Introduction and Light Propagation in Optical Fibers 17.03...

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OPTICAL COMMUNICATIONSS-108.3110

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Course Program6 lectures on Thursdays

First lecture Thursday 17.03 in Room 4I-346 10:15-12:00 (15 minutes break in-between)( )

6 exercises sessions on FridaysExercises must be returned beforehand (will count in final grade)First exercises session 18.03 in Room 4I-34613:15-15:00

2 labworksPreliminary exercises (will count in final grade)

Exam 23.05,XX

55 ov

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Course Schedule

1. Introduction and Optical Fibers (17.03)

2. Nonlinear Effects in Optical Fibers (24.03)

3. Fiber-Optic Components I (31.03)

4. Fiber-Optic Components II (07.04)

5. Transmitters and Receivers (05.05)

6. Fiber-Optic Measurements & Review (14.04)p ( )

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Lecturers

In case of problems, questions...

Course lecturersG. Genty (5 lectures) [email protected]. Manoocheri (1 lectures) [email protected]

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Optical Fiber Concept

Optical fibers are light pipes

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

Concept is a century old

But only used commercially for the last ~30 years when technology had matured

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Why Optical Fiber Systems?

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

Price

SSpeed

Distance

Weight/sizeWeight/size

Immune from interference

Electrical isolationElectrical isolation

Security

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Optical Fiber Applications

> 90% of all long distance telephony

Optical fibers are used in many areas

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 linksMany video surveillance links

Military

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Optical Fiber Technology

An optical fiber consists of two different types of solid glass

Core Cladding Mechanical protection layer

1970: first fiber with attenuation (loss) <20 dB/km1970: first fiber with attenuation (loss) <20 dB/km 1979: attenuation reduced to 0.2 dB/km commercial systems!

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Optical Fiber CommunicationOptical fiber systems transmit modulated infrared light

Fiber

Transmitter ReceiverComponents

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

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Frequencies in Communicationsf

10 km100 km

wire pairs Submarine cableTelephone

frequency

30 kHz3 kHz

100 m1 km

coaxial TV

pTelegraph

3 MHz300 kHz

101 m

10 mcoaxialcable

TVRadio

3 GHz300 MHz30 Mhz

1 cm10 cm

waveguide SatelliteRadar 30 GHz

3 GHz

1 µm opticalfiber

TelephoneDataVideowavelength

300 THz

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a e e gt

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Frequencies in Communications

Optical Fiber: > Gb/sMi 10 Mb/

Data rate

Micro-wave ~10 Mb/sShort-wave radio ~100 kb/sLong-wave radio ~4 Kb/s

Increase of communication capacity and ratesrequires higher carrier frequenciesrequires higher carrier frequencies

Optical Fiber Communications!

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Optical FiberOptical fibers are cylindrical dielectric waveguides

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

Cladding diameter125 µm

Cladding (pure silica)

Core silica doped with Ge, Al…Core diameter

from 9 to 62.5 µm n1

n2

Typical values of refractive indicesCladding: n2 = 1.460 (silica: SiO2)Core: n1 =1 461 (dopants increase ref index compared to cladding)Core: n1 1.461 (dopants increase ref. index compared to cladding)

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

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Fiber Manufacturing

Optical fiber manufacturing is performed in 3 steps

Preform (soot) fabricationdeposition of core and cladding materials onto a rod using vapors of SiCCL4 andGeCCL4 mixed in a flame burnedGeCC 4 ed a a e bu ed

Consolidation of the preformpreform is placed in a high temperature furnace to remove the water vapor and obtainp p g p pa solid and dense rod

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

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Fiber Manufacturing

Step 1 Steps 2&3

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Light Propagation in Optical FibersGuiding principle: Total Internal Reflection

Critical angleNumerical aperturep

Modes

Optical Fiber typesMultimode fibers Single mode fibers

Attenuation

DispersionInter-modal Intra-modal

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Total Internal Reflection

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

Snell’s law:

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

θ1

Snell s law:n1 sin θ1 = n2 sin θ2

θ1Angles θ1 & θ2 defined with respect to normal!!

n2n1

θ1

θ2n1 > n2

1p!

