Nonlinear Fiber Optics - 4 ed. Agrawal

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9.3. Brillouin Fiber Amplifiers 343 Figure 9.8: Schematic illustration of a Brillouin amplifier; ECL, ISO, and PD stand for externalcavity laser, isolator, and photodetector, respectively. Solid and dashed arrows show the path of pump and probe lasers. (After Ref. [61]; c○1986 AIP.) for G A in the range 20−30 dB, where P in is the incident power of the signal being amplified. As discussed in Section 9.3.1, the saturation power of Brillouin amplifiers is ∼1 mW. In spite of gain saturation, Brillouin amplifiers are capable of providing 30 dB gain at a pump power under 10 mW. However, because Δν B < 100 MHz, the bandwidth of such amplifiers is also less than 100 MHz, in sharp contrast with Raman amplifiers whose bandwidth exceeds 5 THz. In fact, the difference between the signal and pump frequencies should be matched to the Brillouin shift ν B (about 11 GHz in the 1.55-μm region) with an accuracy to better than 10 MHz. For this reason, Brillouin amplifiers are not suitable for amplifying signals in fiber-optic communication systems. Brillouin amplifiers may be useful in practice for applications requiring selective amplification [62]–[64]. One such application consists of amplifying the carrier of a modulated signal selectively, while leaving its modulation sidebands unamplified [75]. The underlying principle is similar to that of homodyne detection, except that the amplified carrier acts as a reference signal. This feature eliminates the need of a local oscillator that must be phase locked to the transmitter—a difficult task in general. In a demonstration of this scheme, the carrier was amplified by 30 dB more than the modulation sidebands even at a modulation frequency as low as 80 MHz [62]. With a proper design, sensitivity improvements of up to 15 dB or more are possible at bit rates in excess of 100 Mb/s. The limiting factor is the nonlinear phase shift induced by the pump (a kind of cross-phase modulation), if the difference between the pump and carrier frequencies does not match the Brillouin shift exactly. The calculations show [63] that deviations from the Brillouin shift should be within 100 kHz for a phase stability of 0.1 rad. Nonlinear phase shifts can also lead to undesirable amplitude modulation of a frequency-modulated signal [66]. Another application of narrowband Brillouin amplifiers consists of using them as a tunable narrowband optical filter for channel selection in a densely packed multichannel communication system [64]. If channel spacing exceeds but the bit rate is smaller than the bandwidth Δν B , the pump laser can be tuned to amplify a particular channel selectively. This scheme was demonstrated in 1986 using a tunable color-center laser as a pump [64]. Two 45-Mb/s channels were transmitted through a 10-km-long fiber.
344 Chapter 9. Stimulated Brillouin Scattering Each channel could be amplified by 20 to 25 dB by using 14 mW of pump power when pump frequency was tuned in the vicinity of the Brillouin shift associated with each channel. More importantly, each channel could be detected with a low bit-error rate (
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Preface Since the publication of th
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Chapter 1 Introduction This introdu
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1.2. Fiber Characteristics 3 Figure
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1.2. Fiber Characteristics 7 1.49 1
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1.2. Fiber Characteristics 11 faste
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1.3. Fiber Nonlinearities 13 Figure
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1.3. Fiber Nonlinearities 15 Sectio
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1.3. Fiber Nonlinearities 17 1.3.3
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1.4. Overview 19 briefly. The last
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References 21 1.11 Equation (1.3.2)
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References 23 [63] M. Ibanescu, Y.
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Chapter 2 Pulse Propagation in Fibe
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2.2. Fiber Modes 27 where Ẽ(r,ω)
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2.2. Fiber Modes 29 across the core
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2.3. Pulse-Propagation Equation 31
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2.4. Numerical Methods 41 Equation
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2.4. Numerical Methods 43 Figure 2.
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2.4. Numerical Methods 45 the basic
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References 47 2.5 Derive an express
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References 49 [44] V. I. Karpman an
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Chapter 3 Group-Velocity Dispersion
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3.2. Dispersion-Induced Pulse Broad
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3.3. Third-Order Dispersion 63 This
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3.3. Third-Order Dispersion 65 Figu
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3.3. Third-Order Dispersion 67 6 5
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3.3. Third-Order Dispersion 69 Noti
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3.4. Dispersion Management 71 Figur
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3.4. Dispersion Management 73 10 3
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3.4. Dispersion Management 75 Figur
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References 77 3.10 An optical commu
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Chapter 4 Self-Phase Modulation An
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4.1. SPM-Induced Spectral Changes 8
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4.2. Effect of Group-Velocity Dispe
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4.3. Semianalytic Techniques 103 In
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4.3. Semianalytic Techniques 105 (1
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4.4. Higher-Order Nonlinear Effects
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Problems 115 4.2 Plot the spectrum
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References 117 [40] D. Marcuse, J.
