OPTICAL COMMUNICATIONSOPTICAL …metrology.hut.fi/courses/S-108.3110/2009/Introduction_Light... · Topic to be agreed beforehand ... Angles 1 & 2 defined ... 9Number of modes M supported

OPTICAL COMMUNICATIONSOPTICAL COMMUNICATIONSS 108 3110S-108.3110

1

Course Programg5 lectures on Fridays

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

ExercisesDemo exercises during lecturesgHomework Exercises must be returned beforehand (will count in final grade)

Seminar presentationSeminar presentation27.11, 13:15-16:30 in Room H-402Topic to be agreed beforehand

2 labworks2 labworksPreliminary exercises (will count in final grade)

Exam 17.1215.01

5 op

2

p

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)4. Transmitters and Receivers (4.12)

5. Fiber-Optic Measurements & Review (11.12)

3

Lecturers

In case of problems, questions...p , q

Course lecturersG. Genty (3 lectures) [email protected]. Manoocheri (2 lectures) [email protected]

4

Optical Fiber Concept

Optical fibers are light pipesOptical fibers are light pipes

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

Concept is a century old

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

5

Why Optical Fiber Systems?

Optical fibers have more capacity than other

y p y

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

PricePrice

Speed

Di tDistance

Weight/size

Immune from interference

Electrical isolation

Security

6

Optical Fiber ApplicationsOptical fibers are used in many areas

> 90% of all long distance telephony

50% f ll l l t l h> 50% of all local telephony

Most CATV (cable television) networksMost CATV (cable television) networks

Most LAN (local area network) backbones

Many video surveillance links

Military

7

Optical Fiber Technology

An optical fiber consists of two different types of solid glass

Core Cladding Mechanical protection layerMechanical protection layer

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

8

Optical Fiber CommunicationOptical fiber systems transmit modulated infrared light

FiberFiber

Transmitter ReceiverComponentsp

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

9

Frequencies in Communications

10 k100 km

wire pairs Submarine cable

frequency

30 kHz3 kHz

1 km10 km wire pairs

TelephoneTelegraph

3 MH300 kHz30 kHz

10 m100 m

coaxialcable

TVRadio

300 MH30 Mhz3 MHz

10 cm1 m

waveguide Satellite 3 GHz300 MHz

1 cmwaveguide

Telephone

Radar 30 GHz

1 µm opticalfiber

TelephoneDataVideowavelength

300 THz

10

Frequencies in Communications

Optical Fiber: > Gb/sData rate

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

Increase of communication capacity and ratesrequires higher carrier frequencies

Optical Fiber Communication!

11

Optical FiberOptical fibers are cylindrical dielectric waveguides

Di l t i t i l hi h d t d t l t i it b t t i l t i fi ld

Cladding diameter

Cladding (pure silica)Core diameter

n2

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

Cladding diameter125 µm Core silica doped with Ge, Al…

Core diameterfrom 9 to 62.5 µm n1

Typical values of refractive indicesCladding: n2 = 1.460 (silica: SiO2)Core: n1 =1.461 (dopants increase ref. index compared to cladding)

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

12

Fiber Manufacturing

Optical fiber manufacturing is performed in 3 steps

Preform (soot) fabricationdeposition of core and cladding materials onto a rod using vapors of SiCCL anddeposition of core and cladding materials onto a rod using vapors of SiCCL4 andGeCCL4 mixed in a flame burned

C lid ti f th fConsolidation of the preformpreform is placed in a high temperature furnace to remove the water vapor and obtaina solid and dense rod

Drawing in a towersolid preform is placed in a drawing tower and drawn into a p p gthin continuous strand of glass fiber

13

Fiber Manufacturing

Step 1 Steps 2&3

14

Light Propagation in Optical FibersGuiding principle: Total Internal Reflection

Critical angleNumerical aperture

ModesModes

Optical Fiber typesM lti d fibMultimode fibers Single mode fibers

Attenuation

DispersionpInter-modal Intra-modal

15

Total Internal Reflection

Light is partially reflected and refracted at the interface of two media with different refractive indices:

Reflected ray with angle identical to angle of incidenceRefracted ray with angle given by Snell’s law

Snell’s law:n1 sin θ1 = n2 sin θ2

Refracted ray with angle given by Snell s law

A l θ & θ d fi d

n1θ1

n1 > n2θ1

Angles θ1 & θ2 defined with respect to normal!!

n2θ21 2

Refracted ray with angle: sin θ = n / n sin θRefracted ray with angle: sin θ2 = n1/ n2 sin θ1Solution only if n1/ n2 sin θ1≤1

16

Total Internal Reflection

Snell’s law:sin θ = sin θ

sin θc = n2 / n1If θ >θc No ray is refracted!

