frequency at min. OSNR Hz
Wavelength at min. OSNR nm
Max. OSNR dB
Frequency at max. OSNR Hz
Wavelength at max. OSNR nm
Ratio max/min OSNR dB
907
WDM ANALYZER (WDMA)
Technical backgroundAfter you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser (see Figure 1), or by double-clicking a visualizer in the Main Layout.
Figure 1 Project browser
908
WDM ANALYZER (WDMA)
The WDMA estimates the signal and the noise power for each optical signal channel based on the resolution bandwidth. Click the Analysis tab to view results such as frequency, power, noise, and OSNR.(see Figure 2).
Figure 2 WDMA analysis tab
Click the Details tab to view the detailed analysis of the results, such as the minimum and maximum values for the signals (see Figure 3).
Figure 3 WDMA details tab
909
WDM ANALYZER (WDMA)
Notes:
910
DUAL PORT WDM ANALYZER (DPWDMA)
Dual Port WDM Analyzer (DPWDMA)
Ports
Parameters
Main
Interpolation
Name and description Port type Signal type
Input 1 Input Optical
Input 2 Input Optical
Name and description Default value
Default unit Value range
Resolution bandwidth
Determines whether or not the resolution filter is enabled
0.1 nm [0,+INF[
Minimum value
Minimum value for power when using units in dBm
–100 dBm ]–INF,+INF[
Lower frequency limit
Defines the lower frequency limit for the calculatino bandwidth
185 Hz, THz, and nm
[30,+INF[
Upper frequency limit
Defines the upper frequency limit for the calculation bandwidth
200 Hz, THz, and nm
[30,+INF[
Name and description Default value
Default unit Value range
Noise interpolation
Determines if the noise will be estimated by using the signal
Off — On, Off, Auto
Interpolation offset
Spacing between the signal maximum and the signal value used as noise value
0.1 nm [0,+INF[
911
DUAL PORT WDM ANALYZER (DPWDMA)
Graphs
Simulation
Graphs
Results
Input signal
Name and description Default value
Default unit Value range
Frequency unit
Frequency unit for the horizontal axis
nm — nm, m, Hz, THz
Name and description Default value
Default unit Value range
Enabled
Determines whether or not the component is enabled
True — True, False
Name and description X Title Y Title
Input signal spectrum Wavelength (nm) Power (dBm)
Input noise spectrum Wavelength (nm) Power (dBm)
Output signal spectrum Wavelength (nm) Power (dBm)
Output noise spectrum Wavelength (nm) Power (dBm)
Gain Wavelength (nm) Gain (dB)
Noise figure Wavelength (nm) NF (dB)
Name and description Unit
Input: Min. signal power dBm
Input: Min. signal power W
Input: Frequency at min. signal power Hz
Input: Wavelength at min. signal power nm
Input: Max. signal power dBm
Input: Max. signal power W
Input: Frequency at max. signal power Hz
Input: Wavelength at max. signal power nm
912
DUAL PORT WDM ANALYZER (DPWDMA)
Input noise
Input OSNR
Input: Total signal power dBm
Input: Total signal power W
Input: Ratio max/min signal power dB
Input: Ratio max/min signal power —
Name and description Unit
Input: Min. noise power dBm
Input: Min. noise power W
Input: Frequency at min. noise power Hz
Input: Wavelength at min. noise power nm
Input: Max. noise power dBm
Input: Max. noise power W
Input: Frequency at max. noise power Hz
Input: Wavelength at max. noise power nm
Input: Total noise power dBm
Input: Total noise power W
Input: Ratio max/min noise power dB
Input: Ratio max/min noise power —
Name and description Unit
Input: Min. OSNR dB
Input: Frequency at max. OSNR Hz
Input: Wavelength at max. OSNR nm
Input: Max. OSNR dB
Input: Frequency at min. OSNR Hz
Input: Wavelength at min. OSNR nm
Input: Ratio max/min OSNR dB
Name and description Unit
913
DUAL PORT WDM ANALYZER (DPWDMA)
Output signal
Output noise
Name and description Unit
Output: Min. signal power dBm
Output: Min. signal power W
Output: Frequency at min. signal power Hz
Output: Wavelength at min. signal power nm
Output: Max. signal power dBm
Output: Max. signal power W
Output: Frequency at max. signal power Hz
Output: Wavelength at max. signal power nm
Output: Total signal power dBm
Output: Total signal power W
Output: Ratio max/min signal power dB
Output: Ratio max/min signal power —
Name and description Unit
Output: Min. noise power dBm
Output: Min. noise power W
Output: Frequency at min. noise power Hz
Output: Wavelength at min. noise power nm
Output: Max. noise power dBm
Output: Max. noise power W
Output: Frequency at max. noise power Hz
Output: Wavelength at max. noise power nm
Output: Total noise power dBm
Output: Total noise power W
Output: Ratio max/min noise power dB
Output: Ratio max/min noise power —
914
DUAL PORT WDM ANALYZER (DPWDMA)
Output OSNR
Details
Gain
Noise figure
Name and description Unit
Output: Min. OSNR dB
Output: Frequency at min. OSNR Hz
Output: Wavelength at min. OSNR nm
Output: Max. OSNR dB
Output: Frequency at max. OSNR Hz
Output: Wavelength at max. OSNR nm
Output: Ratio max/min OSNR dB
Name and description Unit
Min. gain dB
Frequency at min. gain Hz
Wavelength at min. gain nm
Max. gain dB
Frequency at max. gain Hz
Wavelength at max. gain nm
Total gain dB
Ratio max/min gain dB
Name and description Unit
Min. noise figure dB
Frequency at min. noise figure Hz
Wavelength at min. noise figure nm
Max. noise figure dB
Frequency at max. noise figure Hz
Wavelength at max. noise figure nm
Ratio max/min noise figure dB
915
DUAL PORT WDM ANALYZER (DPWDMA)
Technical backgroundAfter you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser (see Figure 1), or by double-clicking a visualizer in the Main Layout.
