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Fiber-Optic Communication Systems
Govind P. AgrawalInstitute of OpticsUniversity of RochesterRochester, NY 14627email: [email protected]
c©2003 G. P. Agrawal
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Course Outline
• Introduction
• Fiber Loss, Dispersion, and Nonlinearities
• Receiver Noise and Bit Error Rate
• System Design and Performance
• Loss Management: Optical Amplifiers
• Dispersion Management
•Multichannel Lightwave Systems
• Optical Solitons
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Historical Perspective
• Smoke signals; <1500
• Semaphore Devices; 1500-1800
•Mechanical Coding (Chappe); 1792
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Historical PerspectiveElectrical Era
• Telegraph; 1836
• Telephone; 1876
• Coaxial Cables; 1840
• Microwaves; 1948
Optical Era
• Optical Fibers; 1978
• Optical Amplifiers; 1990
• WDM Technology; 1996
• Multiple bands; 2002
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Communication Technologies
Performance criterion: B×L
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Information Revolution• Industrial revolution of 19th century gave way to
information revolution during the 1990s.
• Internet made the rapid distribution of information possible.
• Fiber-Optic Revolution is a natural consequence of the
Internet growth .
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Five Generations1. 0.8-µm systems (1980); Graded-index fibers
2. 1.3-µm systems (1985); Single-mode fibers
3. 1.55-µm systems (1990); Single-mode lasers
4. WDM systems (1996); Optical amplifiers
5. L and S bands (2001); Raman amplification
1980 1985 1990 1995 2000 2005Year
0.01
0.1
1
10
100
1000
10000
Bit
Rat
e (G
b/s) Research
Commercial
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Basic ConceptsAnalog and Digital Signals
• Lightwave Systems use digital format.
• Optical signal is a stream of 0 and 1 bits.
• Bit rate B determines the time slot TB = 1/B for each bit.
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Analog to Digital Conversion
• Sampling: fs≥ 2∆ f (sampling theorem).
• Quantization: M > Amax/AN (error < noise).
• Coding: M = 2m; m bits/sample (Binary coding).
• Bit rate : B = m fs≥ (2∆ f ) log2M > (∆ f/3)SNR.
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Audio and Video SignalsDigital Audio Signal
• ∆ f = 3.1 kHz (0.3 to 3.4 kHz); SNR = 30 dB.
• Minimum B = (∆ f/3)SNR = 31 kb/s.
• In practice, B = 64 kb/s ( fs = 8 kHz; 8 bits/sample).
Digital Video Signal
• ∆ f = 4 MHz; SNR = 50 dB.
• Minimum B = (∆ f/3)SNR = 66 Mb/s.
• In practice, B = 100Mb/s ( fs = 10 MHz; 10 bits/sample).
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Channel MultiplexingTDM : Time-division multiplexing
FDM : Frequency-division multiplexing
Optical FDM = WDM (wavelength-division multiplexing)
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Evolution of Standards• No standards until 1988.
• US standard: synchronous optical network(SONET).
• ITU standard: synchronous digital hierarchy(SDH).
SONET SDH B (Mb/s) Channels
OC-1 51.84 672
OC-3 STM-1 155.52 2,016
OC-12 STM-4 622.08 8,064
OC-48 STM-16 2,488.32 32,256
OC-192 STM-64 9,953.28 129,024
OC-768 STM-256 39,813.12 516,096
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Modulation FormatsOptical Carrier
E(t) = eAcos(ω0t +φ)
• Amplitude-shift keying (ASK): modulate A
• Frequency-shift keying (FSK): modulate ω0
• Phase-shift keying (PSK): modulate φ
• Polarization-shift keying (PoSK): modulate e
Most lightwave systems employ ASK;
also called on–of keying (OOK) or
Intensity modulation with Direct Detection (IM/DD)
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Optical Bit Stream• Return-to-zero (RZ)
• nonreturn-to-zero (NRZ)
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Lightwave System ComponentsGeneric System
Transmitter Design
Receiver Design
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Optical Fibers• Most suitable as communication channel because of dielectric waveg-
uiding (acts like an optical wire).
