1 optical communications s-108.3110. 2 course program 5 lectures on fridays first lecture friday...

1

OPTICAL COMMUNICATIONS

S-108.3110

2

Course Program 5 lectures on Fridays

First lecture Friday 06.11 in Room H-402 13:15-16:30 (15 minutes break in-between)

Exercises Demo exercises during lectures Homework Exercises must be returned beforehand (will

count in final grade) Seminar presentation

27.11, 13:15-16:30 in Room H-402 Topic to be agreed beforehand

2 labworks Preliminary exercises (will count in final grade)

Exam 17.12 15.01

5 op

3

Course Schedule

1. Introduction and Optical Fibers (6.11)

2. Nonlinear Effects in Optical Fibers (13.11)

3. Fiber-Optic Components (20.11)

4. Transmitters and Receivers (4.12)

5. Fiber-Optic Measurements & Review (11.12)

4

Lecturers

In case of problems, questions...

Course lecturers G. Genty (3 lectures) [email protected] F. Manoocheri (2 lectures)

[email protected]

5

Optical Fiber Concept

Optical fibers are light pipes

Communications signals can be transmitted over these hair thin strands of glass or plastic

Concept is a century old

But only used commercially for the last ~25 years when technology had matured

6

Optical fibers have more capacity than other means (a single fiber can carry more information than a giant copper cable!)

Price

Speed

Distance

Weight/size

Immune from interference

Electrical isolation

Security

Why Optical Fiber Systems?

7

Optical Fiber Applications

> 90% of all long distance telephony

> 50% of all local telephony

Most CATV (cable television) networks

Most LAN (local area network) backbones

Many video surveillance links

Military

Optical fibers are used in many areas

8

Optical Fiber Technology

Core Cladding Mechanical protection layer

An optical fiber consists of two different types of solid glass

1970: first fiber with attenuation (loss) <20 dB/km 1979: attenuation reduced to 0.2 dB/km commercial systems!

9

Optical Fiber Communication

Optical fiber systems transmit modulated infrared light

Transmitter Receiver

Fiber

Components

Information can be transmitted oververy long distances due to the low attenuation of

optical fibers

10

Frequencies in Communications

1 m

1 cm

10 cm

1 m

10 m

100 m

1 km

10 km

100 km

waveguide

coaxialcable

wire pairs

opticalfiber

TelephoneDataVideo

SatelliteRadar

TVRadio

Submarine cableTelephoneTelegraph

wavelength

frequency

300 THz

30 GHz

3 GHz

300 MHz

30 Mhz

3 MHz

300 kHz

30 kHz

3 kHz

11

Frequencies in Communications

Optical Fiber: > Gb/sMicro-wave ~10 Mb/sShort-wave radio ~100 kb/sLong-wave radio ~4 Kb/s

Data rate

Increase of communication capacity and rates

requires higher carrier frequencies

Optical Fiber Communication!

12

Optical fibers are cylindrical dielectric waveguides

Cladding diameter125 µm

Cladding (pure silica)

Core silica doped with Ge, Al… Core diameter

from 9 to 62.5 µm

Typical values of refractive indices Cladding: n2 = 1.460 (silica: SiO2)

Core: n1 =1.461 (dopants increase ref. index compared to cladding)

n1

n2

Optical Fiber

A useful parameter: fractional refractive index difference = (n1-n2) /n1<<1

Dielectric: material which does not conduct electricity but can sustain an electric field

13

Fiber Manufacturing

Preform (soot) fabrication deposition of core and cladding materials onto a rod using vapors of SiCCL4 and GeCCL4 mixed in a flame burned

Consolidation of the preform preform is placed in a high temperature furnace to remove the water vapor and obtain a solid and dense rod

Drawing in a tower solid preform is placed in a drawing tower and drawn into a thin continuous strand of glass fiber

Optical fiber manufacturing is performed in 3 steps

14

Fiber Manufacturing

Step 1 Steps 2&3

15

Light Propagation in Optical Fibers

Guiding principle: Total Internal Reflection Critical angle Numerical aperture

Modes

Optical Fiber types Multimode fibers Single mode fibers

Attenuation

Dispersion Inter-modal Intra-modal

16

Total Internal Reflection

n2

n11

2

Snell’s law:n1 sin 1 = n2 sin 2

n1 > n2

Light is partially reflected and refracted at the interface of two media with different refractive indices: Reflected ray with angle identical to angle of incidence Refracted ray with angle given by Snell’s law

1

Refracted ray with angle: sin 2 = n1/ n2 sin 1

Solution only if n1/ n2 sin 1≤1

Angles 1 & 2 defined with respect to normal!!