Figure 1 Project browser
The Dual Port WDM Analyzer (DPWDMA) estimates the signal and the noise power for each optical signal channel based on the resolution bandwidth for each input port.
916
DUAL PORT WDM ANALYZER (DPWDMA)
Click the Analysis tab to view the results (such as gain and noise figure) comparing the signal from the two input ports (see Figure 2).
Figure 2 DPWDMA analysis tab
Click the Details tab to view the detailed analysis for the results, such as the minimum and maximum values for the signals (see Figure 3).
Figure 3 DPWDMA details tab
917
DUAL PORT WDM ANALYZER (DPWDMA)
Notes:
918
OSCILLOSCOPE VISUALIZER
Oscilloscope Visualizer
Ports
Parameters
Main
Simulation
Name and description Port type Signal type
Electrical Input Electrical
Name and description Default value
Default unit Units Value range
Time unit
Time unit for the horizontal axis
s — — s, bits
Reference bit rate
Reference bit rate to use when the time unit is Bit period
Bit rate Bits/s Bits/s, MBits/s, GBits/s
[0,+INF[
Limit number of points
Determines if you can enter the maximum number of points to display
True — — True, False
Max. number of points
Maximum number of points displayed per graph
128000 — — [100, 1e+008]
Name and description Default value
Default unit Value range
Enabled
Determines whether or not the component is enabled
True — True, False
919
OSCILLOSCOPE VISUALIZER
Random numbers
Graphs
Name and description Default value
Default unit Value range
Generate random seed
Determines if the seed is automatically defined and unique
True — True, False
Random seed index
User-defined seed index for noise generation
0 — [0,4999]
Name and description X Title Y Title
Signal amplitude Time (s) Amplitude (a.u.)
Noise amplitude Time (s) Amplitude (a.u.)
Signal + noise amplitude Time (s) Amplitude (a.u.)
920
OSCILLOSCOPE VISUALIZER
Technical backgroundAfter you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser (see Figure 1), or by double-clicking a visualizer in the Main Layout.
Figure 1 Project browser
Access the Oscilloscope parameters, graphs, and results from the simulation (see Figure 2).
Figure 2 Oscilloscope display
921
OSCILLOSCOPE VISUALIZER
Use the signal index to select the signal to display from the signal buffer.
Use the tabs on the left side of the graph to select the representation that you want to view (see Figure 3).• Signal• Noise• Signal + Noise• All
Figure 3 Multiple signal types display
922
RF SPECTRUM ANALYZER (RFSA)
RF Spectrum Analyzer (RFSA)
Ports
Parameters
Main
Resolution bandwidth
Name and description Port type Signal type
Electrical Input Electrical
Name and description Default value
Default unit Value range
Power unit
Power unit for the vertical axis
dB — dBm, W
Minimum value
Minimum value for power when using units in dBm
–100 dBm [-1e+100, 1e+100]
Negative frequencies False — True, False
Limit number of points
Determines if you can enter the maximum number of points to display
True — True, False
Max. number of points
Maximum number of points displayed per graph
128000 — [100, 1e+008]
Name and description Default value
Default unit Value range
Resolution bandwidth
Determines whether or not the resolution filter is enabled
Off — On, Off
Filter type
Determines the type for the resolution filter
Rectangle — Rectangle, Gaussian, Butterworth
923
RF SPECTRUM ANALYZER (RFSA)
Simulation
Random numbers
Graphs
Bandwidth
Resolution filter bandwidth
10 MHz [0,+INF[
Name and description Default value
Default unit Value range
Enabled
Determines whether or not the component is enabled
True — True, False
Name and description Default value
Default unit Value range
Generate random seed
Determines if the seed is automatically defined and unique
True — True, False
Random seed index
User-defined seed index for noise generation
0 — [0,4999]
Name and description X Title Y Title
Signal spectrum Frequency (GHz) Power (dBm)
Noise spectrum Frequency (GHz) Power (dBm)
Signal + noise spectrum Frequency (GHz) Power (dBm)
Name and description Default value
Default unit Value range
924
RF SPECTRUM ANALYZER (RFSA)
Technical backgroundAfter you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser (see Figure 1), or by double-clicking a visualizer in the Main Layout.
