Fiber Optic Communication Systems by Govind P Agrawal Solution Manual

Create your free account to read unlimited documents.

Govind agrawal's fiber optical communication

You are reading a preview.

Create your free account to continue reading.

Like this presentation? Why not share!

9 Likes
Statistics
Notes

Govind agrawal's fiber optical communication

1. 1/66 Fiber-Optic Communication Systems Govind P. Agrawal Institute of Optics University of Rochester email: gpa@optics.rochester.edu c 2007 G. P. Agrawal Back Close
2. Course Outline • Introduction, Modulation Formats 2/66 • Fiber Loss, Dispersion, and Nonlinearities • Receiver Noise and Bit Error Rate • Loss Management: Optical Ampliﬁers • Dispersion Management Techniques • Management of Nonlinear Eﬀects • WDM Lightwave Systems Back Close
3. Historical Perspective Electrical Era Optical Era 3/66 • Telegraph; 1836 • Optical Fibers; 1978 • Telephone; 1876 • Optical Ampliﬁers; 1990 • Coaxial Cables; 1840 • WDM Technology; 1996 • Microwaves; 1948 • Multiple bands; 2002 • Microwaves and coaxial cables limited to B ∼ 100 Mb/s. • Optical systems can operate at bit rate >10 Tb/s. • Improvement in system capacity is related to the high frequency of optical waves (∼200 THz at 1.5 µm). Back Close
4. Information Revolution • Industrial revolution of 19th century gave way to 4/66 information revolution during the 1990s. • Fiber-Optic Revolution is a natural consequence of the Internet growth. c 2004 TRG, PriMetrica, Inc. Back Close
5. Five Generations • 0.8-µm systems (1980); Graded-index ﬁbers 5/66 • 1.3-µm systems (1985); Single-mode ﬁbers • 1.55-µm systems (1990); Single-mode lasers • WDM systems (1996); Optical ampliﬁers • L and S bands (2002); Raman ampliﬁcation 10000 1000 R es earch B it R ate (G b/s ) 100 10 C ommercial 1 0.1 0.01 1980 1985 1990 1995 2000 2005 Y ear Back Close
6. Lightwave System Components Generic System 6/66 Electrical Electrical Input Optical Optical Output Communication Channel Transmitter Receiver Transmitter and Receiver Modules Driving Modulator Electrical Driving Demodulator Circuit Electronics Input Circuit Electronics Optical Optical Electrical Output Input Output Optical Optical Electrical Photodetector Source Modulator Demodulator Fiber-Optic Communication Channel Back Close
7. Modulation Formats Optical Carrier has the form 7/66 ˆ E(t) = eA cos(ω0t + φ ) • Amplitude-shift keying (ASK): modulate A • Frequency-shift keying (FSK): modulate ω0 • Phase-shift keying (PSK): modulate φ • Polarization-shift keying (PoSK): information encoded in the polar- ˆ ization state e of each bit (not practical for optical ﬁbers). Most lightwave systems employ ASK. ASK is also called on–of keying (OOK). Diﬀerential PSK (DPSK) is being studied in recent years. Back Close
8. Optical Bit Stream • Return-to-zero (RZ) 8/66 • nonreturn-to-zero (NRZ) Back Close
9. Bit-Stream Generation NRZ Data Clock 9/66 CW Data NRZ RZ NRZ-to-RZ DFB Laser Modulator Converter LiNbO3 Modulators Contacts CW Input NRZ Output MZI • Employ a Mach–Zehnder for PM to AM conversion. • RZ Duty Cycle is 50% or 33% depending on biasing. Back Close