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

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Total Internal Reflection

Snell’s law:n1 sin θ1 = n2 sin θ2

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

n1θ1 n1

θcn1 > n2

θ1

n2θ2n2

n1 n2

n2

n2

n2n1 θn2

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

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Numerical Aperture

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

Example: n1 = 1.47

n2n1 θ n2 = 1.46

NA = 0.17θc

θmax

1 with 2sin 211

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21max1 <<

−=≈−==

nnnnnnnNA δδθ

1n

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

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p g max g g

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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

∇ × E = −∂B∂

(1)M ti fl d it∂T

( )

∇ × H = J +∂D∂T

(2)

∇ D (3)

B = µ0H + M : Magnetic flux densityD = ε0E + P : Electric flux density J = 0 : Current density

with

∇ ⋅ D = ρ f (3)∇ ⋅ B = 0 (4)

yρ f = 0 : Charge density

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P r,t( )= PL r,t( )+ PNL r,t( )PL r,t( )= ε0 χ (1) t − t1( )E r,t1( )

−∞

+∞∫ dt1 : Linear Polarization χ(1): linear susceptibility

PNL r,T( ): Nonlinear Polarizationsusceptibility

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

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02 2 2

( , )1 ( , )( , ) LP r tE r tE r tc t t

µ ∂∂∇×∇× + = −

∂ ∂

( )

We now introduce the Fourier transform: ( , )

( , ) ( )

i t

-k

k

c t t

E r E(r,t)e dt

E r t i E r

ωω

ω ω

+∞

∞

∂ ∂

=

∂⇔

∫%

%( )2

(1) 20 02

( , )

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

k i E rt

E r E r E rc

ω ω

ωω ω µ ε χ ω ω ω

⇔∂

∇×∇× − = +% % %

which can be rec

22 (1)

0 02

written as

( , ) 1 ( ) ( , ) 0E r c E rcωω µ ε χ ω ω⎡ ⎤∇×∇× − + =⎣ ⎦

% %

2

2i.e. ( , ) ( ) ( , ) 0

c

E r E rcωω ε ω ω

⎣ ⎦

∇×∇× − =% %

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Theory of Propagation in Optical Fiber

ε(ω) = n + i αc⎡ ⎣⎢

⎤ ⎦⎥

2

with n =1+1

ℜ χ (1)(ω)[ ] f ti i dε(ω) n + i2ω⎣ ⎢ ⎦ ⎥ with n 1+

2ℜ χ (ω)[ ]

and α =ω

cn(ω)ℑ χ (1)(ω)[ ]

n: refractive indexα: absorption

∇ × ∇ × ˜ E (r,ω) = ∇ ∇ ⋅ ˜ E (r,ω)( )− ∇2 ˜ E (r,ω) = −∇2 ˜ E (r,ω)

∇ ⋅ ˜ E (r,ω) ∝∇ ⋅ ˜ D (r,ω) = 0( )

∇2 ˜ E (r,ω) + n2 ω 2

c 2˜ E (r,ω) = 0 : Helmoltz Equation!

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Each components of E(x,y,z,t)=U(x,y,z)ejωt must satisfy the Helmoltz equationn = n1 for r ≤ a⎧

⎪

Assumption: the cladding radius is infinite

∇2U + n2k02U = 0 with

1

n = n2 for r > ak0 = 2π /λ

⎨ ⎪

⎩ ⎪ Note: λ=ω /c

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

∂2U+

1 ∂U+

1 ∂2U+

∂2U+ n2k 2U 0 with

n = n1 for r ≤ an n for r > a

⎧

⎨ ⎪

∂r2 +

r ∂r+

r2 ∂ϕ 2 +∂z2 + n k0 U = 0 with n = n2 for r > a

k0 = 2π /λ0

⎨

⎩ ⎪

x Er φ

yz

Ez

Eφ

rφ

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

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

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

⎪⎨

⎧>=≤=

=⎞

⎜⎜⎛

−−++ 2

1222

02

2

01 β arnnarnn

FlkndFFd for for

with

:gets one Eq. Helmoltz the into Plugging

⎪⎩

⎨=

>⎠

⎜⎜⎝

++

00

2202

/20

λπβ

karnnF

rkn

drrdrfor with

One can define an effective index of refraction n β = k is the

One can define an effective index of refraction neff

such that β =ωc

neff , n2 < neff < n1

β = k0 neff is the propagation

constant

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A light wave is guided only if 0102 knkn ≤≤ β2 ( )2 2

We introduceκ 2 = n1k0( )2 − β 2

γ 2 = β 2 − n2k0( )2

κ 2 + γ 2 k 2 n2 n2( ) k 2NA2 : constant!

Note : κ 2,γ 2 ≥ 0 κ,γ :real

We then get :

κ + γ = k0 n1 − n2( )= k0 NA : constant!