Figure 1 Project browser
925
RF SPECTRUM ANALYZER (RFSA)
Access the RF Spectrum Analyzer (RFSA) parameters, graphs, and results from the simulation (see Figure 2).
Figure 2 RFSA display
Use the signal index to select the signal to display from the signal buffer.
Use the tabs on the left side of the graph to select the representation that you want to view (see Figure 3).• Signal• Noise• Signal + Noise• All
Figure 3 Multiple signal types display
926
EYE DIAGRAM ANALYZER
Eye Diagram Analyzer
Ports
Parameters
Main
Clock
Name and description Port type Signal type
Bit sequence Input Binary
Reference Input Electrical
Input Input Electrical
Name and description Default value
Default unit Value range
Time window
Time window for the eye diagram display
1.5 bit [1,3]
Ignore start bits
Number of start bits to be ignored in the eye diagram
1 bits [0,+INF[
Ignore end bits
Number of end bits to be ignored in the eye diagram
1 bits [0,+INF[
Name and description Default value
Default unit Value range
Clock recovery
Determines if the delay compensation between the reference and the received signal will be applied
On — On, Off
927
EYE DIAGRAM ANALYZER
Threshold
Graphs
Simulation
Noise
Name and description Default value
Default unit Value range
Threshold mode
Determines the value mode for the user-defined threshold
Relative — Relative, Absolute
Absolute threshold
Amplitude value for the threshold
0 (a.u.) ]–INF,+INF[
Relative threshold
Relative value for the threshold, relative to the average values of 1s and 0s
50 % [0,100]
Decision instant
The user-defined decision instant for the eye analysis
0.5 Bit [0,1]
Name and description Default value
Default unit Value range
Time unit Bit period — s, Bit period
Ratio unit dB — none, dB, %
Limit number of points
Determines if you can enter the maximum number of points to display
True — True, False
Max. number of points
Maximum number of points displayed per graph
128000 — [100, 1e+008]
Name and description Default value
Default unit Value range
Enabled
Determines whether or not the component is enabled
True — True, False
Name and description Default value
Default unit Value range
Add noise to signal True — True, False
928
EYE DIAGRAM ANALYZER
Random numbers
Graphs
Results
Name and description Default value
Default unit Value range
Generate random seed
Determines if the seed is automatically defined and unique
True — True, False
Random seed index
User-defined seed index for noise generation
0 — [0,49999]
Name and description X Title Y Title
Eye diagram Time (s) Amplitude (a.u.)
Min. BER Time (s) log (BER)
Q-factor Time (s) Q
Threshold at min. BER Time (s) Amplitude (a.u.)
Eye Height Time (s) Amplitude (a.u.)
Eye Amplitude Time (s) Amplitude (a.u.)
Eye Closure Time (s) Amplitude (a.u.)
Eye Opening Factor Time (s) Ratio (dB)
Eye Extinction Ratio Time (s) Ratio (dB)
Name and description Unit
Total Power dBm
Total Power W
Signal Power dBm
Signal Power W
Noise Power dBm
Noise Power W
Signal Delay s
Signal Delay samples
Bit Rate Bits/s
Max. Q Factor —
929
EYE DIAGRAM ANALYZER
Min. BER —
Min. log of BER —
Max. Eye Height a.u.
Threshold at Min. BER a.u.
Decision Instant at Min. BER Bit period
Max. Eye Amplitude a.u.
Max. Eye Closure a.u.
Max. Eye Opening Factor dB
Max. Eye Opening Factor —
Max. Eye Opening Factor %
Extinction Ratio at Min. BER dB
Extinction Ratio at Min. BER —
Extinction Ratio at Min. BER %
Q Factor at User Defined Decision Instant —
Eye Height at User Defined Decision Instant a.u.
Min. BER at User Defined Decision Instant —
Min. log of BER at User Defined Decision Instant —
BER at User Defined Threshold —
BER at User Defined Decision Instant and Threshold —
log of BER at User Defined Threshold —
log of BER at User Defined Decision Instant and Threshold —
Eye Amplitude at User Defined Decision Instant a.u.