• Total internal reflection at the core-cladding interface.
• Single-mode propagation for core size < 10 µm.
What happens to Signal?
• Fiber losseslimit the transmission distance (minimum loss near
1.55 µm).
• Chromatic dispersion limits the bit rate through pulse broadening.
• Nonlinear effects distort the signal and limit the system perfor-
mance.
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Fiber Fundamentals
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Total internal reflection• Refraction at the air–glass interface: n0sinθi = n1sinθr
• Total internal reflection at the core-cladding interface
if φ > φc = sin−1(n2/n1).
Numerical Aperture: Maximum angle of incidence
n0sinθmaxi = n1sin(π/2−φc) = n1cosφc =
√n2
1−n22
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Modal Dispersion• Multimode fibers suffer from modal dispersion.
• Shortest path length Lmin = L (along the fiber axis).
• Longest path length for the ray close to the critical angle
Lmax = L/sinφc = L(n1/n2).
• Pulse broadening: ∆T = (Lmax−Lmin)(n1/c).
• Modal dispersion: ∆T/L = n21∆/(n2c).
• Limitation on the bit rate
∆T < TB = 1/B; B∆T < 1; BL <n2c
n21∆
.
• Single-mode fibersessential for high performance.
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Graded-Index Fibers
• Refractive index n(ρ) =
n1[1−∆(ρ/a)α ]; ρ < a,
n1(1−∆) = n2 ; ρ ≥ a.
• Ray path obtained by solving d2ρ
dz2= 1
ndndρ
.
• For α = 2, ρ = ρ0cos(pz)+(ρ ′0/p)sin(pz).
• All rays arrive simultaneouslyat periodic intervals.
• Limitation on the Bit Rate: BL < 8cn1∆2.
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Fiber Modes• Shape-preserving solutions of Maxwell’s equations
∇×E =−∂B/∂ t
∇×H = ∂D/∂ t
∇ ·D = 0
∇ ·B = 0
• Constitutive Relations
D = ε0E+P
B = µ0H +M
• Linear Susceptibility
P(r , t) = ε0
∫ ∞
−∞χ(r , t− t ′)E(r , t ′)dt′
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Fiber Modes (cont.)• It is easier to work in the Fourier domain:
E(r ,ω) =∫ ∞
−∞E(r , t)exp(iωt)dt
• Helmholtz Equation: Each frequency component satisfies
∇2E+n2(ω)k20E = 0.
k0 = ω/c = 2π/λ , n(ω) = (1+Reχ)1/2.
• n = n1 inside the core but changes to n2 in the cladding.
• Frequency dependence of n responsible for dispersion.
• Material absorption governed by Im χ .
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Fiber Modes (cont.)• Any solution must satisfy boundary conditions at the
core–cladding interface (x2+y2 = a2).
• Useful to work with cylindrical coordinates ρ,φ ,z.
• Only two components of E and H are independent.
• Common to choose Ez and Hz as independent components.
• Equation for Ez in cylindrical coordinates:
∂ 2Ez
∂ρ2+
1ρ
∂Ez
∂ρ+
1ρ2
∂ 2Ez
∂φ 2+
∂ 2Ez
∂z2+n2k2
0Ez = 0.
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Fiber Modes (cont.)• Use the method of separation of variables:
Ez(ρ,φ ,z) = F(ρ)Φ(φ)Z(z).
• We then obtain three ODEs:
d2Z/dz2+β2Z = 0,
d2Φ/dφ2+m2Φ = 0,
d2Fdρ2
+1ρ
dFdρ
+(
n2k20−β
2−m2
ρ2
)F = 0.
• β and m are two constants (m must be an integer).
• First two equations can be solved easily to obtain
Z = exp(iβz), Φ = exp(imφ).
• F(ρ) satisfies the Bessel equation.
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Fiber Modes (cont.)• General solution for Ez and Hz:
Ez =
AJm(pρ)exp(imφ)exp(iβz) ; ρ ≤ a,
CKm(qρ)exp(imφ)exp(iβz); ρ > a.