θ1

n1 sin θ1 = n2 sin θ2

θ

is refracted!

θ1

n2n1

θ1

θ2n2n1

θcn1 > n2 n2

θ1

2

n2n1 θ1 θn2

For angle θ such that θ >θC , light is fully reflected at the core-cladding interface: optical fiber principle!

17

Numerical Aperture

For angle θ such that θ <θ max, light propagates inside the fiberFor angle θ such that θ >θ light does not propagate inside the fiber

n2

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

Example: n1 = 1.47n2 = 1.46NA = 0.17

n1 θcθmax

1 with 2sin1

211

22

21max <<

−=≈−==

nnnnnnNA δδθ

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

18

Theory of Light Propagation in Optical Fiber

Geometrical optics can’t describe rigorously light propagation in fibers

Must be handled by electromagnetic theory (wave propagation)

Starting point: Maxwell’s equations

(1)

∂∂∂

−=×∇

DTBE

densityflux Magnetic : 0 += MHB µ

(3)

(2)

=⋅∇∂∂

+=×∇

DTDJH

fρd itChdensity Current :

density flux Electric :

00

0

=+=

JPED εwith

(4) 0=⋅∇ Bf densityCharge: 0=fρ

19


( ) ( ) ( )( ) ( ) ( ) onPolarizatiLinear:(1) dttEtttP

trPtrPtrP NLL ,,,

∫∞+

+=

χ(1): linear( ) ( ) ( )( ) onPolarizati Nonlinear :

onPolarizatiLinear:(1)

TrP

dttrEtttrP

NL

L

,

,, 1110 ∫ ∞−−= χε χ( ): linear

susceptibility

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

20


22 ( , )1 ( , )( ) LP r tE r tE r t µ ∂∂∇×∇× + = 02 2 2( , )

We now introduce the Fourier transform: ( , ) i t

-

E r tc t t

E r E(r,t)e dtω

µ

ω+∞

∞

∇×∇× + = −∂ ∂

= ∫%

( )2

( , ) ( , )k

kk

E r t i E rt

ω ω∂⇔

∂%

2(1) 2

0 02And we get: ( , ) ( , ) ( ) ( , )

which can be re

E r E r E rcωω ω µ ε χ ω ω ω∇×∇× − = +% % %

written as2

2 (1)0 02( , ) 1 ( ) ( , ) 0E r c E r

cωω µ ε χ ω ω⎡ ⎤∇×∇× − + =⎣ ⎦

% %

2

2i.e. ( , ) ( ) ( , ) 0E r E rcωω ε ω ω∇×∇× − =% %

21

Theory of Propagation in Optical Fiber

[ ]12α ⎤⎡ c [ ]

[ ])(and

)(211 with

2)(

)1(

)1(

ωχωα

ωχω

αωε

ℑ

ℜ+=⎥⎦⎤

⎢⎣⎡ += ncin n: refractive index

α: absorption[ ])(

)(and )( ωχ

ωα ℑ=

cn

( )( )0),(~),(~

),(~),(~),(~),(~ 22

=⋅∇∝⋅∇

−∇=∇−⋅∇∇=×∇×∇

ωω

ωωωω

rDrE

rErErErE

( ))()(

2ω Equation! Helmoltz : 0),(~),(~ 222 =+∇ ωωω rE

cnrE

22


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

⎪⎩

⎪⎨

⎧

=>=≤=

=+∇λπ /2

0

0

2

12

022

karnnarnn

UknU for for

with Note: λ=ω /c

Assumption: the cladding radius is infiniteIn cylindrical coodinates the Helmoltz equation becomes