Eye Closure at User Defined Decision Instant a.u
Eye Opening Factor at User Defined Decision Instant dB
Eye Opening Factor at User Defined Decision Instant —
Eye Opening Factor at User Defined Decision Instant %
Extinction Ratio at User Defined Decision Instant dB
Extinction Ratio at User Defined Decision Instant —
Extinction Ratio at User Defined Decision Instant %
Name and description Unit
930
EYE DIAGRAM ANALYZER
Technical backgroundAfter you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser (see Figure 1), or by double-clicking a visualizer in the Main Layout.
Figure 1 Project browser
931
EYE DIAGRAM ANALYZER
The Eye Diagram Analyzer generates eye diagrams and BER analysis. Double-click the Eye Diagram Analyzer to access the parameters, graphs, and results from the simulation (see Figure 2).
Figure 2 Eye diagram display
Use the signal index to select the signal to display from the signal buffer.
The available results are:• Max Q-factor: Maximum value for the Q-factor in the eye time window.• Min BER: Minimum value for the bit error rate in the eye time window.• Eye height: Maximum value for the eye height in the eye time window.• Threshold: Value of the threshold at the decision instant for the maximum Q-
factor / minimum BER.• Decision inst: Value of the decision instant for the maximum Q-factor/minimum
BER.
932
EYE DIAGRAM ANALYZER
Figure 3 Eye diagram analysis
933
EYE DIAGRAM ANALYZER
BER and Q-Factor EstimationThe BER estimation method in this visualizer compare the bits generated by a binary signal and the signal received.
Assuming Gaussian noise with the standard deviations and the BER is [1]
(1)
where P0 and P1 are the probabilities of the symbols, M is the number of samples for the logical 0, and N is the number of samples for the logical 1.
Pe0 and Pe1 are:
(2)
(3)
where , , , and are average values and variances of the sampled values respectively, and S is the threshold value.
The Q-factor is calculated by:
(4)
The eye height is calculated by [2]
(5)
σ0 σ1
PeM
N M+----------------Pe0
NN M+----------------Pe1+=
Pe012---erfc
S µ0–
2σ0
---------------
,=
Pe112---erfc
µ1 S–
2σ1
---------------
=
µ0 µ1 σ0 σ1
Qµ1 µ0–σ1 σ0+--------------------=
EH µ1 3σ1–( ) µ0 3σ0+( )–=
934
EYE DIAGRAM ANALYZER
The eye amplitude is calculated by:
(6)
The eye closure is calculated by:
(7)
where min(V1) is the minimum value of the amplitude for the marks and max(V0) is the maximum value for the amplitude of the spaces.
The eye-opening factor is calculated by:
(8)
The extinction ratio is:
(9)
EA µ1 µ0–=
Ec min V1( ) max V0( )–=
E0µ1 σ1–( ) µ0 σ0–( )–
µ1 µ0–( )---------------------------------------------------=
ERµ1µ0-----=
935
EYE DIAGRAM ANALYZER
References[1] G.P. Agrawal, "Fiber Optic Communication Systems," John Wiley & Sons, New York, 1997.
[2] D. Derickson, "Fiber Optic Test and Measurement," Prentice Hall, New Jersey, 1998.
936
BER ANALYZER
BER Analyzer
Ports
Parameters
Main
Name and description Port type Signal type
Bit sequence Input Binary
Reference Input Electrical
Input Input Electrical
Name and description Default value
Default unit Value range
Algorithm
Determines the algorithm used to estimate the BER
Gaussian — Gaussian, Average Gaussian, Gaussian Worse Case
Time window
Time window for the eye diagram display
1.5 bit [1, 3]
Ignore start bits
Number of start bits to be ignored in the eye diagram
1 bits [0,+INF[
Ignore end bits
Number of end bits to be ignored in the eye diagram
1 bits [0,+INF[
Lower calculation limit
Defines the lower calculation limit for the time window
0 Bit period [0,1.5]
Upper calculation limit
Defines the upper calculation limit for the time window
1 Bit period [0,1.5]
937
BER ANALYZER
Clock
FEC
Threshold
Name and description Default value
Default unit Value range
Clock recovery
Determines if the delay compensation between the reference and the received signal will be applied
On — On, Off
Name and description Default value
Default unit Value range
Enabled FEC gain estimation False — True, False
Name and description Default value
Default unit Value range
Threshold mode
Determines the value mode for the user-defined threshold
Relative — Relative, Absolute
Absolute threshold
Amplitude value for the threshold
0 (a.u.) ]–INF,+INF[
Relative threshold
Relative value for the threshold, relative to the average values of 1s and 0s
50 % [0,100]
Load threshold from file
Defines whether the threshold will be loaded from a file or not
False — True, false
Measured threshold filename
Threshold file name
Threshold.dat — —
Reload before calculation
Defines whether the file should be reloaded when the calculation starts
False — True, false
Decision instant
The user-defined decision instant for the eye analysis
0.5 Bit period [0,100]
938
BER ANALYZER
Graphs
Graphs
BER patterns
Name and description Default value
Default unit Value range
Time unit Bit period — s, Bit period
Ratio unit None — none, dB, %
Limit number of points
Determines if you can enter the maximum number of points to display
True — True, False
Max. number of points
Maximum number of points displayed per graph
128000 — [100, 1e+008]
Name and description X Title Y Title
Measured Threshold Time (Bit period) Amplitude (a.u.)