Hz =
BJm(pρ)exp(imφ)exp(iβz) ; ρ ≤ a,
DKm(qρ)exp(imφ)exp(iβz); ρ > a.
where p2 = n21k
20−β 2, q2 = β 2−n2
2k20.
• Boundary conditions: Ez, Hz, Eφ , and Hφ should be continuous
across the core–cladding inteface (ρ = a).
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Fiber Modes (cont.)Eigenvalue Equation[
J′m(pa)pJm(pa)
+K′
m(qa)qKm(qa)
][J′m(pa)pJm(pa)
+n2
2
n21
K′m(qa)
qKm(qa)
]
=m2
a2
(1p2
+1q2
)(1p2
+n2
2
n21
1q2
)where p2 = n2
1k20−β 2 and q2 = β 2−n2
2k20.
• This equation should be solved numerically.
• Multiple solutions for β for a given fiber.
• Each solution represents an optical mode.
• Number of modes governed by V = k0a√
n21−n2
2.
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Fiber Modes (cont.)
• Effective mode indexn = β/k0 between n1 and n2.
• Useful to introduce a normalized quantity
b = (n−n2)/(n1−n2), (0 < b < 1).
• Modes quantified through β (ω) or b(V).
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Single-Mode Condition• Modes denoted as HEmn or EHmn, where n = 1,2, . . . in decreasing
order of the eigenvalues βmn.
• Also labelled as TE0n and TM0n for m= 0.
• Number of modes increases rapidly with V paprameter.
• A mode ceases to exist when q = 0 (no decay in the cladding).
• TE01 and TM01 reach cutoff when J0(V) = 0.
• Single-mode fibersrequire V < 2.405.
• Typically core radius a < 5 µm and n1−n2 < 0.005.
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Single-Mode Fibers• Fibers support only the HE11 mode when the core size is such that
V = k0a(n21−n2
2) < 2.405.
• This mode is almost linearly polarized (|Ez|2 |ET|2).
• Spatial mode distribution approximately Gaussian
Ex(x,y,z,ω) = A0(ω)exp
(−x2+y2
w2
)exp[iβ (ω)z].
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Single-Mode Properties• Spot size: w/a≈ 0.65+1.619V−3/2+2.879V−6.
• Mode index:
n = n2+b(n1−n2)≈ n2(1+b∆),
b(V)≈ (1.1428−0.9960/V)2.
• Confinement factor:
Γ =Pcore
Ptotal=∫ a
0 |Ex|2ρ dρ∫ ∞0 |Ex|2ρ dρ
= 1−exp
(−2a2
w2
).
• Γ≈ 0.8 for V = 2 but drops to 0.2 for V = 1.
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Fiber Birefringence• Real fibers exhibit some birefringence (nx 6= ny).
• Modal birefringence quite small (Bm = |nx− ny| ∼ 10−6).
• Beat length: LB = λ/Bm.
• State of polarization evolves periodically.
• Birefringence varies randomly along fiber length (PMD) because
of stress and core-size variations.
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Fiber DispersionOrigin: Frequency dependence of the mode index n(ω):
β (ω) = n(ω)ω/c = β0+β1(ω−ω0)+β2(ω−ω0)2+ · · · ,
where ω0 is the carrier frequency of the optical pulse.
• Transit time for a fiber of length L : T = L/vg = β1L.
• Different frequency components travel at different speeds and arrive
at different times at output end (pulse broadening).
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Fiber Dispersion (continued)Pulse broadening governed by group-velocity dispersion:
∆T =dTdω
∆ω =d
dω
Lvg
∆ω = Ldβ1
dω∆ω = Lβ2∆ω,
where ∆ω is pulse bandwidth and L is fiber length.
GVD parameter: β2 =(
d2β
dω2
)ω=ω0
.
Alternate definition : D = ddλ
(1vg
)=−2πc
λ 2 β2.
Limitation on the bit rate : ∆T < TB = 1/B, or
B(∆T) = BLβ2∆ω ≡ BLD∆λ < 1.