10. Variants of RZ Format • Optical phase is changed selectively in addition to amplitude. 10/66 • Three-level or ternary codes: 1 0 −1 bits • CSRZ format: Phase of alternate bits is shifted by π. • Alternate-phase (AP-RZ): Phase shift of π/2 for alternate bits. • Alternate mark inversion: Phase of alternate 1 bits shifted by π. • Duobinary format: Phase shifted by π after odd number of zeros. • RZ-DPSK format: Information encoded in phase variations • Phase diﬀerence φk − φk−1 is changed by 0 or π depending on whether kth bit is a 0 or 1. Back Close
11. DPSK Transmitters and Receivers 11/66 • Two modulators used at the transmitter end; second modulator is called a "pulse carver." • A Mach–Zehnder interferometer employed at receiver to convert phase information into current variations. Back Close
12. Comparison of Signal Spectra 12/66 Back Close
13. Optical Fibers • Most suitable as communication channel because of dielectric 13/66 waveguiding (acts like an optical wire). • Total internal reﬂection at the core-cladding interface conﬁnes light to ﬁber core. • Single-mode propagation for core size < 10 µm. What happens to optical signal? • Fiber losses limit 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 performance. Back Close
14. Fiber Losses Pout Deﬁnition: α(dB/km) = − 10 log10 L Pin ≈ 4.343α. 14/66 • Material absorption (silica, impurities, dopants) • Rayleigh scattering (varies as λ −4) • Waveguide imperfections (macro and microbending) Conventional Fiber Dispersion Dry Fiber Back Close
15. Fiber Dispersion Origin: Frequency dependence of the mode index n(ω): 15/66 β (ω) = n(ω)ω/c = β0 + β1(ω − ω0) + β2(ω − ω0)2 + · · · , ¯ where ω0 is the carrier frequency of 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 the output end (pulse broadening). Back Close
16. Fiber Dispersion (continued) Pulse broadening governed by group-velocity dispersion: 16/66 dT d L dβ1 ∆T = ∆ω = ∆ω = L ∆ω = Lβ2∆ω, dω dω vg dω where ∆ω is pulse bandwidth and L is ﬁber length. d2β • GVD parameter: β2 = dω 2 . ω=ω0 1 d • Alternate deﬁnition: D = dλ vg = − 2πc β2. λ2 • Limitation on the bit rate: ∆T < TB = 1/B, or B(∆T ) = BLβ2∆ω ≡ BLD∆λ < 1. • Dispersion limits the BL product for any lightwave system. Back Close
17. Higher-Order Dispersion • Dispersive eﬀects do not disappear at λ = λZD. 17/66 • D cannot be made zero at all frequencies within the pulse spectrum. • Higher-order dispersive eﬀects are governed by the dispersion slope S = dD/dλ . • S can be related to third-order dispersion β3 as S = (2πc/λ 2)2β3 + (4πc/λ 3)β2. • At λ = λZD, β2 = 0, and S is proportional to β3. • Typical values: S ∼ 0.05–0.1 ps/(km-nm2). Back Close
18. Polarization-Mode Dispersion • Real ﬁbers exhibit some birefringence (nx = ny). ¯ ¯ 18/66 • Orthogonally polarized component travel at diﬀerent speeds. Relative delay for ﬁber of length L is given by L L ∆T = − = L|β1x − β1y| = L(∆β1). vgx vgy • Birefringence varies randomly along ﬁber length (PMD) because of stress and core-size variations. • Root-mean-square Pulse broadening: √ σT ≈ (∆β1) 2lcL ≡ D p L. √ • PMD parameter D p ∼ 0.01–10 ps/ km • PMD can degrade system performance considerably (especially for old ﬁbers and at high bit rates). Back Close
19. Commercial Fibers Parameter values for some commercial ﬁbers 19/66 Fiber Type and Aeff λZD D (C band) Slope S Trade Name (µm2) (nm) ps/(km-nm) ps/(km-nm2) Corning SMF-28 80 1302–1322 16 to 19 0.090 Lucent AllWave 80 1300–1322 17 to 20 0.088 Alcatel ColorLock 80 1300–1320 16 to 19 0.090 Corning Vascade 101 1300–1310 18 to 20 0.060 TrueWave-RS 50 1470–1490 2.6 to 6 0.050 Corning LEAF 72 1490–1500 2 to 6 0.060 TrueWave-XL 72 1570–1580 −1.4 to −4.6 0.112 Alcatel TeraLight 65 1440–1450 5.5 to 10 0.058 Back Close