17

Total Internal Reflection

n2

n11

2

Snell’s law:n1 sin 1 = n2 sin 2

n2

n1c

n1 > n2

sin c = n2 / n1If >c No

ray is refracted!

For angle such that >C , light is fully reflected at the core-cladding interface:

optical fiber principle!

n2n1

n2

n2

1

18

Example: n1 = 1.47 n2 = 1.46

NA = 0.17

Numerical Aperture

n2n1 c

max

For angle such that < max, light propagates inside the fiber

For angle such that >max, light does not propagate inside the fiber

1 with 2sin1

211

22

21max

n

nnnnnNA

Numerical aperture NA describes the acceptance angle max for light to be guided

19

Geometrical optics can’t describe rigorously light propagation in fibers

Must be handled by electromagnetic theory (wave propagation)

Starting point: Maxwell’s equations

Theory of Light Propagation in Optical Fiber

(4)

(3)

(2)

(1)

0

B

DT

DJH

T

BE

f density Charge :

density Current :

density flux Electric :

densityflux Magnetic :

0

00

0

f

J

PED

MHB

with

20


onPolarizati Nonlinear :

onPolarizati Linear :(1)

TrP

dttrEtttrP

trPtrPtrP

NL

L

NLL

,

,,

,,,

1110

We consider only linear propagation: PNL(r,T) negligible

(1): linear susceptibility

21


22

02 2 2

2(1) 2

0 02

( , )1 ( , )( , )

We now introduce the Fourier transform: ( , )

( , )( , )

And we get: ( , ) ( , ) ( ) ( , )

which can be re

L

i t

-

kk

k

P r tE r tE r t

c t t

E r E(r,t)e dt

E r ti E r

t

E r E r E rc

22 (1)

0 02

2

2

written as

( , ) 1 ( ) ( , ) 0

i.e. ( , ) ( ) ( , ) 0

E r c E rc

E r E rc

22

Theory of Propagation in Optical Fiber

)()(

and

)(2

11 with

2)(

)1(

)1(2

cn

nc

in

0),(

~),(

~),(

~),(

~),(

~),(

~ 22

rDrE

rErErErE

Equation! Helmoltz : 0),(~

),(~

2

222 rE

cnrE

n: refractive index: absorption

23


Each components of E(x,y,z,t)=U(x,y,z)ejt must satisfy the Helmoltz equation

Assumption: the cladding radius is infinite In cylindrical coodinates the Helmoltz equation becomes

/2

0

0

2

12

022

k

arnn

arnn

UknU for

for

with

00

2

12

02

2

2

2

2

22

2

/2

011

k

arnn

arnn

Uknz

UU

rr

U

rr

U for

for

with

x

yz

ErEz

Eφ

r

φ

Note: =/c

24


U = U(r,φ,z)= U(r)U(φ) U(z) Consider waves travelling in the z-direction U(z) =e-jz

U(φ) must be 2 periodic U(φ) =e-j lφ , l=0,±1,±2…integer

00

2

1

2

222

02

2

2

/2

01

...2,1,0)(),,(

k

arnn

arnn

Fr

lkn

dr

dF

rdr

Fd

leerFzrU zjjl

for

for

with

:gets one Eq. Helmoltz the into Plugging

with

,such that

refraction ofindex effectivean definecan One

12 nnnnc

n

effeff

eff

= k0 neff is the propagation

constant

25


A light wave is guided only if

We introduce

arFr

l

dr

dF

rdr

Fd

arFr

l

dr

dF

rdr

Fd

for

for

:get then We

01

01

2

22

2

2

2

22

2

2

0102 knkn

constant! :22

022

21

20

22

202

22

2201

2

NAknnk

kn

kn

real:,

0, :Note 22

26


lK

arKrF

lJ

arJrF

l

ll

l

ll

order with kind 1 offunction Bessel Modified :