⎩ 0

⎪⎩

⎪⎨

⎧

=>=≤=

=+∂∂

+∂∂

+∂∂

+∂∂

00

2

12

02

2

2

2

2

22

2

/2011

λπϕ

karnnarnn

UknzUU

rrU

rrU for

for with

⎩ 00 /2 λπk

x ErE

φ

yz

Ez

Eφ

r

23


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

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

⎧ ≤

±±== −− ...2,1,0)(),,( ϕ βϕ leerFzrU zjjl

f:gets one Eq. Helmoltz the into Plugging

with

⎪⎩

⎪⎨

⎧

=>=≤=

=⎟⎟⎠

⎞⎜⎜⎝

⎛−−++ 2

1

2

222

02

2

2

/201

λπβ

karnnarnn

Frlkn

drdF

rdrFd for

for with

⎩ = 00 /2 λπk

refraction ofindex effectivean definecan One neff β = k0 neff is the ti

,such that 12 nnnnc effeff <<=ωβ

propagation constant

24


A light wave is guided only if 0102 knkn ≤≤ βg g y

We introduce

0102 β

( )( )222

2201

2

kn

kn

−=

−=

βγ

βκ

real:0, :Note 22

γκγκ ≥

( )( ) constant! :22

022

21

20

2202

NAknnk

kn

=−=+

=

γκ

βγ real:, γκ

ldFFd ⎞⎛

:get then We

1 22

ldFFd

arFrl

drdF

rdrFd

⎞⎛

≤=⎟⎟⎠

⎞⎜⎜⎝

⎛−++ for

1

01

22

2

22

2

2

κ

arFrl

drdF

rdrFd

>=⎟⎟⎠

⎞⎜⎜⎝

⎛+−+ for 01

22

2 γ

25


( )lJ

arJrF ll

orderithkind1off nctionBessel:

for )(:form theofareequationstheofsolutions The

st

≤= ρκ

( )lK

arKrFlJ

ll

l

orderwithkind1offunctionBesselModified:

for )(order with kind1offunction Bessel :

st

st

>= ργ

lKl order with kind1offunction BesselModified :

with

( )( )2

0222

2201

2

kn

kn

−=

−=

βγ

βκ

( ) constant! :220

22

21

20

22 NAknnk =−=+ γκ

26

Examples

l=0 l=3

K0(γr)J0(κr)K0(γr) K3(γr)J3(κr)K3(γr)r

a aar

⎨⎧ ≤

∝arrJ

rF for )(

)( 0 κ⎨⎧ ≤

∝arrJ

rF for )(

)( 3 κ

⎩⎨ < arrK

rFfor)(

)(0 γ ⎩

⎨ < arrKrF

for)()(

3 γ

27

Characteristic Equation

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

β:equationsticscharacterithe

solvingby found becan constant n propagatio The

βkn

lK

KJ

Jnn

KK

JJ lm

l

l

l

l

l

l

l

l⎥⎦⎤

⎢⎣⎡

Γ+

Κ=⎥

⎦

⎤⎢⎣

⎡ΓΓ

Γ+

ΚΚΚ

×⎥⎦

⎤⎢⎣

⎡ΓΓ

Γ+

ΚΚΚ 11

)()(

)()(

)()(

)()(

q2

2220

22

22''

22

21

''

γκ aa =Γ=Κ and with

For each l value there are m solutions for βEach value βlm corresponds to a particualr fiber mode

28

Number of Modes Supported by an Optical Fiberpp y pSolution of the characteristics equation U(r,φ,z)=F(r)e-jlϕe-jβlmz iscalled a mode, each mode corresponds to a particularp pelectromagnetic field pattern of radiation

The modes are labeled LPlThe modes are labeled LPlm

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

22

210

2 nnaNAakV −==λπ

M is an increasing function of V !