20. Pulse Propagation Equation • Neglecting third-order dispersion, pulse evolution is governed by 20/66 ∂ A iβ2 ∂ 2A + = 0. ∂z 2 ∂t 2 • Compare it with the paraxial equation governing diﬀraction: ∂ A ∂ 2A 2ik + = 0. ∂ z ∂ x2 • 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. Back Close
21. Dispersion Limitations 21/66 • Even a 1-nm spectral width limits BL < 0.1 (Gb/s)-km. • DFB lasers essential for most lightwave systems. • For B > 2.5 Gb/s, dispersion management required. Back Close
22. Major Nonlinear Effects • Stimulated Raman Scattering (SRS) 22/66 • 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. Back Close
23. Nonlinear Schr¨ dinger Equation o • Nonlinear eﬀects can be included by adding a nonlinear term to the 23/66 equation used earlier for dispersive eﬀects. • This equation is known as the Nonlinear Schr¨dinger Equation: o ∂ A iβ2 ∂ 2A + 2 = iγ|A|2A. ∂z 2 ∂t • Nonlinear parameter: γ = 2π n2/(Aeffλ ). ¯ • Fibers with large Aeff help through reduced γ. • Known as large eﬀective-area ﬁber or LEAF. • Nonlinear eﬀects leads to formation of optical solitons. Back Close
24. Optical Receivers • A photodiode converts optical signal into electrical domain. 24/66 • Ampliﬁers and ﬁlters shape the electrical signal. • A decision circuit reconstructs the stream of 1 and 0 bits. • Electrical and optical noises corrupt the signal. • Performance measured through bit error rate (BER). • BER < 10−9 required for all lightwave systems. • Receiver sensitivity: Minimum amount of optical power required to realize the desirable BER. Back Close
25. Bit Error Rate 25/66 0.9 • BER = Error probability per bit BER = p(1)P(0/1) + p(0)P(1/0) = 1 [P(0/1) + P(1/0)]. 2 • P(0/1) = conditional probability of deciding 0 when 1 is sent. • Since p(1) = p(0) = 1/2, BER = 1 [P(0/1) + P(1/0)]. 2 • It is common to assume Gaussian statistics for the current. Back Close
26. Bit Error Rate (continued) • P(0/1) = Area below the decision level ID 26/66 1 ID (I − I1)2 1 I1 − ID P(0/1) = √ exp − 2 dI = erfc √ . σ1 2π −∞ 2σ1 2 σ1 2 • P(1/0) = Area above the decision level ID 1 ∞ (I − I0)2 1 ID − I0 P(1/0) = √ exp − 2 dI = erfc √ . σ0 2π ID 2σ0 2 σ0 2 2 ∞ 2 • Complementary error function erfc(x) = √π x exp(−y ) dy. • Final Answer 1 I1 − ID ID − I0 BER = erfc √ + erfc √ . 4 σ1 2 σ0 2 Back Close
27. Bit Error Rate (continued) • BER depends on the decision threshold ID. 27/66 • Minimum BER occurs when ID is chosen such that (ID − I0)2 (I1 − ID)2 σ1 2 = 2 + ln . 2σ0 2σ1 σ0 • Last term negligible in most cases, and (ID − I0)/σ0 = (I1 − ID)/σ1 ≡ Q. σ0I1 + σ1I0 I1 − I0 ID = , Q= . σ0 + σ1 σ1 + σ0 • Final Expression for BER 1 Q exp(−Q2/2) BER = erfc √ ≈ √ . 2 2 Q 2π Back Close
28. Q Factor 0 10 28/66 −2 10 −4 10 BER −6 10 −8 10 −10 10 −12 10 0 1 2 3 4 5 6 7 Q Factor I −I0 • Q = σ1+σ0 is a measure of SNR. 1 • Q > 6 required for a BER of < 10−9. • Common to use dB scale: Q2(in dB) = 20 log10 Q Back Close