for )(

order with kind 1 offunction Bessel :

for )(

:form theof are equations theof solutions The

st

st

constant! :

with

220

22

21

20

22

202

22

2201

2

NAknnk

kn

kn

27

Examples

a a

K0(r)J0(r)K0(r) K3(r)J3(r)K3(r)

a

r

r

l=0 l=3

arrK

arrJrF

for

for

)(

)()(

0

0

arrK

arrJrF

for

for

)(

)()(

3

3

28

Characteristic Equation

aa

kn

l

K

K

J

J

n

n

K

K

J

J lm

l

l

l

l

l

l

l

l

and with

11

)(

)(

)(

)(

)(

)(

)(

)(

:equation sticscharacteri the

solvingby found becan constant n propagatio The

2

2220

22

22''

22

21

''

Boundary conditions at the core-cladding interface give a condition on the propagation constant (characteristics equation)

For each l value there are m solutions for Each value lm corresponds to a particualr fiber

mode

29

Number of Modes Supported by an Optical Fiber

Solution of the characteristics equation U(r,φ,z)=F(r)e-jle-jlmz is called a mode, each mode corresponds to a particular electromagnetic field pattern of radiation

The modes are labeled LPlm

Number of modes M supported by an optical fiber is related to the V parameter defined as

M is an increasing function of V !

If V <2.405, M=1 and only the mode LP01 propagates: the fiber is said Single-Mode

22

210

2nn

aNAakV

30

Number of Modes Supported by an Optical Fiber

Number of modes well approximated by:

If V <2.405, M=1 and only the mode LP01 propagates: Single-Mode fiber!

2

2 2 2 21 2

2/ 2, where

aM V V n n

cladding

Example:2a =50 mn1 =1.46 V=17.6=0.005 M=155=1.3 m

core

1.0 LP01

0.8 21

02 0.6 31 12 41

22 0.4 32 61

51 13 03 23

42 0.2 71 04 52 81

33 0 2 4 6 8 10 12

V

21

2

nn

nneff

LP11

31

Examples of Modes in an Optical Fiber

=0.6328 m a =8.335 m n1 =1.462420 =0.034

32

Examples of Modes in an Optical Fiber

=0.6328 m a =8.335 m n1 =1.462420 =0.034

33

Cut-Off Wavelength

The propagation constant of a given mode depends on the wavelength [ ()]

The cut-off condition of a mode is defined as 2()-k02

n22= 2()-42 n2

2/

There exists a wavelength c above which only the fundamental mode LP01 can propagate

11

11

54.02

405.2

84.12405.2

2405.2

nna

ananV

cc

C

ly equivalent or

Example:2a =9.2 mn1 =1.4690=0.0034c~1.2 m

34

Single-Mode Guidance

In a single-mode fiber, for wavelengths >c~1.26 m

only the LP01 mode can propagate

35

Mode Field Diameter

Fiber Optics Communication Technology-Mynbaev & Scheiner

The fundamental mode of a single-mode fiber is well approximated by a Gaussian function

42for )ln(

4221for 879.2619.1

65.0

from obtained is size mode for theion approximat goodA

size mode the andconstant a is where

)(

0

62/30

0

2

0

.VV

aw

.V.VV

aw

wC

CeF w

36

Step-index single-mode

Types of Optical Fibers

Refractive index profile

Cladding diameter125 µm

Core diameterfrom 8 to 10 µm n1

n2

n

n2

n1

r

37

Step-index multimode



Cladding diameterfrom 125 to 400 µm


n2

n

n2

n1

r

38

Graded-index multimode



Cladding diameterfrom 125 to 140 µm


n2

n

n2

n1

r

39

Attenuation Signal attenuation in optical fibers results form 3

phenomena: Absorption Scattering Bending

Loss coefficient:

depends on the wavelength

For a single-mode fiber, dB= 0.2 dB/km @ 1550 nm

343.4

343.4)10ln(

10log10 10

dB :dB/km of units in expressedusually is

LLP

P

ePP

in

Out

LinOut

40

Scattering and Absorption

Short wavelength: Rayleigh scattering induced by inhomogeneity of the

refractive index and proportional to 1/4

Absorption Infrared bandUltraviolet band

3 Transmission windows 820 nm 1300 nm 1550 nm

4 1st window 2nd 3rd

820 nm 1.3 µm 1.55 µm 2

IR absorption

1.0 0.8 Rayleigh

Water peaks scattering

0.4 1/4

0.2 UV absorption

0.1 0.8 1.0 1.2 1.4 1.6 1.8

Wavelength (µm)