BER at Measured Threshold Time (s) log of BER
Name and description Default value
Default unit Value range
Calculate patterns
Determines whether or not the component will generate BER patterns
False — True, False
Number of points
Number of vertical points for the patterns
16 — [10, 1e+008]
BER for pattern 1 1e-012 — [0,1]
BER for pattern 2 1e-011 — [0,1]
BER for pattern 3 1e-010 — [0,1]
BER for pattern 4 1e-009 — [0,1]
BER for pattern 5 1e-008 — [0,1]
Calculate 3D graph
Determines whether or not the component generates a 3D graph with the BER
False — True, False
939
BER ANALYZER
Penalty calculations
Name and description Default value Default unit Value range
Reference values setup User-defined — User defined, First sweep iteration, Current sweep iteration
Total power –1000 dBm [-1e+100, 1e+100]
Signal power –1000 dBm [-1e+100, 1e+100]
Noise power –1000 dBm [-1e+100, 1e+100]
Min. BER 1 — [0, 1]
Q factor from min. BER 0 — [0, 1000]
Max. Q factor 0 — [0, 1000]
Max. eye height 0 a.u. [-1e+100, 1e+100]
Max. eye amplitude 0 a.u. [-1e+100, 1e+100]
Max. eye closure 0 a.u. [-1e+100, 1e+100]
Max. eye opening factor 0 dB [-1e+100, 1e+100]
Extinction ratio at min. BER 0 dB [-1e+100, 1e+100]
Min. BER at user defined decision instant
1 — [0, 1]
Q factor from min. BER at user defined decision instant
0 — [0, 1000]
Q factor at user defined decision instant
0 — [0, 1000]
BER at user-defined threshold 1 — [0, 1]
Q factor from BER at user defined threshold
0 — [0, 1000]
BER at user defined decision instant and threshold
1 — [0, 1]
Q factor from BER at user defined decision instant and threshold
0 — [0, 1000]
Eye height at user defined decision instant
0 a.u. [-1e+100, 1e+100]
Eye amplitude at user defined decision instant
0 a.u. [-1e+100, 1e+100]
Eye closure at user defined decision instant
0 a.u. [-1e+100, 1e+100]
Eye opening factor at user defined decision instant
0 dB [-1e+100, 1e+100]
940
BER ANALYZER
Simulation
Noise
Random numbers
Graphs
Extinction ratio at user defined decision instant
0 dB [-1e+100, 1e+100]
Name and description Default value
Default unit Value range
Enabled
Determines whether or not the component is enabled
True — True, False
Name and description Default value
Default unit Value range
Add noise to signal True — True, False
Name and description Default value
Default unit Value range
Generate random seed
Determines if the seed is automatically defined and unique
True — True, False
Random seed index
User-defined seed index for noise generation
0 — [0,4999]
Name and description X Title Y Title
Eye diagram Time (s) Amplitude (a.u.)
Min. BER Time (s) log of BER
Q-factor Time (s) Q
Threshold at min. BER Time (s) Amplitude (a.u.)
Eye height Time (s) Amplitude (a.u.)
Eye Amplitude Time (s) Amplitude (a.u.)
Eye Closure Time (s) Amplitude (a.u.)
Eye Opening Factor Time (s) Ratio (dB)
Name and description Default value Default unit Value range
941
BER ANALYZER
Results
Eye Extinction Ratio Time (s) Ratio (dB)
BER pattern 1 Time (s) Amplitude (a.u.)
BER pattern 2 Time (s) Amplitude (a.u.)
BER pattern 3 Time (s) Amplitude (a.u.)
BER pattern 4 Time (s) Amplitude (a.u.)
BER pattern 5 Time (s) Amplitude (a.u.)
BER pattern 3D graph Amplitude (a.u.) Time (s)
Name and description Unit
Total Power dBm
Total Power W
Signal Power dBm
Signal Power W
Noise Power dBm
Noise Power W
Signal Delay s
Signal Delay samples
Bit Rate Bits/s
Max. Q Factor —
Q Factor from Min. BER —
Min. BER —
Min. log of BER —
Max. Eye Height a.u.
Threshold at Min. BER a.u.
Decision Instant at Min. BER Bit period
Max. Eye Amplitude a.u.
Max. Eye Closure a.u.