29. Forward Error Correction • Widely used for electrical devices dealing with transfer of digital 29/66 data (CD and DVD players, hard drives). • Errors corrected at the receiver without retransmission of bits. • Requires addition of extra bits at the transmitter end using a suitable error-correcting codes: Overhead = Be/B − 1. • Examples: Cyclic, Hamming, Reed–Solomon, and turbo codes. • Reed–Solomon (RS) codes most common for lightwave systems. • RS(255, 239) with an overhead of 6.7% is often used; RS(255, 207) has an overhead of 23.2%. • Redundancy of a code is deﬁned as ρ = 1 − B/Be. Back Close
30. Loss Management 30/66 • Periodic regeneration of bit stream expensive for WDM systems: Regenerator = Receiver + Transmitter • After 1990, periodic placement of optical ampliﬁers was adopted. • Ampliﬁer spacing is an important design parameter. • Distributed ampliﬁcation oﬀers better performance. Back Close
31. Optical Ampliﬁers • Used routinely for loss compensation since 1995. 31/66 • Amplify input signal but also add some noise. • Several kinds of ampliﬁers have been developed. Semiconductor optical ampliﬁers Erbium-doped ﬁber ampliﬁers Raman ﬁber ampliﬁers Fiber-Optic parametric ampliﬁers • EDFAs are used most commonly for lightwave systems. • Raman ampliﬁers work better for long-haul systems. • Parametric ampliﬁers are still at the research stage. Back Close
32. Ampliﬁer Noise • Optical ampliﬁers introduce noise and degrade SNR. 32/66 • Source of noise: Spontaneous emission Im(A) Spontaneously emitted photon with random phase |A + δA| |A| δφ φ Re(A) • Noise spectral density Ssp(ν) = (G − 1)nsphν. • Population inversion factor nsp = N2/(N2 − N1) > 1. Back Close
33. Ampliﬁer Noise Figure (SNR)in • Noise ﬁgure Fn is deﬁned as Fn = (SNR)out . 33/66 • Beating of signal and spontaneous emission produces √ I = R| GEin + Esp|2 ≈ RGPin + 2R(GPinPsp)1/2 cos θ . • Randomly ﬂuctuating phase θ reduces SNR. • Noise ﬁgure of lumped ampliﬁers 1 1 Fn = 2nsp 1 − + ≈ 2nsp. G G • SNR degraded by 3 dB even for an ideal ampliﬁer. • SNR degraded considerably for a chain of cascaded ampliﬁers. Back Close
34. ASE-Induced Timing Jitter • Ampliﬁers induce timing jitter by shifting pulses from their 34/66 original time slot in a random fashion. • This eﬀect was ﬁrst studied in 1986 and is known as the Gordon–Haus jitter. • Spontaneous emission aﬀects the phase and changes signal frequency by a small but random amount. • Group velocity depends on frequency because of dispersion. • Speed at which pulse propagates through the ﬁber is aﬀected by each ampliﬁer in a random fashion. • Such random speed changes produce random shifts in the pulse position at the receiver and leads to timing jitter. Back Close
35. Dispersion Management • Standard ﬁbers have large dispersion near 1.55 µm. 35/66 • Transmission distance limited to L < (16|β2|B2)−1 even when DFB lasers are used. • L < 35 km at B =10 Gb/s for standard ﬁbers with |β2| ≈ 21 ps2/km. • Operation near the zero-dispersion wavelength not realistic for WDM systems because of the onset of four-wave mixing. • Dispersion must be managed using a suitable technique. Dispersion Compensation Fiber Link Transmitter Receiver Back Close
36. Basic Idea • Pulse propagation in the linear case governed by 36/66 2 ∂ A iβ2 ∂ A + = 0. ∂z 2 ∂t 2 • Using the Fourier-transform method, the solution is 1 ∞ ˜ i A(z,t) = A(0, ω) exp β2zω 2 − iωt dω. 2π −∞ 2 • Phase factor exp(iβ2zω 2/2) is the source of degradation. • A dispersion-management scheme cancels this phase factor. • Actual implementation can be carried out at the transmitter, at the receiver, or along the ﬁber link. • Such a scheme works only if nonlinear eﬀects are negligible. Back Close