41

Macrodending losses are caused by the bending of fiber

Bending of fiber affects the condition < C

For single-mode fiber, bending losses are important for curvature radii < 1 cm

Macrobending Losses

42

Microdending losses are caused by the rugosity of fiber

Micro-deformation along the fiber axis results in scattering and

power loss

Microbending Losses

43

Fundamental mode

Higher order mode

Attenuation: Single-mode vs. Multimode Fiber

Light in higher-order modes travels longer optical paths

Multimode fiber attenuates more than single-mode fiber

Wavelength (µm)

4

2 MMF

1

0.4 SMF

0.2

0.1 0.8 1.0 1.2 1.4 1.6 1.8

44

Dispersion

What is dispersion? Power of a pulse travelling though a fiber is dispersed in time Different spectral components of signal travel at different speeds Results from different phenomena

Consequences of dispersion: pulses spread in time

3 Types of dispersion: Inter-modal dispersion (in multimode fibers) Intra-modal dispersion (in multimode and single-mode fibers) Polarization mode dispersion (in single-mode fibers)

t t

45

Input pulse

Dispersion in Multimode Fibers (inter-modal)

t

Input pulseOutput pulse

t

In a multimode fiber, different modes travel at different speed temporal spreading (inter-modal dispersion)

Inter-modal dispersion limits the transmission capacity

The maximum temporal spreading tolerated is half a bit period

The limit is usually expressed in terms of bit rate-distance product

46

Dispersion in Multimode Fibers (Inter-modal)

Ln

n

θ

L

θπL

θ

LL

LL

n

cvv

v

Land T

v

Lwith T

TTΔT

CSLOW

FAST

SLOWFAST

SLOW

SLOWSLOW

FAST

FASTFAST

FASTSLOW

2

1

1

sin2

coscos

δc

L

n

n

n

n

c

L

n

nL

cn

nL

c

nΔT

2

212

2

21

2

211

11

n2n1 c

L

Slow ray Fast ray

Fastest ray guided along the core center

Slowest ray is incident at the critical angle

sin

47

Dispersion in Multimode Fibers

21

2

2

21

1

2

2

1

2

1

n

cnBL

Bn

n

c

L

BT

sbB

or

i.e.

have must We

rate bit If

Example: n1 = 1.5 and = 0.01 →B L< 10 Mb∙s-1

Capacity of multimode-step index index fibers B×L≈20 Mb/s×km

×

48

Input pulse

Fast mode travels a longer physical path

Slow mode travels a shorter physical path

Dispersion in graded-index Multimode Fibers

t

Input pulseOutput pulse

t

Temporal spreading is small

Capacity of multimode-graded index fibers B×L≈2 Gb/s×km

49

Intra-modal Dispersion

In a medium of index n, a signal pulse travels at the group velocity g defined as

Intra-modal dispersion results from 2 phenomena Material dispersion (also called chromatic dispersion) Waveguide dispersion

Different spectral components of signal travel at different speeds

The dispersion parameter D characterizes the temporal pulse broadening T per unit length per unit of spectral bandwidth : T = D × × L

kmps/nm of units in modalIntra

2

22

2

1

d

d

cvd

dD

g

12

2

d

d

cd

dvg

50

Material Dispersion

Refractive index n depends on the frequency/wavelength of light

Speed of light in material is therefore dependent on frequency/wavelength

Input pulse, 1

t

Input pulse, 2

t

t

51

Material Dispersion

nm 9896.161 0.8974794,

nm 116.2414 0.4079426,

nm 68.4043 0.6961663, with

33

22

11

223

23

222

22

221

211)(

A

A

A

AAAn

Refractive index of silica as a function of wavelength is given by the Sellmeier Equation