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Material Dispersion• Refractive index of of any material is frequency dependent (chro-
matic dispersion).
• Material dispersion for silica is governed by the Sellmeier equation
n2(ω) = 1+M
∑j=1
B jω2j
ω2j −ω2
.
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Waveguide Dispersion• Mode index n(ω) = n2(ω)+δnW(ω).
• Material dispersion DM results from n2(ω) (silica index).
• Waveguide dispersion DW results from δnW(ω) and depends on
core sizeand dopant distribution .
• Total dispersion D = DM +DW can be controlled.
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Higher-Order Dispersion• dispersive effects do not disappear at λ = λZD.
• D cannot be made zero at all frequencies within the pulse spectrum.
• Higher-order dispersive effects are governed by the dispersion slopeS= dD/dλ .
• S can be related to third-oder dispersion β3 as
S= (2πc/λ2)2
β3+(4πc/λ3)β2.
• At λ = λZD, β2 = 0, and S is proportional to β3.
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Polarization-Mode Dispersion• Real fibers exhibit some birefringence (nx 6= ny).
• Orthogonally polarized components of a pulse travel at different
speeds. The relative delay is given by
∆T =∣∣∣∣ Lvgx− L
vgy
∣∣∣∣= L|β1x−β1y|= L(∆β1).
• Birefringence varies randomly along fiber length (PMD) because
of stress and core-size variations.
• RMS Pulse broadening :
σT ≈ (∆β1)√
2lcL≡ Dp
√L.
• PMD parameter Dp∼ 0.01–10 ps/√
km
• PMD can degrade the system performance considerably (especially
for old fibers).
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Commercial Fibers
Fiber Type and Aeff λZD D (C band) SlopeSTrade Name (µm2) (nm) ps/(km-nm) ps/(km-nm2)Corning SMF-28 80 1302–1322 16 to 19 0.090Lucent AllWave 80 1300–1322 17 to 20 0.088Alcatel ColorLock 80 1300–1320 16 to 19 0.090Corning Vascade 101 1300–1310 18 to 20 0.060TrueWave-RS 50 1470–1490 2.6 to 6 0.050Corning LEAF 72 1490–1500 2 to 6 0.060TrueWave-XL 72 1570–1580 −1.4 to−4.6 0.112Alcatel TeraLight 65 1440–1450 5.5 to 10 0.058
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Pulse Propagation Equation• Optical Field at frequency ω at z= 0:
E(r ,ω) = xF(x,y)B(0,ω)exp(iβz).
• Optical field at a distance z:
B(z,ω) = B(0,ω)exp(iβz).
• Expand β (ω) is a Taylor series around ω0:
β (ω) = n(ω)ω
c≈ β0+β1(∆ω)+
β2
2(∆ω)2+
β3
6(∆ω)3.
• Introduce Pulse envelope:
B(z, t) = A(z, t)exp[i(β0z−ω0t)].
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Pulse Propagation Equation• Pulse envelope is obtained using
A(z, t) =1
2π
∫ ∞
−∞d(∆ω)A(0,∆ω)exp
[iβ1z∆ω +
i2
β2z(∆ω)2 +i6
β3z(∆ω)3− i(∆ω)t].
• Calculate ∂A/∂z and convert to time domain by replacing
∆ω with i(∂A/∂ t).
• Final equation:
∂A∂z
+β1∂A∂ t
+iβ2
2∂ 2A∂ t2
− β3
6∂ 3A∂ t3
= 0.
• With the transformation t ′ = t−β1z and z′ = z, it reduces to
∂A∂z′
+iβ2
2∂ 2A∂ t ′2
− β3
6∂ 3A∂ t ′3
= 0.
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Pulse Propagation Equation• If we neglect third-order dispersion, pulse evolution is governed by
∂A∂z
+iβ2
2∂ 2A∂ t2
= 0.
• Compare with the paraxial equation governing diffraction:
2ik∂A∂z
+∂ 2A∂x2
= 0.
• Slit-diffraction problem identical to pulse propagation problem.
• The only difference is that β2 can be positive or negative.