37. Dispersion Management Schemes Precompensation Accumulated Dispersion 37/66 DCF Distance along Fiber Link (a) Accumulated Dispersion Distance along Fiber Link Postcompensation DCF (b) Accumulated Dispersion Distance along Fiber Link Periodic Dispersion Map (c) Back Close
38. Dispersion-Compensating Fibers • Fibers with opposite dispersion characteristics used. 38/66 • Two-section map: D1L1 + D2L2 = 0. • Special dispersion-compensating ﬁbers (DCFs) developed with D2 ∼ −100 ps/(nm-km). • Required length L2 = −D1L1/D2 (typically 5-10 km). • DCF modules inserted periodically along the link. • Each module introduces 5–6 dB losses whose compensation increases the noise level. • A relatively small core diameter of DCFs leads to enhancement of nonlinear eﬀects. Back Close
39. Two-Mode DCFs 39/66 (a) (b) • A new type of DCF uses a two-mode ﬁber (V > 2.405). • Long-period ﬁber gratings transfer power from one mode to another. • Dispersion for the higher-order mode can be as large as −500 ps/(km-nm). • Low insertion losses and a large mode area of such DCFs meke them quite attractive. Back Close
40. Photonic-Crystal Fibers 40/66 • A new approach to DCF design makes use of photonic-crystal (or microstructure) ﬁbers. • Such ﬁbers contain a two-dimensional array of air holes around a central core. • Holes modify dispersion characteristics substantially. • Values of D as large as −2000 ps/(km-nm) are possible over a narrower bandwidth. Back Close
41. Optical Phase Conjugation 41/66 • Four-wave mixing used to generate phase-conjugated ﬁeld in the middle of ﬁber link. • β2 reversed for the phase-conjugated ﬁeld: ∂ A iβ2 ∂ 2A ∂ A∗ iβ2 ∂ 2A∗ + =0 → − = 0. ∂z 2 ∂t 2 ∂z 2 ∂t 2 • Pulse shape restored at the ﬁber end. • Basic idea patented in 1979. • First experimental demonstration in 1993. Back Close
42. Management of Nonlinear Effects • Reduce launch power as much as possible. But, ampliﬁer noise 42/66 forces certain minimum power to maintain the SNR. • Pseudo-linear Systems employ short pulses that spread rapidly. • Resulting decrease in peak power reduces nonlinear eﬀects. • Overlapping of pulses leads to intrachannel nonlinear eﬀects. • Another solution: Propagate pulses as solitons by launching an op- timum amount of power. • Manage loss and dispersion: Dispersion-Managed Solitons are used in practice. Back Close
43. Fiber Solitons • Combination of SPM and anomalous GVD required. 43/66 • GVD broadens optical pulses except when the pulse is initially chirped such that β2C < 0. • SPM imposes a chirp on the optical pulse such that C > 0. • Soliton formation possible only when β2 < 0. • SPM-induced chirp is power dependent. • SPM and GVD can cooperate when input power is adjusted such that SPM-induced chirp just cancels GVD-induced broadening. • Nonlinear Schr¨dinger Equation governs soliton formation o ∂ A β2 ∂ 2 A i − + γ|A|2A = 0. ∂z 2 ∂t 2 Back Close
44. Bright Solitons √ • Normalized variables: ξ = z/LD, τ = t/T0, and U = A/ P0 44/66 ∂U 1 ∂ 2U i ± + N 2|U|2U = 0. ∂ ξ 2 ∂ τ2 • Solution depends on a single parameter N deﬁned as 2 LD γP0T02 N = = . LNL |β2| • Dispersion and nonlinear lengths: LD = T02/|β2|, LNL = 1/(γP0). • The two are balanced when LNL = LD or N = 1. • NLS equation can be solved exactly with the inverse scattering method. Back Close