λ

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

29

Number of Modes Supported by an Optical FiberNumber of modes well approximated by: ( )

22 2 2 2

1 22/ 2, where aM V V n nπ

λ⎛ ⎞≈ ≈ −⎜ ⎟⎝ ⎠

1.0LP01

0.8 LP11

Example:2a =50 µmn1 =1.46 V=17.6core

21020.6

31 12 4122 32

2

nnnneff −

1 δ=0.005 M=155λ=1.3 µm

220.4 3261

51 1303 23

420.2 71045281

21 nn −

528133

0 2 4 6 8 10 12V

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

30cladding

Examples of Modes in an Optical Fiberλ =0.6328 µm a =8.335 µm n1 =1.462420 δ =0.034

31

Examples of Modes in an Optical Fiberλ =0.6328 µm a =8.335 µm n1 =1.462420 δ =0.034

32

Cut-Off Wavelength

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

The cut-off condition of a mode is defined as β2(λ)-k02 n2

2= β2(λ)-β ( ) 0 2 β ( )4π2 n2

2/λ2=0

Th i t l th λ b hi h l th f d t lThere exists a wavelength λc above which only the fundamental mode LP01 can propagate

λλ

δδπλ 11

4052

84.12405.22405.2 ananV C ==⇔<

Example:2a =9.2 µmn1 =1.4690

δλ

δλ

π 11

54.02405.2

nna cc ==ly equivalent or

1 δ=0.0034λc~1.2 µm

33

Single-Mode Guidance

In a single-mode fiber, for wavelengths λ >λc~1.26 µm l th LP d tonly the LP01 mode can propagate

34

Mode Field Diameter

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

2⎞

⎜⎛ ρ

fb i diidf hiidAsize mode the andconstant a is where

)(

0

0

wCCeF w=

⎟⎠

⎞⎜⎜⎝

⎛−

ρ

ρ

4221for 879.2619.165.0

fromobtainedissizemodefor theion approximatgoodA

62/30 .V.VV

aw <<⎟⎠⎞

⎜⎝⎛ ++=

42for )ln(0 .V

Vaw >=

35Fiber Optics Communication Technology-Mynbaev & Scheiner

Types of Optical Fibers

Step index single modeStep-index single-mode

Cladding diameter125 µm

Core diameterfrom 8 to 10 µm n1

n2

Refractive index profile

n

δ 0 001n1p

δ = 0.001n2

r

36


Step index multimodeStep-index multimode

Cladding diameterfrom 125 to 400 µm


n2


n

δ 0 01n1p

δ = 0.01n2

r

37


G d d i d lti dGraded-index multimode

Cladding diameterfrom 125 to 140 µm


n2


nn1p

n2r

38

AttenuationSignal attenuation in optical fibers results form 3 phenomena:

AbsorptionScatteringBending

Loss coefficient: αα= −ePP L

inOut

αα

3434

343.4)10ln(

10log10 10 −=−=⎟⎟⎠

⎞⎜⎜⎝

⎛

dB/kfitidlli

LLPP

in

Out

α depends on the wavelength

ααα 343.4=dB:dB/kmofunitsinexpressedusually is

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

39

Scattering and AbsorptionShort wavelength: Rayleigh scattering

induced by inhomogeneity of the 41 t i d 2 d 3 dinduced by inhomogeneity of the

refractive index and proportional to 1/λ4

1st window 2nd 3rd820 nm 1.3 µm 1.55 µm2

IR absorption1 0

AbsorptionInfrared band

1.00.8 Rayleigh

Water peaksscattering

0.4α ∝1/λ4

UV absorptionInfrared bandUltraviolet band 0.2

UV absorption

0.1 0 8 1 0 1 2 1 4 1 6 1 83 Transmission windows

820 nm

0.8 1.0 1.2 1.4 1.6 1.8Wavelength (µm)

1300 nm1550 nm

40

Macrobending Losses

Macrodending losses are caused by the bending of fiberMacrodending losses are caused by the bending of fiber

Bending of fiber affects the condition θ < θCBending of fiber affects the condition θ < θC

For single-mode fiber, bending losses are importantfor curvature radii < 1 cmfor curvature radii < 1 cm

41

Microbending Losses

Mi d di l d b th it f fibMicrodending losses are caused by the rugosity of fiber

Micro-deformation along the fiber axis results in scattering and power loss

42

Attenuation: Single-mode vs. Multimode Fiber

4

Fundamental mode2

MMF1

Higher order mode0.4 SMF

0.2

Wavelength (µm)