• Many results from diffraction theory can be used for pulses.
• A Gaussian pulse should spread but remain Gaussian in shape.
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Pulse BroadeningChirped Gaussian Pulse
A(0, t) = A0exp
[−(1+ iC)t2
2T20
].
• Input pulse width TFWHM = 2(ln2)1/2T0≈ 1.665T0.
• Input chirp : δω(t) =−∂φ
∂ t = CT2
0t.
• Pulse spectrum
A(0,ω) = A0
(2πT2
0
1+ iC
)1/2
exp
[− ω2T2
0
2(1+ iC)
]• Spectral width: ∆ω0 =
√1+C2/T0.
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Pulse Broadening (cont.)Optical Pulse after propagation (β3 = 0):
A(z, t) =A0√Q(z)
exp
[−(1+ iC)t2
2T20 Q(z)
], Q(z) = 1+(C− i)
β2z
T20
.
• Pulse maintains its Gaussian shape.
• Its chirp changes to C1(z) = C+(1+C2)β2z/T20 .
• Its width is given by
T1
T0=
[(1+
Cβ2z
T20
)2
+(
β2z
T20
)2]1/2
.
• Unchirped pulse broadens by a factor√
1+(z/LD)2.
• LD = T20 /|β2| is called the dispersion length.
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Effect of Chirp
• Broadening depends on the sign of β2C.
• Pulse compressesinitially if β2C < 0.
• Pulse becomes shortest and unchirped at a certain distance:
zmin =[|C|/(1+C2)
]LD, Tmin
1 = T0/(1+C2)1/2.
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Third-Order Dispersion• When β2 = 0, pulse broadening depends on β3.
• Analytic solution exists in terms of an Airy function.
• Pulse does not maintain its Gaussian shapeand develops consid-
erable structure (subpulses near an edge).
• A proper measure of the pulse width is the RMS width defined as
σ =[< t2 >−< t >2
]1/2,
< tm >=∫ ∞−∞ tm|A(z, t)|2dt∫ ∞−∞ |A(z, t)|2dt
.
• Broadening factor:
σ2
σ20
=(
1+Cβ2L
2σ20
)2
+(
β2L
2σ20
)2
+(1+C2)2
(β3L
4√
2σ30
)2
.
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Source Spectral Width• Source spectral width can exceed pulse spectral width when a low-
coherence source (LED) is used.
• Introduce a parameter Vω = 2(∆ωs)σ0 for a source with Gaussian
spectrum of RMS width ∆ωs.
• RMS pulse width then increases as
σ2
σ20
=(
1+Cβ2L
2σ20
)2
+(1+V2ω)(
β2L
2σ20
)2
+(1+C2+V2ω)2
(β3L
4√
2σ30
)2
.
• Quite useful for analyzing the GVD effects.
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Dispersion LimitationsLarge Source Spectral Width: Vω 1
• Assume input pulse to be unchirped (C = 0).
• Set β3 = 0 when λ 6= λZD:
σ2 = σ
20 +(β2Lσω)2≡ σ
20 +(DLσλ)2.
• 96% of pulse energy remains within the bit slot if 4σ < TB = 1/B.
• Using 4Bσ ≤ 1, and σ σ0, BL|D|σλ ≤ 14.
• Set β2 = 0 when λ = λZD to obtain
σ2 = σ
20 + 1
2(β3Lσ2ω)2≡ σ2
0 + 12(SLσ2
λ)2.
• Dispersion limit: BL|S|σ2λ≤ 1/
√8.
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Dispersion LimitationsSmall Source Spectral Width: Vω 1
• When β3 = 0 and C = 0,
σ2 = σ
20 +(β2L/2σ0)2.
• One can minimize σ by adjusting input width σ0.
• Minimum occurs for σ0 = (|β2|L/2)1/2 and leads to σ = (|β2|L)1/2.
• Dispersion limit when β3 = 0:
B√|β2|L≤ 1
4.
• Dispersion limit when β2 = 0:
B(|β3|L)1/3≤ 0.324.
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Dispersion Limitations (cont.)