Max. Eye Opening Factor dB
Max. Eye Opening Factor —
Max. Eye Opening Factor %
Name and description X Title Y Title
942
BER ANALYZER
Extinction Ratio at Min. BER dB
Extinction Ratio at Min. BER —
Extinction Ratio at Min. BER %
Q Factor at User Defined Decision Instant —
Eye Height at User Defined Decision Instant a.u.
Min. BER at User Defined Decision Instant —
Q Factor from Min. BER at User Defined Decision Instant —
Min. log of BER at User Defined Decision Instant —
BER at User Defined Threshold —
BER at User Defined Decision Instant and Threshold —
Q Factor from BER at User Defined Threshold —
Q Factor from BER at User Defined Decision Instant and Threshold —
log of BER at User Defined Threshold —
log of BER at User Defined Decision Instant and Threshold —
Eye Amplitude at User Defined Decision Instant a.u.
Eye Closure at User Defined Decision Instant a.u.
Eye Opening Factor at User Defined Decision Instant dB
Eye Opening Factor at User Defined Decision Instant —
Eye Opening Factor at User Defined Decision Instant %
Extinction Ratio at User Defined Decision Instant dB
Extinction Ratio at User Defined Decision Instant —
Extinction Ratio at User Defined Decision Instant %
Penalty: Total Power dB
Penalty: Signal Power dB
Penalty: Noise Power dB
Penalty: Max. Q Factor dB
Penalty: Q Factor from Min. BER dB
Penalty: Min. BER dB
Penalty: Max. Eye Height dB
Penalty: Max. Eye Amplitude dB
Penalty: Max. Eye Closure dB
Name and description Unit
943
BER ANALYZER
Penalty: Max. Eye Opening Factor dB
Penalty: Extinction Ratio at Min. BER dB
Penalty: Q Factor at User Defined Decision Instant dB
Penalty: Eye Height at User Defined Decision Instant dB
Penalty: Min. BER at User Defined Decision Instant dB
Penalty: Q Factor from Min. BER at User Defined Decision Instant dB
Penalty: BER at User Defined Threshold dB
Penalty: BER at User Defined Decision Instant and Threshold dB
Penalty: Q Factor from BER at User Defined Threshold dB
Penalty: Q Factor from BER at User Defined Decision Instant and Threshold
dB
Penalty: Eye Amplitude at User Defined Decision Instant dB
Penalty: Eye Closure at User Defined Decision Instant dB
Penalty: Eye Opening Factor at User Defined Decision Instant dB
Penalty: Extinction Ratio at User Defined Decision Instant dB
Min. BER after FEC —
Min. log of BER after FEC —
Min. BER after FEC at User Defined Decision Instant —
Min. log of BER after FEC at User Defined Decision Instant —
BER after FEC at User Defined Threshold —
BER after FEC at User Defined Decision Instant and Threshold —
log of BER after FEC at User Defined Threshold —
log of BER after FEC at User Defined Decision Instant and Threshold —
Name and description Unit
944
BER ANALYZER
Technical backgroundAfter you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser (see Figure 1), or by double-clicking a visualizer in the Main Layout.
Figure 1 Project browser
The BER Analyzer estimates and analyzes the BER of the signal received. Double-click the BER Analyzer to access the parameters, graphs, and results from the simulation (see Figure 2).
945
BER ANALYZER
Figure 2 BER Analyzer display
Use the signal index to select the signal to display from the signal buffer (see Figure 3).
The available results are:• Max Q-factor: Maximum value for the Q-factor in the eye time window.• Min BER: Minimum value for the bit error rate in the eye time window.• Eye height: Maximum value for the eye height in the eye time window.• Threshold: Value of the threshold at the decision instant for the maximum Q-
factor / minimum BER.• Decision inst: Value of the decision instant for the maximum Q-factor/minimum
BER.
946
BER ANALYZER
Figure 3 BER analysis
When the parameter Calculate 3D graph is enabled, you can visualize a 3D graph that shows the values of BER versus the decision instant and threshold (see Figure 4).
Figure 4 3D BER graph
947
BER ANALYZER
BER and Q-factor estimationThe parameter Algorithm defines the numerical method to use for the BER estimation.
GaussianAssuming Gaussian noise with the standard deviations and , the BER is [1]:
(1)
where P0 and P1 are the probabilities of the symbols, M is the number of samples for the logical 0, and N is the number of samples for the logical 1.
Also, Pe0 and Pe1 are:
(2)
(3)
where , , , and are average values and variances of the sampled values respectively, and S is the threshold value.
