Introduction and Light Propagation in Optical Fibers 17.03 ... · Fiber-Optic Components I (31.03)...
Transcript of Introduction and Light Propagation in Optical Fibers 17.03 ... · Fiber-Optic Components I (31.03)...
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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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Theory of Light Propagation in Optical Fiber
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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Theory of Light Propagation in Optical Fiber
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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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Theory of Light Propagation in Optical Fiber
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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Theory of Light Propagation in Optical Fiber
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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Theory of Propagation in Optical Fiber
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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Theory of Propagation in Optical Fiber
: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
22
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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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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Types of Optical Fibers
Step-index multimode
n2Cladding diameterfrom 125 to 400 µm
Core diameterfrom 50 to 200 µm n1
nn1Refractive index profile
δ = 0.01n2
n1
r
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Types of Optical Fibers
Graded-index multimode
n2Cladding diameterfrom 125 to 140 µm
Core diameterfrom 50 to 100 µm n1
nn1Refractive index profile
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
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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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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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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
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
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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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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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