52

Material Dispersion

ddnn

c

d

d

cvg /2

12

L

Input pulse, 1

t

Input pulse, 2

t

1 2

2

21

d

nd

c

L

vd

dLDLΔT

g

t

T

53

Material Dispersion

km)ps/nm :(units Material 2

2

d

nd

cD

DM

ater

ial (

ps/

nm

/km

)

0

-200

-400

-600

-800

-1000

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Wavelength (µm)

[email protected] m

54

Waveguide Dispersion

The size w0 of a mode depends on the ratio a/:

Consequence: the relative fraction of power in the core and cladding varies

This implies that the group-velocity g also depends on a/

1 2>1

size mode the is whereWaveguide 020

22

1w

wd

d

ncvd

dD

g

62/30

879.2619.165.0

VVaw

55

Total Dispersion

Waveguide dispersion shifts the wavelength of zero-dispersion to 1.32 m

WaveguideMaterialmodalIntra DDD

DIntra-modal<0: normal dispersion regionDIntra-modal>0: anomalous dispersion

region

56

Dispersion can be changed by changing the refractive index

Change in index profile affects the waveguide dispersion

Total dispersion is changed

n2

n1

Single-mode Fiber

n2

n1

Dispersion shifted Fiber

Single-mode fiber: D=0 @ 1310 nm Dispersion shifted Fiber: D=0 @ 1550 nm

20

10 Single-mode Fiber

0

-10 1.3 1.4 1.5

Wavelength (µm)

Dispersion shifted Fiber

Tuning Dispersion

57

Dispersion Related Parameters

/kms of units in parameter dispersionvelocity group:

s/km of units indelay group :

22

modalIntra

2211

1

21

1

c

d

d

d

d

d

d

vd

dD

d

d

v

nc

g

g

eff

58

Polarization Mode Dispersion

Optical fibers are not perfectly circular

In general, a mode has 2 polarizations (degenerescence): x and y

Causes broadening of signal pulse

LDvv

LTgygx

onPolarizati11

x

y

x

59

Effects of Dispersion: Pulse Spreading

Total pulse spreading is determined as the geometric sum of

pulse spreading resulting from intra-modal and inter-modal dispersion

22

22

222

LDLDT

LDLDT

TTTT

onPolarizatimodalIntra

modalIntramodalInter

onPolarizatimodal-IntraIntermodal

:Fiber Mode-Single

:Fiber Multimode

Examples: Consider a LED operating @ .85 m =50 nm after L=1 km, T=5.6 ns

DInter-modal =2.5 ns/km DIntra-modal =100 ps/nm×km

Consider a DFB laser operating @ 1.5 m =.2 nm after L=100 km, T=0.34 ns!

DIntra-modal =17 ps/nm×km DPolarization=0.5 ps/ √km

60

Effects of Dispersion: Capacity Limitation

modalIntra

modalIntra

effects) onpolarizati g(neglectin

Fiber, Mode-Single For

DLB

LDTB

T

2

1

2

1

Capacity limitation: maximum broadening<half a bit period

Example: Consider a DFB laser operating @ 1.55 m =0.2 nm LB<150 Gb/s ×km

D =17 ps/nm×km If L=100 km, BMax=1.5 Gb/s

61

Advantage of Single-Mode Fibers

No intermodal dispersion

Lower attenuation

No interferences between multiple modes

Easier Input/output coupling

Single-mode fibers are used in long transmission systems

62

Summary

Attractive characteristics of optical fibers:

Low transmission loss

Enormous bandwidth

Immune to electromagnetic noise

Low cost

Light weight and small dimensions

Strong, flexible material

63

Summary

Important parameters: NA: numerical aperture (angle of acceptance) V: normalized frequency parameter (number of modes) c: cut-off wavelength (single-mode guidance) D: dispersion (pulse broadening)

Multimode fiber Used in local area networks (LANs) / metropolitan area

networks (MANs) Capacity limited by inter-modal dispersion: typically 20

Mb/s x km for step index and 2 Gb/s x km for graded index

Single-mode fiber Used for short/long distances Capacity limited by dispersion: typically 150 Gb/s x km

1 optical communications s-108.3110. 2 course program 5 lectures on fridays first lecture friday...

Documents