Average GaussianAn enhancement of the simple Gaussian approximation can be achieved by averaging the separately estimated BERs for different sampled symbols [2]. For M sampled values for the logical 0 and N sampled values for the logical 1, the corresponding error rates are:
(4)
(5)
σ0 σ1
PeM
N M+----------------Pe0
NN M+----------------Pe1+=
Pe012---erfc
S µ0–
2σ0
---------------
,=
Pe112---erfc
µ1 S–
2σ1
---------------
=
µ0 µ1 σ0 σ1
Pe01
2M-------- erfc
S µ0i–
2σ0i
----------------
i 1=
M
∑=
Pe11
2N------- erfc
µ1i S–
2σ1i
----------------
i 1=
N
∑=
948
BER ANALYZER
If the signal is mixed with the noise, the Average Gaussian method is modified to calculate the average error patterns. The detailed description is [4]:
where NP is the number of one occurrence of any pattern, N is the total number of patterns, and are average values and variances of the sampled values for each pattern respectively, and S is the threshold value.
Worst-case GaussianSince the Average Gaussian method can estimate the BER per bit or per pattern, the Worst-case Gaussian searches for the min BER for each bit or pattern instead of calculating the average values.
Calculating results
There are two modes to calculate the Q-Factor:
The Q-Factor from BER is calculated numerically by:
(6)
where the Q-factor is calculated
(7)
The eye height is calculated by [2]:
(8)
The eye amplitude is calculated by:
(9)
The eye closure is calculated by:
(10)
where min(V1) is the minimum value of the amplitude for the marks and max(V0) is the maximum value for the amplitude of the spaces.
PeNP
N------erfc
µi S–
2σi
--------------
i 1=
8
∑=
µi σi
Pe12---erfc Q
2-------
=
Qµ1 µ0–σ1 σ0+--------------------=
EH µ1 3σ1–( ) µ0 3σ0+( )–=
EA µ1 µ0–=
Ec min V1( ) max V0( )–=
949
BER ANALYZER
The eye-opening factor is calculated by:
(11)
The extinction ratio is calculated by:
(12)
For the user defined threshold, the input file, given by the parameter Measured threshold filename, is formatted with two items per line, the time and threshold amplitude. Time is given in ratio of the bit period, and amplitude is given in arbitrary units (voltage or current)
As an example of input file, we have:
References[1] G.P. Agrawal, "Fiber Optic Communication Systems," John Wiley & Sons, New York, 1997.
[2] J.C. Cartledge, G.S. Burley, "The Effect of Laser Chirping on Lightwave System Performance," Journal of Lightwave Technology, Vol. 7, Nr. 3, 1989, S. 568-573.
[3] D. Derickson, "Fiber Optic Test and Measurement," Prentice Hall, New Jersey, 1998.
[4] C.J. Anderson, J.A. Lyle, “Technique for evaluation of systems performance using Q in numerical simulation exhibiting intersymbol interference,” Electronic Letters, Vol. 30, No. 1, 1994, S. 71-72.
0 0.5
0.1 0.5
0.2 0.5
...
0.9 0.5
E0µ1 σ1–( ) µ0 σ0–( )–
µ1 µ0–( )---------------------------------------------------=
ERµ1µ0-----=
950
ELECTRICAL POWER METER
Electrical Power Meter
Ports
Parameters
Main
Simulation
Results
Name and description Port type Signal type
Input Input Electrical
Name and description Default value
Default unit Value range
Minimum value
Minimum value for power when using units in dBm.
-100 dBm —
Name and description Default value
Default unit Value range
Enabled
Determines whether or not the component is enabled
True — True, False
Name and description Unit
Total Power dBm
Total Power W
Signal Power dBm
Signal Power W
Noise Power dBm
Noise Power W
951
ELECTRICAL POWER METER
Technical BackgroundVisualizers are similar to components, however they generate graphs and results based on the signal input. You can access the results generated by the visualizer with the Project Browser.
Figure 1 Project Browser
The graphs and results can be accessed by the project browser or by using Displays.
Displays is the visualizer interface; in the EPMV, you can access the parameters and results from the simulation using the EPMV display.
Figure 2 EPMV Display
952
ELECTRICAL CARRIER ANALYZER (ECAN)
Electrical Carrier Analyzer (ECAN)
The Electrical Carrier Analyzer (ECAN) measures and compares different results in two different frequencies. It can also calculate carrier to noise ratio.
Ports
Parameters
Main
Name and description Port type Signal type
Input Input Electrical
Name and description Default value
Default unit Value range
Frequency 1
Center frequency of the first filter.
50 MHz, Hz, kHz, THz
[0,+INF[
Bandwidth 1
Bandwidth of the first filter.
10 MHz, Hz, kHz, GHz
[0,+INF[
Frequency 2
Center frequency of the second filter.
50 MHz, Hz, kHz, THz
[0,+INF[
Bandwidth 2
Bandwidth of the second filter.
10 MHz, Hz, kHz, GHz
[0,+INF[
Filter type Gaussian — Gaussian, Rectangle
Filter order
Order of the Gaussian filter.
1 — [1,+INF[
Minimum value
Minimum value for power when using units in dBm.