We then get :

d2Fdr2 +

1r

dFdr

+ κ 2 −l2

r2

⎛

⎝ ⎜

⎞

⎠ ⎟ F = 0 for r ≤ a

d2Fdr2 +

1r

dFdr

− γ 2 +l2

r2

⎛

⎝ ⎜

⎞

⎠ ⎟ F = 0 for r > a

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:form theof are equations theof solutions The( )

( )KFlJ

arJrF

l

ll

f)(order with kind 1 offunction Bessel :

for )(st

>

≤= ρκ

( )lK

arKrF

l

ll

order with kind 1 offunction Bessel Modified :

for )(st

>= ργ

with

κ 2 = n1k0( )2 − β 2

2 β 2 k( )2

γ 2 = β 2 − n2k0( )2

κ 2 + γ 2 = k02 n1

2 − n22( )= k0

2NA2 : constant!

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Examples

l=0 l=3

a a

K0(γr)J0(κr)K0(γr) K3(γr)J3(κr)K3(γr)

a

r

r

J0(κr) for r ≤ a⎧ ⎨

J3(κr) for r ≤ a⎧ ⎨

F(r) ∝

J0(κr) for r ≤ aK0(γr) for r < a

⎧ ⎨ ⎩

F(r) ∝J3(κr) for r ≤ aK3(γr) for r < a

⎧ ⎨ ⎩

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Characteristic Equation

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

β solvingbyfoundbecanconstantnpropagatioThe

g p p g β ( q )

β

β

lKJnKJ lmllll⎥⎤

⎢⎡ +=⎥

⎤⎢⎡ Γ

+Κ

×⎥⎤

⎢⎡ Γ

+Κ 11)()()()(

:equation sticcharacteri thesolvingby foundbecan constant n propagatio The

222''21

''

γκ aaknKJnKJ llll

=Γ=Κ

⎥⎦⎢⎣ Γ+

Κ=⎥

⎦⎢⎣ ΓΓ

+ΚΚ

×⎥⎦

⎢⎣ ΓΓ

+ΚΚ

and with )()()()( 222

022

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

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Number of Modes Supported by an Optical FiberSolution of the characteristics equation U(r,φ,z)=F(r)e-jlϕe-jβlmz iscalled a mode, each mode corresponds to a particularelectromagnetic field pattern of radiationg p

The modes are labeled LPlm

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

2 aπ

M is an increasing function of V !

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210

2 nnaNAakV −==λπ

M is an increasing function of V !

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

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g

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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 0

Example:2 50

1.0LP01

0.821

020 6

LP11

2a =50 µmn1 =1.46 V=17.6δ=0.005 M=155λ=1 3 µm

core

020.631 12 41

220.4 3261

51 1303 23

21

2

nnnneff

−

−

λ=1.3 µm23420.2 7104

528133

0 2 4 6 8 10 12V

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

V

30cladding

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

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

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Cut-Off Wavelength

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

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

2= β2(λ)-4π2

n22/λ2=0

There exists a wavelength λc above which only the fundamental mode LP01 can propagate01 p p g

δδπλ 11 84.12405.22405.2 ananV C ==⇔<

Example:2a =9.2 µm

δλ

δλ

π 11

54.02405.2ly equivalentor

405.2

nna cc ==

n1 =1.4690δ=0.0024λc~1.2 µm

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Single-Mode Guidance

In a single-mode fiber, for wavelengths λ >λc~1.26 µm only the LP01 mode can propagate

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Mode Field Diameter

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

)(

2

0CeF w=⎟⎟⎠

⎞⎜⎜⎝

⎛−

ρ

ρ

4221f879.2619.1650

from obtained is size mode for theion approximat goodA size mode the andconstant a is where

)(

0

V

wCCeF

<<⎞⎜⎛ ++

=ρ

42for )ln(

4221for 65.0

0

62/30

.VV

aw

.V.VV

aw

>=

<<⎠⎞

⎜⎝⎛ ++=

35Fiber Optics Communication Technology-Mynbaev & Scheiner

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Types of Optical Fibers

Step-index single-mode

n2Cladding diameter

125 µmCore diameter

from 8 to 10 µm n1

nn1Refractive index profile

δ = 0.001n2

n1

r

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Step-index multimode

n2Cladding diameterfrom 125 to 400 µm

Core diameterfrom 50 to 200 µm n1


δ = 0.01n2

n1

r

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Graded-index multimode

n2Cladding diameterfrom 125 to 140 µm

Core diameterfrom 50 to 100 µm n1


n2

n1

r

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AttenuationSignal attenuation in optical fibers results form 3 phenomena:

AbsorptionScatteringScatteringBending

Loss coefficient: αα

343410l10⎞

⎜⎛

= −

LLP

ePP

Out

LinOut

α depends on wavelengthααα

αα

343.4 :dB/km of unitsin expressedusually is

343.4)10ln(

log10

dB

10

=

−=−=⎠

⎜⎜⎝

LLPin

Out

α depends on wavelength

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

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Scattering and AbsorptionShort wavelength: Rayleigh scattering

induced by inhomogeneity of the f i i d d i l

41st window 2nd 3rd

820 nm 1 3 µm 1 55 µmrefractive index and proportional to 1/λ4

820 nm 1.3 µm 1.55 µm2IR absorption

1.00.8 Rayleigh

W t kscattering

AbsorptionInfrared bandUltraviolet band

Water peaks0.4

α ∝1/λ4

0.2UV absorption

3 Transmission windows820 nm

0.1 0.8 1.0 1.2 1.4 1.6 1.8Wavelength (µm)

820 nm1300 nm1550 nm

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Macrobending Losses

Macrodending losses are caused by the bending of fiber

Bending of fiber affects the condition θ < θC

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

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Microbending Losses

Microdending losses are caused by the rugosity of fiber

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

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Attenuation: Single-mode vs. Multimode Fiber

4

2 MMFFundamental mode

Hi h d d

MMF1

0.4 SMFHigher order mode

0.2

0.10.8 1.0 1.2 1.4 1.6 1.8

Light in higher-order modes travels longer optical paths

Wavelength (µm)0.8 1.0 1.2 1.4 1.6 1.8

Multimode fiber attenuates more than single-mode fiber

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Dispersion

What is dispersion?Power of a pulse travelling though a fiber is dispersed in timeDifferent spectral components of signal travel at different speedsResults from different phenomena

C f di i l d i iConsequences of dispersion: pulses spread in time

t t

3 Types of dispersion: Inter-modal dispersion (in multimode fibers)

t t

Intra-modal dispersion (in multimode and single-mode fibers)Polarization mode dispersion (in single-mode fibers)

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Dispersion in Multimode Fibers (inter-modal)

Input pulse

Input pulseOutput pulse

Input pulse

tt t

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

Inter-modal dispersion limits the transmission capacity

The maximum temporal spreading tolerated is 1/2 bit period

The limit is usually expressed in terms of bit rate x distance

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

Slowest ray is incident at the critical angle

LLTT∆T

SLOWFAST

FASTSLOW −=n2

Slowest ray is incident at the critical angle

ncvv

vLand T

vLwith T

SLOWFAST

SLOW

SLOWSLOW

FAST

FASTFAST

1

==

==n1 θcθ

Slow ray Fast ray

Lnn

θL

θπL

θLL

LL

CSLOW

FAST

2

1

1

sincos==

⎞⎜⎛

==

=

Lθ C 2s

2coscos

⎠⎞

⎜⎝⎛ −

δcL

nn

nn

cL

nnL

cnnL

cn∆T

2

212

2

21

2

211

11 =⎥⎦

⎤⎢⎣⎡ −=−=

sin

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Dispersion in Multimode Fibers

1 ratebit If sbB ⋅= −

2 121 havemust We

nLB

T <∆

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

22

2

1

or

21 i.e.

cnBL

Bnn

cL

<×

<δp 1

212nδ

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

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Dispersion in graded-index Multimode Fibers

Input pulse

Input pulseOutput pulse

Input pulse

t

Fast mode travels a longer physical path

t t

Temporal spreading

Slow mode travels a shorter physical path

Temporal spreadingis small

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

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Intra-modal Dispersion

In a medium of index n, a signal pulse travels at the groupvelocity νg defined as: 12 −

⎞⎜⎛ βλω ddg

Intra-modal dispersion results from 2 phenomena

2 ⎟⎠

⎞⎜⎜⎝

⎛−==

λβ

πλ

βω

dd

cddvg

Material dispersion (also called chromatic dispersion)Waveguide dispersion

Different spectral components of signal travel at different speedsDifferent 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 × Lp g p p

kmps/nm of unitsin 2

12

22

modalIntra ×−=⎟⎟⎠

⎞⎜⎜⎝

⎛=− λ

βπλ

λ dd

cvddD

g

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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, λ1