0.10.8 1.0 1.2 1.4 1.6 1.8

Light in higher-order modes travels longer optical paths

Multimode fiber attenuates more than single-mode fiber

43

Dispersion

What is dispersion?P f l t lli th h fib i di d i tiPower of a pulse travelling though a fiber is dispersed in timeDifferent spectral components of signal travel at different speedsResults from different phenomena

Consequences of dispersion: pulses spread in time

3 T f di i

t t

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

44

Dispersion in Multimode Fibers (inter-modal)

Input pulseOutput pulse


t 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 periodThe maximum temporal spreading tolerated is half a bit period

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

45

Dispersion in Multimode Fibers (Inter-modal)Fastest ray guided along the core center

TT∆T −=

Slowest ray is incident at the critical angle

vLand T

vLwith T

TT∆T

SLOW

SLOWSLOW

FAST

FASTFAST

FASTSLOW

==

=n2n1 θc Slow ray Fast ray

LLncvv

FAST

SLOWFAST1

=

==θ

Lnn

θL

θπL

θLL

CSLOW

FAST

2

1

sin2

coscos==

⎟⎠⎞

⎜⎝⎛ −

==Lsin

2 ⎠⎝

δcL

nn

nn

cL

nnL

cnnL

cn∆T

2

212

2

21

2

211

11 =⎥⎦

⎤⎢⎣⎡ −=−=

46

Dispersion in Multimode Fibers

1bB −tbitIf 1

21B

T

sbB

<∆

⋅= −

have must We

ratebitIf

2

21

21

2

Bnn

cL

B

< i.e. δExample: n1 = 1.5 and δ = 0.01 → B L< 10 Mb·s-1×

21

2

2ncnBL <× or

δ

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

47

Dispersion in graded-index Multimode Fibers



t t

Fast mode travels a longer physical path Temporal spreadingis smallSlow mode travels a shorter physical path is small

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

48

Intra-modal Dispersion

In a medium of index n, a signal pulse travels at the groupl it d fi dvelocity νg defined as: 12

2

−

⎟⎟⎠

⎞⎜⎜⎝

⎛−==

λβ

πλ

βω

dd

cddvg

Intra-modal dispersion results from 2 phenomenaMaterial dispersion (also called chromatic dispersion)Waveguide dispersiong p

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 ∆λ: ∆T = D × ∆λ × L

⎞⎛kmps/nm of units in modalIntra ×−=⎟

⎟⎠

⎞⎜⎜⎝

⎛=− 2

22

21

λβ

πλ

λ dd

cvddD

g

49

Material Dispersion

Refractive index n depends on the frequency/wavelength of light

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

Input pulse, λ1

t

Input pulse, λ2 t

t

50

Material Dispersion

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

23

22

21)( λλλλ AAA

nm 68.4043 0.6961663, with ==

−+

−+

−+=

11

223

322

2

222

1

11)(

λλλ

λλλ

λλλ

λλ

A

AAAn

nm 9896.161 0.8974794, nm 116.2414 0.4079426,

====

33

22

λλ

AA

51

Material Dispersion

βλ cdv12

=⎞

⎜⎜⎛

−=−

λ1 λ2λλλπ ddnndc

vg /2 −⎠⎜⎜⎝

λ

∆λ

∆TInput pulse, λ1

∆T

L

t

Input pulse, λ2

t

L

t21 dLd ⎞

⎜⎛

2

21λ

λλλ

λλd

ndcL

vddLDL∆T

g

∆−=⎟⎠

⎞⎜⎜⎝

⎛∆=∆=

52

Material Dispersion)

2λ dnm/k

m)

0-200

km)ps/nm :(units Material ×−= 2

2

λλ

dnd

cD

ial(p

s/n -400

-600-800

DM

ater

i 800-1000

0 4 0 6 0 8 1 0 1 2 1 4 1 6 1 8

[email protected] µm

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Wavelength (µm)