-100 dBm ]-INF,+INF[
953
ELECTRICAL CARRIER ANALYZER (ECAN)
Simulation
Results
Frequency 1
Frequency 2
Name and description Default value
Default unit Value range
Enabled
Determines whether or not the component is enabled
True — True, False
Name and description Unit
Total Power1 dBm
Total Power1 W
Signal Power1 dBm
Signal Power1 W
Noise Power1 dBm
Noise Power1 W
SNR1 dB
Name and description Unit
Total Power2 dBm
Total Power2 W
Signal Power2 dBm
Signal Power2 W
Noise Power2 dBm
Noise Power2 W
SNR2 dB
954
ELECTRICAL CARRIER ANALYZER (ECAN)
Details
Total Power
Signal
Noise
Name and description Unit
Min. Total Power dBm
Min. Total Power W
Frequency at Max. Total Power Hz
Max. Total Power dBm
Max. Total Power W
Frequency at Min. Signal Power Hz
Ratio Max/Min Signal Power dB
Ratio Max/Min Signal Power —
Name and description Unit
Min. Total Power dBm
Min. Total Power W
Frequency at Max. Total Power Hz
Max. Total Power dBm
Max. Total Power W
Frequency at Min. Signal Power Hz
Ratio Max/Min Signal Power dB
Ratio Max/Min Signal Power —
Name and description Unit
Min. Total Power dBm
Min. Total Power W
Frequency at Max. Total Power Hz
Max. Total Power dBm
Max. Total Power W
Frequency at Min. Signal Power Hz
955
ELECTRICAL CARRIER ANALYZER (ECAN)
SNR
Ratio Max/Min Signal Power dB
Ratio Max/Min Signal Power —
Name and description Unit
Min. SNR dB
Frequency at Min. SNR Hz
Max. SNR dB
Frequency at Max. SNR Hz
Ratio Max/Min SNR dB
Name and description Unit
956
ELECTRICAL CARRIER ANALYZER (ECAN)
Technical BackgroundVisualizers are similar to components, however they generate graphs and results based on the signal input. You can access the results generated by the visualizer with the Project Browser.
Figure 1 Project Browser
The graphs and results can be accessed by the project browser or by using Displays.
Displays is the visualizer interface; in the ECAN, you can access the parameters and results from the simulationusing the ECAN display.
957
ELECTRICAL CARRIER ANALYZER (ECAN)
The ECAN will estimate the signal and the noise power for each electrical signal channel based on the central frequency of the internal filters. The analysis tab displays results such as frequency, power, noise, and SNR.
Figure 2 Analysis tab
The Details tab displays the detailed analysis for the results shown in the Analysis tab, including the minimum and maximum values for the signals.
Figure 3 Details tab
958
ELECTRICAL CONSTELLATION VISUALIZER
Electrical Constellation Visualizer
Displays the In-Phase and Quadrature-Phase electrical signals in a constellation diagram.
Ports
Parameters
Graphs
Simulation
Name and description Port type Signal type
Electrical - I Input Electrical
Electrical - Q Input Electrical
Name and description Default value
Default unit Value range
Limit number of points
Defines whether you can enter the maximum number of points to be displayed.
True — [0,+INF[
Maximum number of points
Maximum number of points that can be displayed in a graph.
128,000 —
Name and description Default value
Default unit Value range
Enabled
Determines whether or not the component is enabled
True — True, False
959
ELECTRICAL CONSTELLATION VISUALIZER
Random numbers
Graphs
Technical BackgroundVisualizers are similar to components, however they generate graphs and results based on the signal input. You can access the results generated by the visualizer with the Project Browser.
Figure 1 Project Browser
Name and description Default value
Default unit Value range
Generate random seed
Defines whether the seed is automatically defined and unique.
True — True, False
Random seed index
User defined seed index for noise generation.
0 — [0,4999]
Name and description X Title Y Title
Signal Amplitude Amplitude - I (a.u.) Amplitude - Q (a.u.)
Noise Amplitude Amplitude - I (a.u.) Amplitude - Q (a.u.)
Signal + Noise Amplitude Amplitude - I (a.u.) Amplitude - Q (a.u.)
960
ELECTRICAL CONSTELLATION VISUALIZER
The graphs and results can be accessed by the project browser or by using Displays.
Displays is the visualizer interface; in the constellation visualizer, you can access the parameters and results from the simulation using the constellation display.
Figure 2 Constellation display
You can select the signal to be displayed from the signal buffer by selecting the signal index. The vertical tab gives access to the signal types:• Signal• Noise• Signal and Noise
Figure 3 Multiple signal types display
961
ELECTRICAL CONSTELLATION VISUALIZER
Notes:
962
Optiwave Corporation7 Capella CourtOttawa, Ontario, K2E 8A7, Canada
Tel.: 1.613.224.4700Fax: 1.613.224.4706
E-mail: [email protected]: www.optiwave.com