es918 assignment 1314

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1Copyright 2013 ES4C4/918 Optical Communication Systems

ES918/ES4C4 OpticalCommunication Systems

Background to the Assignment

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Introduction

For long distance transmission we need to

compensate for attenuation losses.

This was initially via a optoelectronic process of

optical receiver, a regeneration and equalization

system, and an optical transmitter

This is limited by the optical to electrical (OE) and

electrical to optical (EO) conversions.

Hence optical amplifiers were developed.

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Concept

The idea of an optical amplifier is the same as that of an electrical amplifier, to

increase the size of the input signal.

G

Pin

GPin

Pump

Power

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Amplifier Types

Optical amplifiers have become near essential components in optical fibre

systems. A working knowledge of them is now extremely important in optical fibrecommunications.

Several different types of optical amplifier including:

Rare earth (erbium, neodymium, praseodymium) doped fibre amplifier

(EDFA, NDFA, PDFA)

Semiconductor optical amplifier (SOA)

Non-linear fibre amplifiers: Raman fibre amplifier and Brillouin fibre amplifier

EDFAs are important for point to point long haul communications

SOAs are very noisy so have struggled to find achieve mass application

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Applications

Power Amplifier

Fibre

G

Tx

RxG

Line Amplifier

G

Preamplifier

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Basic Concepts

Most amplify light through stimulated emission Similar to a laser but without the feedback

The gain medium must be supplied energy by a pumpto create population inversion

Fibre amplifiers use optical pumps

SOAs use electrical pumps

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7/267Copyright 2013 ES4C4/918 Optical Communication Systems

Energy LevelsElectrons (and holes) may occupy only a range of energy bands within materials

for quantum mechanical reasons.

Electrons normally occupy their state of lowest energy known as the ground

state.

An energy state greater than the ground state is known as an excited state.

E2

E1

Excited State

Ground State

Energy

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Photon-Electron Interactions: Spontaneous Absorption

1. Spontaneous Absorption is

when an incident photon is

absorbed in a material causing the

excitation of an electron to a higherlevel, the basis of photodiode

operation. The energy of the

photon, hf, must be the same as

E2-E1

E2

E1

Left to their own devices, all materials absorb light via this

mechanism rather than emitting any light.

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Photon-Electron Interactions: Spontaneous Emission

2. Spontaneous Emissionis when

an electron falls to a lower energy

level, the basis of LED action.

E2

E1

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Photon-Electron Interactions: Stimulated Emission

3. Stimulated Emissionis when a

photon incident upon an electron in

a high energy level causes the

electron to fall to a lower levelgenerating a second photon. This is

the basis of Light Amplification by

Stimulated Emission of Radiation

(LASER) action.

E2

E1

The photon generated has the same frequency as the incident one and thus laser light is

highly monochromatic and coherent (in phase).

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Conditions for Amplification

More electrons in higher energy levels than in lower ones (population inversion) so that

stimulated emission becomes more likely that spontaneous absorption.

We need to pump electrons into excited states by either electrical or optical means.

P

ump

E2

E1

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EDFA Energy Levels

Energy

E3

E1

E2980 nm pump

1480 nm pump 1530 nm emission

Fast non-radiative transitions

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Optical Preamplifier Configuration

Weak

Input

Signal

EDFA FilterCoupler

Pump

Laser

Isolator

Amplified

Output Signal

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EDFAAmplified Spontaneous Emission (ASE)

There will also be spontaneous emission in the amplifier. This will get amplified as

well as the signal, producing amplified spontaneous emission (ASE) noise.

The PSD of ASE noise is nearly constant (white noise) and for an amplifier with

gain G, can be written as

Note that the assignment uses photons per bit so the ASE will be in photons persecond

1spASE GhfnfS

1sp0 GnN

spontaneous-emission factor 122sp NNNn excited state

atomic

population

ground state

atomic

population

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Performance Modelling

Although the noise at the receiver is not Gaussian, we can approximate it by a

Gaussian with parameters drawn from the properties of the amplifier (see later).

The BER is then given by:

The means and variances have to be derived as on the assignment sheet.

2erfc

2

1 QPe

01

01

Q

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Moment Generating Functions

Often, the form of the noise statistics is not easy to work with.

We can make use of the moment generating function (mgf), which is defined for a

probability functionp(x)in a similar way to the Laplace transform

dxexpsM sx

There are methods based on MGFs that make the calculation of errorprobabilities much easier.

Also if we have the sum of two noise sourcesxandythe resultant pdf

is

sMsMsM YXYX But for the mgfs

ypxpyxp YX *

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Getting the Moments from mgfs - mean

As you might expect, the mgf may be used to obtain moments.

0'MxE

sMsM

dssMd ln

00

MM

Consider the log of the mgf:

10 dxxpM

0

ln

sds

sMd

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Getting the Moments from mgfs - variance

20'0''var MM 0''2 MxE

sM

sMsMsM

sM

sM

ds

d

ds

sMd2

2

2

2 ln

2

2

2

0

000

M

MMM

2

0

2

2 ln

sds

sMd

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Example: Zero mean Gaussian

Complete the square:

dxee

dxe

dxeesM

sxs

sx

sxx

22222

222

22

22

22

2

2

1

2

1

2

1

22 22222 1

sys edyeesM

22 2:Subst sxy

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Example continued

0

2ln

0

2

0

22

0

s

ss

sds

sd

ds

sMd

Zero mean Gaussian

20

2

0

lnvar

ss ds

sd

ds

sMd

ds

d

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MGF for Optical Preamplifier

sN

mGs

sN

sMmt

02

0

1exp

1

1

OOK system; includes polarisation too; we can reduce the ASE

(random, unpolarised) by keeping only one polarisation

Product of the optical filter

bandwidth and the bit time

Number of

photons in

the bit

Number of polarisations

Quantum efficiency

Simplified model

ignoring shot noise

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Assignment Guide (1)

We can use the mgf to get the mean and variance and then use these to

describe a Gaussian pdf to approximate the real one.

Assignment entails obtaining the Gaussian mean and variance then making

approximate calculations for the performance of the preamplifier as its

parameters vary.

One aim (a) is to prove:-

200,10,1

MmNGm t

22 20

2

00,1

22

0,1

MmNGNm t

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Assignment Guide (2)Hint

sN

mGs

sN

sMmt

020

1exp

1

1

sN

mGssN

Mms t

0

01

1ln2

ln

Differential of a quotientDifferential of a logarithm

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Follow the instructions on the sheet to complete the

other tasks from (b)-(j)

MATLAB is suggested

Also produce a one page discussion and summary of

your conclusions

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Finally:-

A one page review (excluding references) of DEVELOPMENTS inoptical amplifier MODELLING that have enhanced the modelling process

beyond that considered here (this should refer to relevant literature,

factors that are not included above and any developments in

amplifiers/communication systems themselves).

This should comprise a literature SEARCH to find examples of improved

modelling of optical preamplifiers to address questions such as:

How does the shot noise actually impact the performance?

What other effects have been left out here?What about different modulation schemes?

Ten or more references would be a good effort here.

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26i h ES4C4/918 O ti l C i ti S t


References must be presented correctly.

Figure/equation numbers, titles, axis labels, units etc. should be

presented correctly.

Code (MATLAB preferred or otherwise) should be commented.

Any questions should be addressed to me early.

es918 assignment 1314

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