45. Pulse Evolution 45/66 • Periodic evolution for a third-order soliton (N = 3). • When N = 1, solitons preserve their shape. Back Close
46. Fundamental Soliton Solution • For fundamental solitons, NLS equation becomes 46/66 ∂ u 1 ∂ 2u i + 2 + |u|2u = 0. ∂ξ 2∂τ d 2V • If u(ξ , τ) = V (τ) exp[iφ (ξ )], V satisﬁes dτ 2 = 2V (K −V 2). • Multiplying by 2 (dV /dτ) and integrating over τ (dV /dτ)2 = 2KV 2 −V 4 +C. • C = 0 from the boundary condition V → 0 as |τ| → ∞. • Constant K = 1 using V = 1 and dV /dτ = 0 at τ = 0. 2 • Final Solution: u(ξ , τ) = sech(τ) exp(iξ /2). Back Close
47. Stability of Fundamental Solitons • Very stable; can be excited using any pulse shape. 47/66 • Evolution of a Gaussian pulse with N = 1: • Nonlinear index ∆n = n2I(t) larger near the pulse center. • Temporal mode of a SPM-induced waveguide. Back Close
48. Loss-Managed Solitons • Fiber losses destroy the balance needed for solitons. 48/66 • Soliton energy and peak power decrease along the ﬁber. • Nonlinear eﬀects become weaker and cannot balance dispersion completely. • Pulse width begins to increase along the ﬁber. • Solution: Compensate losses periodically using ampliﬁers. • Solitons sustained through periodic ampliﬁcation are called loss-managed solitons. • They need to be launched with a higher energy. Back Close
49. Soliton Ampliﬁcation 49/66 • Optical ampliﬁcation necessary for long-haul systems. • System design identical to non-soliton systems. • Lumped ampliﬁers placed periodically along the link. • Distributed Raman ampliﬁcation is a better alternative. Back Close
50. Dispersion-Managed solitons Lm 50/66 β21 l1 ... β22 l2 ... ... LA Nonlinear Schr¨dinger Equation o ∂ B β2(z) ∂ 2B i − + γ p(z)|B|2B = 0. ∂z 2 ∂t 2 • β2(z) is a periodic function with period Lmap. • p(z) accounts for loss-induced power variations. • LA = mLmap, where m is an integer. • Often LA = LD (m = 1) in practice. • DM solitons are solutions of the modiﬁed NLS equation. Back Close
51. Pulse Width and Chirp Evolution 5 5 5 5 51/66 4 4 4 4 Pulse width (ps) Pulse width (ps) 3 3 3 3 Chirp Chirp 2 2 2 2 1 1 1 1 0 0 0 0 -1 -1 -1 -1 -2 -2 -2 -2 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 Distance (km) Distance (km) (a) (b) • Pulse width and chirp of DM solitons for two pulse energies. • Pulse width minimum where chirp vanishes. • Shortest pulse occurs in the middle of anomalous-GVD section. • DM soliton does not maintain its chirp, width, or peak power. Back Close
52. WDM Systems 52/66 • Optical ﬁbers oﬀer a huge bandwidth (∼100 THz). • Single-channel bit rate limited to 40 Gb/s by electronics. • Solution: Wavelength-division multiplexing (WDM). • Many 10 or 40-Gb/s channels sent over the same ﬁber. Back Close
53. Point-to-Point WDM Links λ1 Tx Rx 53/66 Precom- in-line Postcom- λ2 Tx Rx pensation amplifiers pensation Demultiplexer Multiplexer in-line Optical Fibers compensation λn Tx Rx • Bit streams from several transmitters are multiplexed together. • A demultiplexer separates channels and feeds them into individual receivers. • Channel spacing in the range 25–100 GHz. • ITU grid speciﬁes source wavelengths from 1530 to 1610 nm. Back Close