• Even a 1-nm spectral width limits BL < 0.1 (Gb/s)-km.
• DFB lasers essentialfor most lightwave systems.
• For B > 2.5 Gb/s, dispersion managementrequired.
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Dispersion Limitations (cont.)Effect of Frequency chirp
• Numerical simulations necessary for more realistic pulses.
• Super-Gaussian pulse shape often used: A(0,T)= A0exp
[−1+iC
2
(t
T0
)2m].
• Chirp can affect the system performance drastically.
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Fiber LossesDefinition: α(dB/km) =−10
L log10
(PoutPin
)≈ 4.343α .
• Material absorption (silica, impurities, dopants)
• Rayleigh scattering (varies as λ−4)
• Waveguide imperfections (macro and microbending)
DispersionConventional Fiber
Dry Fiber
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Major Nonlinear Effects• Stimulated Raman Scattering (SRS)
• Stimulated Brillouin Scattering (SBS)
• Self-Phase Modulation (SPM)
• Cross-Phase Modulation (XPM)
• Four-Wave Mixing (FWM)
Origin of Nonlinear Effects in Optical Fibers
• Ultrafast third-order susceptibility χ (3).
• Real part leads to SPM, XPM, and FWM.
• Imaginary part leads to SBS and SRS.
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Brillouin Scattering• Scattering of light from acoustic waves (electrostriction).
• Energy and momentum conservation laws require
ΩB = ωp−ωs and kA = kp−ks.
• Brillouin shift : ΩB = |kA|vA = 2vA|kp|sin(θ/2).
• only possibility θ = π for single-mode fibers (backward propagating
Stokes wave).
• Using kp = 2πn/λp, νB = ΩB/2π = 2nvA/λp.
• With vA = 5.96 km/s and n = 1.45, νB≈ 11 GHz near 1.55 µm.
• Stokes wave grows from noise.
• Not a very efficient process at low pump powers.
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Stimulated Brillouin Scattering• Becomes a stimulated process at high input power levels.
• Governed by two coupled equations:
dIpdz
=−gBIpIs−αpIp, −dIsdz
= +gBIpIs−αsIs.
• Brillouin gain has a narrow Lorentzian spectrum
(TB≈ 10 ns; ∆ν ∼ 20 MHz)
gB(Ω) =gB(ΩB)
1+(Ω−ΩB)2T2B
.
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SBS Threshold• Threshold condition: gBPthLeff/Aeff ≈ 21.
• Effective fiber length: Leff = [1−exp(−αL)]/α .
• Effective core area: Aeff ≈ 50–80 µm2.
• Peak Brillouin gain: gB≈ 5×10−11 m/W.
• Low threshold power for long fibers (∼5 mW).
• Most of the power reflected backward after SBS threshold.
Threshold can be increasedusing
• Phase modulation at frequencies >0.1 GHz.
• Sinusoidal strain along the fiber.
• Nonuniform core radius or dopant density.
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Stimulated Raman Scattering• Scattering of light from vibrating molecules.
• Scattered light shifted in frequency.
• Raman gain spectrum extends over 40 THz.
(a)
(b)
• Raman shift at Gain peak: ΩR = ωp−ωs∼ 13 THz).
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SRS Threshold• SRS governed by two coupled equations:
dIpdz
=−gRIpIs−αpIp,dIsdz
= gRIpIs−αsIs.
• Threshold condition: gRPthLeff/Aeff ≈ 16.
• Peak Raman gaingR≈ 6×10−14 m/W near 1.5 µm.
• Threshold power relatively large (∼ 0.6 W).
• SRS is not of concern for single-channel systems.
• Leads to interchannel crosstalk in WDM systems.
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Self-Phase Modulation• Refractive index depends on intensity as
n(ω, I) = nL(ω)+n2I(t).
• n2 = 2.6×10−20 m2/W for silica fibers.
• Propagation constant: β ′ = β +k0n2P/Aeff ≡ β + γP.
• Nonlinear parameter γ = 2πn2/(Aeffλ ).