53

Waveguide Dispersion

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

⎜⎝⎛ ++= 62/30

879.2619.165.0VV

aw0 pλ1 λ2>λ1

⎠⎝ 62/30 VV

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

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

⎞⎛size mode the is whereWaveguide 02

022

1 w wd

dncvd

dDg

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟

⎟⎠

⎞⎜⎜⎝

⎛=

λλπ

λλ

54

Total Dispersion

WaveguideMaterialmodalIntra DDD +=−

DIntra-modal<0: normal dispersion regionD >0 l di i iDIntra-modal>0: anomalous dispersion region

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

55

Tuning Dispersion

Dispersion can be changed by changing the refractive indexChange in index profile affects the waveguide dispersionTotal dispersion is changed

20

Single-mode Fiber

n2

n1

n2

n1

10

0Single-mode Fiber Dispersion shifted Fiber

Single mode fiber: D=0 @ 1310 nm

0

-10 1 3 1 4 1 5

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

10 1.3 1.4 1.5Wavelength (µm)

56

Dispersion Related Parameters

ωβ = nc eff

s/km of units indelay group :

ββ

βωβ

⎞⎛⎞⎛

== 1

21

1

dddd

dd

vg

/kmsofunitsinparameterdispersionvelocitygroup: 2

modalIntra

β

λπβ

λω

ωβ

λβ

λ⎟⎠⎞

⎜⎝⎛−===⎟

⎟⎠

⎞⎜⎜⎝

⎛=− 22

11 21 cdd

dd

dd

vddD

g

/kmsofunitsinparameterdispersionvelocity group:2β

57

Polarization Mode Dispersion

Optical fibers are not perfectly circularp p y

x

y

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

x x

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

Causes broadening of signal pulse g g p

LDLT ≈∆11 LD

vvLT

gygxonPolarizati≈−=∆

58

Effects of Dispersion: Pulse SpreadingTotal pulse spreading is determined as the geometric sum of

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

222 TTTT ∆+∆+∆=∆onPolarizatimodal-IntraIntermodal

( ) ( )

( ) ( )22

22 LDLDT ×∆×+×=∆ −− modalIntramodalInter :Fiber Multimode

λ

( ) ( )22 LDLDT ×+×∆×=∆ − onPolarizatimodalIntra:FiberMode-Single λ

Examples: Consider a LED operating @ .85 µm∆λ =50 nm after L=1 km, ∆T=5.6 nsλ 50 a te , 5.6 sDInter-modal =2.5 ns/kmDIntra-modal =100 ps/nm×km

Consider a DFB laser operating @ 1 5 µmConsider a DFB laser operating @ 1.5 µm∆λ =.2 nm after L=100 km, ∆T=0.34 ns!

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

59

Effects of Dispersion: Capacity Limitation

Capacity limitation: maximum broadening<half a bit period

<∆T 1

Capacity limitation: maximum broadening half a bit period

λ∆≈∆

<∆

−modalIntra

effects)onpolarizatig(neglectin Fiber, Mode-Single For LDT

BT

2

λ∆<⇒

−modalIntra

e ec s)opo a ag( eg ec

DLB

21

Example: Consider a DFB laser operating @ 1.55 µm∆λ =0 2 nm LB<150 Gb/s ×km∆λ 0.2 nm LB<150 Gb/s ×kmD =17 ps/nm×km If L=100 km, BMax=1.5 Gb/s

60

Advantage of Single-Mode Fibers

No intermodal dispersionp

Lower attenuation

No interferences between multiple modes

Easier Input/output couplingEasier Input/output coupling

Single-mode fibers are used in long transmission systems

61

Summary

Attractive characteristics of optical fibers:p

Low transmission loss

Enormous bandwidth

Immune to electromagnetic noise

Low cost

Light weight and small dimensions

Strong, flexible materialg,

62

SummaryImportant parameters:

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

Multimode fiberUsed in local area networks (LANs) / metropolitan area networks (MAN )(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 fiberUsed for short/long distancesCapacity limited by dispersion: typically 150 Gb/s x kmCapacity limited by dispersion: typically 150 Gb/s x km

63

Documents

OPTICAL COMMUNICATIONSOPTICAL …metrology.hut.fi/courses/S-108.3110/2009/Introduction_Light... · Topic to be agreed beforehand ... Angles 1 & 2 defined ... 9Number of modes M supported