54. High-capacity Experiments Channels Bit Rate Capacity Distance NBL Product 54/66 N B (Gb/s) NB (Tb/s) L (km) [(Pb/s)-km] 120 20 2.40 6200 14.88 132 20 2.64 120 0.317 160 20 3.20 1500 4.80 82 40 3.28 300 0.984 256 40 10.24 100 1.024 273 40 10.92 117 1.278 • Capacity increased using C and L bands simultaneously. C band = 1525–1565 nm; L band = 1570–1610 nm. • Other bands deﬁned to cover 1.3–1.6 µm range. • Total ﬁber capacity exceeds 30 Tb/s. Back Close
55. Crosstalk in WDM Systems • System performance degrades whenever power from one channel 55/66 leaks into another. • Such a power transfer can occur because of the nonlinear eﬀects in optical ﬁbers (nonlinear crosstalk). • Crosstalk occurs even in a perfectly linear channel because of im- perfections in WDM components. • Linear crosstalk can be classiﬁed into two categories. • Heterowavelength or Out-of-band crosstalk: Leaked power is at a diﬀerent wavelength from the channel wavelength. • Homowavelength or In-band crosstalk: Leaked power is at the same wavelength as the channel wavelength. Back Close
56. Nonlinear Raman Crosstalk • SRS not of concern for single-channel systems because of its 56/66 high threshold (about 500 mW). • In the case of WDM systems, ﬁber acts as a Raman ampliﬁer. • Long-wavelength channels ampliﬁed by short-wavelength channels. • Power transfer depends on the bit pattern: ampliﬁcation occurs only when 1 bits are present in both channels simultaneously. • SRS induces power ﬂuctuations (noise) in all channels. • Shortest-wavelength channel most depleted. • One can estimate Raman crosstalk from the depletion and noise level of this channel. Back Close
57. Four-Wave Mixing • FWM generates new waves at frequencies ωi jk = ωi + ω j − ωk . 57/66 • In the case of equally spaced channels, new frequencies coincide with the existing frequencies and produce in-band crosstalk. • Coherent crosstalk is unacceptable for WDM systems. • In the case of nonuniform channel spacing, most FWM components fall in between the channels and produce out-of-band crosstalk. • Nonuniform channel spacing not practical because many WDM components require equal channel spacings. • A practical solution oﬀered by the periodic dispersion management technique. • GVD high locally but its average value is kept low. Back Close
58. Cross-Phase Modulation • XPM-induced phase shift depends on bit pattern of channels. 58/66 • Dispersion converts pattern-dependent phase shifts into power ﬂuctuations (noise). • Level of ﬂuctuations depends on channel spacing and local GVD. • Fluctuations as a function of channel spacing for a 200-km link. Thiele et al, PTL 12, 726, 2000 Fluctuation Level No dispersion management ◦ With dispersion management ∇ Field conditions Channel Spacing (nm) Back Close
59. Control of Nonlinear Effects • SPM, XPM, and FWM constitute the dominant sources of power 59/66 penalty for WDM systems. • FWM can be reduced with dispersion management. • modern WDM systems are limited by the XPM eﬀects. • Several techniques can be used for reducing the impact of nonlinear eﬀects. Optimization of Dispersion Maps Use of Raman ampliﬁcation Polarization interleaving of channels Use of CSRZ, DPSK, or other formats Back Close
60. Prechirping of Pulses 60/66 • Use of CRZ format (Golovchenko et al., JSTQE 6, 337, 2000); 16 channels at 10 Gb/s with 100-GHz channel spacing. • A phase modulator was used for prechirping pulses. • Considerable improvement observed with phase modulation (PM). • A suitably chirped pulse undergoes a compression phase. Back Close