• Leads to nonlinear Phase shift:
φNL =∫ L
0(β ′−β )dz=
∫ L
0γP(z)dz= γPinLeff.
• Optical field modifies its own phase (SPM).
• Phase shift varies with time for pulses (chirping).
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SPM-Induced Chirp
• Chirp depends on the pulse shape.
• Gaussian pulses (m= 1): Nearly linear chirp across the pulse.
• Super-Gaussian pulses (m= 1): Chirping only near pulse edges.
• In all cases, SPM leads to spectral broadening.
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Cross-Phase Modulation• Nonlinear refractive index seen by one wave depends on the
intensity of other copropagating channels.
• Nonlinear index for two channels:
∆nNL = n2(|A1|2+2|A2|2).
• Total nonlinear phase shift for multiple channels
φNLj = γLeff
(Pj +2 ∑
m6= j
Pm
).
• XPM induces a nonlinear coupling among channels.
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Nonlinear Schrodinger Equation• SPM and XPM effects can be included by adding a nonlinear term
to the equation used earlier for dispersive effects.
• This equation is known as the nonlinear Schrodinger equation:
∂A∂z
+iβ2
2∂ 2A∂ t2
= iγ|A|2A.
• Fibers with large Aeff help through reduced γ .
• New fiber: large effective-area fiber or LEAF .
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Four-Wave Mixing• FWM converts two photons from one or two pump beams into two
new frequency-shifted photons.
• Energy conservation: ω1+ω2 = ω3+ω4.
• Degenerate FWM: 2ω1 = ω3+ω4.
• Momentum conservation or phase matchingis required.
• FWM efficiency governed by phase mismatch:
∆ = β (ω3)+β (ω4)−β (ω1)−β (ω2).
• In the degenerate case (ω1 = ω2), ω3 = ω1+Ω, and ω4 = ω1−Ω.
• Expanding β in a Taylor series, ∆ = β2Ω2.
• FWM becomes important for dense WDM systems designed with
low β2 fibers.
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FWM: Good or Bad?• FWM leads to interchannel crosstalk in WDM systems.
• It can be avoided through dispersion management.
On the other hand . . .
FWM can be used beneficially for
• Parametric amplification
• Optical phase conjugation
• Demultiplexing of OTDM channels
• Wavelength conversion of WDM channels
• Supercontinuum generation
64/100
Fiber Design
• Core doped with GeO2; cladding with fluorine.
• Index profile rectangular for standard fibers.
• Triangular index profile for dispersion-shifted fibers.
• Raised or depressed cladding for dispersion control.
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Commercial FibersCorning SMF-28 λZD = 1.31 µm, D (1.55 µm) = 17 ps/(km-nm),
S = 0.09 ps/(km-nm2), α = 0.21 dB/km,
Aeff = 60 µm2, Dp > 0.2 ps/√
km.
Lucent TrueWave RS λZD = 1.45 µm, D (1.55 µm)
= 4.4 ps/(km-nm), S = 0.04 ps/(km-nm2), α = 0.205 dB/km,
Aeff = 55 µm2, Dp < 0.05 ps/√
km.
Corning LEAF λZD = 1.50 µm, D (1.55 µm) = 4.2 ps/(km-nm),
S = 0.085 ps/(km-nm2), α = 0.21 dB/km,
Aeff = 72 µm2, Dp < 0.07 ps/√
km.
Lucent AllWave λZD = 1.31 µm, D (1.55 µm) = 17 ps/(km-nm),
S = 0.09 ps/(km-nm2), α = 0.19 dB/km,
Aeff = 80 µm2, Dp < 0.05 ps/√
km.
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Fabrication MethodsTwo-Stage Fabrication
• preform: Length 1 m, diameter 2 cm; correct index profile.
• Preform drawn into fiber using a draw tower.
Preform Fabrication Techniques
• Modified chemical vapor deposition (MCVD).
• Outside vapor deposition (OVD).
• Vapor Axial deposition (VAD).
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Fiber Draw Tower
68/100
Fiber CablesLight-Duty Cables
Heavy-Duty Cables
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