t

Input pulse, λ2 t

t

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Material Dispersion

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

1)( 223

23

222

22

221

21

−+

−+

−+=

λλλ

λλλ

λλλλ AAAn

nm9896.1610.8974794,nm 116.2414 0.4079426, nm 68.4043 0.6961663,with

33

22

11

======

λλλ

AA

A

nm9896.161 0.8974794, 33 λA

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52

Material Dispersion

λλλβ

πλ

ddnnc

dd

cvg /2

12

−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

−

λ1 λ2

∆λ ⎠⎝

Input pulse, λ1

λ

∆λ

∆Tp p 1

t t

LInput pulse, λ2

tt

2

21λ

λλλ

λλd

ndcL

vddLDLT

g

∆−=⎟⎟⎠

⎞⎜⎜⎝

⎛∆=∆=∆

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Material Dispersionm

)

0

km)ps/nm :(units 2

2

Material ×−=λ

λd

ndDps/n

m/k

m 0-200-400600 2λdc

Mat

eria

l(p -600

-800-1000

[email protected] µm

DM

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Wavelength (µm)

Material 0@ µ

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Waveguide Dispersion

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

⎟⎠⎞

⎜⎝⎛ ++= 62/30

879.2619.165.0VV

aw

λ1 λ2>λ1

Consequence: 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 theis where2

102

02Waveguide w

wdd

ncvddD

g⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟

⎟⎠

⎞⎜⎜⎝

⎛=

λλπ

λλ

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Total Dispersion

DIntra−modal = DMaterial + DWaveguide

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

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

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Tuning Dispersion

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

20

n2n2

10Single-mode Fiber

n1

Single-mode Fiber

n1

Dispersion shifted Fiber0

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

-10 1.3 1.4 1.5Wavelength (µm)

Dispersion shifted Fiber

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57

Dispersion Related Parameters

s/km ofunitsin delay group:11ββ

ωβ

==

=

d

nc eff

21

yg p

2211

modalIntra

1

λπβ

λω

ωβ

λβ

λ

βω

⎟⎠⎞

⎜⎝⎛−===⎟

⎟⎠

⎞⎜⎜⎝

⎛=−

cdd

dd

dd

vddD

dv

g

g

/kms of unitsin parameter dispersion velocity group: 22β

λλωλλ ⎠⎝⎠⎝ dddvd g

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Polarization Mode Dispersion

Optical fibers are not perfectly circular

x

y

x

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

Causes broadening of signal pulse

LDvv

LTgygx

onPolarizati11

≈−=∆

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

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

2

onPolarizati

2

modal-Intra

2

Intermodal

TTTT ∆+∆+∆=∆

( ) ( )

( ) ( )2onPolarizati2

modalIntra

2modalIntra

2modalInter

:Fiber Mode-Single

:Fiber Multimode

LDLDT

LDLDT

×+×∆×=∆

×∆×+×=∆

−

−−

λ

λ

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

Consider a DFB laser operating @ 1.5 µm ∆λ =.2 nm after L=100 km, ∆T=0.34 ns!DIntra-modal =17 ps/nm×km

DPolarization=0.5 ps/ √km

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Effects of Dispersion: Capacity Limitation

Capacity limitation: maximum broadening<1/2f a bit period

λ∆∆

<∆

FibM dSi lF21

LDTB

T

λ

<⇒

∆≈∆ −modalIntra

1effects)on polarizati g(neglectin

Fiber,Mode-SingleFor

LB

LDT

λ∆−modalIntra2D

Example: Consider a DFB laser operating @ 1 55 µmExample: Consider a DFB laser operating @ 1.55 µm∆λ =0.2 nm LB<150 Gb/s ×kmD =17 ps/nm×km If L=100 km, BMax=1.5 Gb/s

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Advantage of Single-Mode Fibers

No intermodal dispersion

Lower attenuation

No interferences between multiple modesp

Easier Input/output coupling

Single-mode fibers are used in long transmission systems

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Summary

Attractive characteristics of optical fibers:

Low transmission loss

Enormous bandwidth

Immune to electromagnetic noise

Low costLow cost

Light weight and small dimensions

Strong, flexible material

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SummaryImportant parameters:

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

M lti d fibMultimode fiberUsed in local area networks (LANs) / metropolitan area networks (MANs) Capacity limited by inter-modal dispersion: typically 20 Mb/s x km f i d d 2 Gb/ k f d d i dfor step index and 2 Gb/s x km for graded index

Single-mode fiberUsed for short/long distancesUsed for short/long distancesCapacity limited by dispersion: typically 150 Gb/s x km

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Introduction and Light Propagation in Optical Fibers 17.03...

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