61. Mid-Span Spectral Inversion 61/66 Woods et al., PTL 16, 677, (2004) Left: No phase conjugation Right: With phase conjugation • Simulated eye patterns at 2560 km for 10-Gbs/s channels. • A phase conjugator placed in the middle of ﬁber link. • XPM eﬀects nearly vanish as dispersion map appears symmetric, • XPM-induced frequency shifts accumulated over ﬁrst half are can- celled in the second-half of the link. Back Close
62. Distributed Raman Ampliﬁcation 62/66 • Use of Raman ampliﬁcation for reducing nonlinear eﬀects. • Distributed ampliﬁcation lowers accumulated noise. • Same value of Q factor obtained at lower launch powers. • Lower launch power reduces all nonlinear eﬀects in a WDM system. • In a 2004 experiment, 64 channels at 40 Gb/s transmitted over over 1600 km (Grosz et al., PTL 16, 1187, 2004). Back Close
63. Polarization Interleaving of Channels • Neighboring channels of a WDM system are orthogonally polarized. 63/66 • XPM coupling depends on states of polarization of interacting channels and is reduced for orthogonally polarized channels. δ n = n2(P1 + 2P2) =⇒ δ n = n2(P1 + 2 P2). 3 • Both amplitude and timing jitter are reduced considerably. • PMD reduces the eﬀectiveness of this technique. • Polarization-interleaving technique helpful when ﬁbers with low PMD are employed and channel spacing is kept <100 GHz. • This technique is employed often in practice. Back Close
64. Use of DPSK Format 64/66 • Eye diagrams at 3000 km for 10-Gb/s channels with 100-GHz spacing (Leibrich et al., PTL 14, 155 2002). • XPM is harmful because of randomness of bit patterns. • In a RZ-DPSK system, information is coded in pulse phase. • Since a pulse is present in all bit slots, channel powers vary in a periodic fashion. • Since all bits are shifted in time by the same amount, little timing jitter is induced by XPM. Back Close
65. Concluding Remarks • Optical ampliﬁers have solved the ﬁber-loss problem. 65/66 • Dispersion management solves the dispersion problem and also reduces FWM among WDM channels. • Nonlinear eﬀects, PMD, and ampliﬁer noise constitute the major limiting factors of modern systems. Research Directions • Extend the system capacity by opening new transmission bands (L, S, S+, etc.) • Develop new ﬁbers with low loss and dispersion over the entire 1300–1650 nm wavelength range. • Improve spectral eﬃciency (New formats: DPSK, DQPSK, etc.) Back Close
66. Bibliography • G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. 66/66 (Wiley, Hoboken, NJ, 2002) • R. Ramaswami and K. Sivarajan, Optical Networks 2nd ed. (Morgan, San Francisco, 2002). • G. E. Keiser, Optical Fiber Communications, 3rd ed. (McGraw-Hill, New York, 2000). • G. P. Agrawal, Lightwave Technology: Components and Devices (Wiley, Hoboken, NJ, 2004). • G. P. Agrawal, Lightwave Technology: Telecommunication Systems (Wiley, Hoboken, NJ, 2005). Back Close

Fiber Optic Communication Systems by Govind P Agrawal Solution Manual

Source: https://www.slideshare.net/smartknight/govind-agrawals-fiber-optical-communication

Stephensen Whaters

Fiber Optic Communication Systems by Govind P Agrawal Solution Manual

You are reading a preview.

Govind agrawal's fiber optical communication

Menu Halaman Statis