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References 119 [109] J. Santhanam a
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5.1. Modulation Instability 121 of
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5.1. Modulation Instability 123 2 L
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5.1. Modulation Instability 125 Fig
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5.1. Modulation Instability 127 Fig
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5.2. Fiber Solitons 129 Figure 5.5:
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5.2. Fiber Solitons 131 and write i
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5.2. Fiber Solitons 133 Physically,
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5.3. Other Types of Solitons 141 1
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5.3. Other Types of Solitons 143 pr
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5.3. Other Types of Solitons 145 Th
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5.4. Perturbation of Solitons 147 w
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5.4. Perturbation of Solitons 149 w
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5.4. Perturbation of Solitons 151 t
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5.4. Perturbation of Solitons 153 b
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5.4. Perturbation of Solitons 155 F
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5.5. Higher-Order Effects 157 where
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5.5. Higher-Order Effects 159 Figur
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5.5. Higher-Order Effects 161 1 N =
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5.5. Higher-Order Effects 163 Integ
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5.5. Higher-Order Effects 165 Figur
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5.5. Higher-Order Effects 167 that
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Problems 169 Problems 5.1 Solve Eq.
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References 171 [27] E. Brainis, D.
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References 173 [93] L. F. Mollenaue
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References 175 [165] V. V. Afanasje
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Chapter 6 Polarization Effects As d
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6.1. Nonlinear Birefringence 179 wh
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6.1. Nonlinear Birefringence 181 re
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6.2. Nonlinear Phase Shift 183 dA y
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6.2. Nonlinear Phase Shift 185 wher
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6.2. Nonlinear Phase Shift 187 side
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6.3. Evolution of Polarization Stat
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6.4. Vector Modulation Instability
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6.5. Birefringence and Solitons 207
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6.6. Random Birefringence 213 where
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6.6. Random Birefringence 215 PMD,
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6.6. Random Birefringence 217 As in
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6.6. Random Birefringence 219 Figur
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References 221 6.9 Derive the dispe
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References 223 [63] P. Kockaert, M.
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References 225 [140] A. El Amari, N
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7.1. XPM-Induced Nonlinear Coupling
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7.2. XPM-Induced Modulation Instabi
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7.2. XPM-Induced Modulation Instabi
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7.3. XPM-Paired Solitons 233 This t
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7.3. XPM-Paired Solitons 235 The co
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7.3. XPM-Paired Solitons 237 It is
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7.4. Spectral and Temporal Effects
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7.5. Applications of XPM 249 Probe
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7.5. Applications of XPM 251 by hig
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7.5. Applications of XPM 253 Figure
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7.6. Polarization Effects 255 where
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7.6. Polarization Effects 257 Figur
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7.6. Polarization Effects 259 1 0.8
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7.6. Polarization Effects 261 4 Pum
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7.6. Polarization Effects 263 Figur
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7.7. XPM Effects in Birefringent Fi
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7.7. XPM Effects in Birefringent Fi
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Problems 269 7.2 Derive the dispers
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References 271 [33] M. Lisak, A. H
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References 273 [105] B. V. Vu, A. S
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8.1. Basic Concepts 275 Figure 8.1:
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8.1. Basic Concepts 277 set of two
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8.1. Basic Concepts 279 10 mW. Howe
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8.1. Basic Concepts 281 0.5 Raman R
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8.2. Quasi-Continuous SRS 283 four
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8.2. Quasi-Continuous SRS 285 Figur
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8.2. Quasi-Continuous SRS 291 wavel
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Page 334 and 335: Chapter 9 Stimulated Brillouin Scat
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10.4. Parametric Amplification 393
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10.5. Polarization Effects 401 Bril
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10.5. Polarization Effects 403 foll
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10.5. Polarization Effects 405 Jone
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10.5. Polarization Effects 407 to s
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10.5. Polarization Effects 409 Figu
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10.6. Applications of Four-Wave Mix
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Problems 417 Figure 10.24: Output s
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References 419 [5] R. W. Boyd, Nonl
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References 421 [79] A. Durécu-Legr
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References 423 [140] M. D. Levenson
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11.1. Nonlinear Parameter 425 11.1.
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11.1. Nonlinear Parameter 427 Figur
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11.1. Nonlinear Parameter 433 when
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11.2. Fibers with Silica Cladding 4
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11.3. Tapered Fibers with Air Cladd
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11.3. Tapered Fibers with Air Cladd
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11.4. Microstructured Fibers 441 he
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11.4. Microstructured Fibers 443 Ef
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11.5. Non-Silica Fibers 445 0.05 0.
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11.5. Non-Silica Fibers 447 Figure
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References 449 wavelength range of
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References 451 [57] H. Yokota, E. S
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Chapter 12 Novel Nonlinear Phenomen
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12.1. Intrapulse Raman Scattering 4
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12.2. Four-Wave Mixing 465 Figure 1
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12.2. Four-Wave Mixing 467 Figure 1
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12.3. Supercontinuum Generation 469
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12.4. Temporal and Spectral Evoluti
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12.5. Harmonic Generation 495 Figur
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12.5. Harmonic Generation 497 traps
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12.5. Harmonic Generation 501 analy
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12.5. Harmonic Generation 505 The p
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References 507 12.6 Derive an expre
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References 509 [45] J. E. Sharping,
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References 511 [111] J. Y. Y. Leong
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References 513 [180] A. L. Calvez,
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Appendix A 515 converted into decib
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Appendix B 517 % This code solves t
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Appendix C List of Acronyms Each sc
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Index acoustic response function, 4
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Index 523 distributed fiber sensors
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Index 525 four-photon, 412 gain-swi
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Index 527 Raman amplification with,
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Index 529 spectral hole burning, 36
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Nonlinear Fiber Optics - 4 ed. Agrawal

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