Nonlinear Fiber Optics - 4 ed. Agrawal

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References 273 [105] B. V. Vu, A. Szoke, and O. L. Landen, Opt. Lett. 18, 723 (1993). [106] S. Kumar, A. Selvarajan, and G. V. Anand, J. Opt. Soc. Am. B 11, 810 (1994). [107] Q. Lin and G. P. Agrawal, IEEE J. Quantum Electron. 20, 959 (2004). [108] Q. Lin and G. P. Agrawal, Opt. Lett. 30, 921 (2005). [109] J. N. Damask, Polarization Optics in Telecommunications (Springer, New York, 2005), Chap. 2. [110] Q. Lin and G. P. Agrawal, J. Opt. Soc. Am. B 20, 1616 (2003). [111] D. Awschalom, D. Loss, and N. Samarth, Eds., Semiconductor Spintronics and Quantum Computation (Springer, New York, 2002).
Chapter 8 Stimulated Raman Scattering Stimulated Raman scattering (SRS) is an important nonlinear process that can turn optical fibers into broadband Raman amplifiers and tunable Raman lasers. It can also severely limit the performance of multichannel lightwave systems by transferring energy from one channel to the neighboring channels. This chapter is devoted to a thorough study of SRS phenomenon in optical fibers. Section 8.1 presents the basic theory behind SRS with emphasis on the pump power required to reach the Raman threshold. SRS under continuous-wave (CW) and quasi-CW conditions is considered in Section 8.2, where we also discuss the performance of fiber-based Raman lasers and amplifiers. Ultrafast SRS occurring for pulses of 100-ps width or less is considered in Sections 8.3 and 8.4 for normal and anomalous group-velocity dispersion (GVD), respectively. In both cases, attention is paid to the walk-off effects together with those resulting from self-phase modulation (SPM) and cross-phase modulation (XPM). Section 8.5 focuses on the polarization effects. 8.1 Basic Concepts In any molecular medium, spontaneous Raman scattering can transfer a small fraction (typically ∼10 −6 ) of power from one optical field to another field, whose frequency is downshifted by an amount determined by the vibrational modes of the medium. This process was discovered by Raman in 1928 and is known as the Raman effect [1]. It can be described quantum mechanically as scattering of a photon of energy ¯hω p by a molecule to a lower-frequency photon with energy ¯hω s , as the molecule makes transition to a vibrational state (see Figure 8.1). From a practical perspective, incident light acts as a pump and generates the frequency-shifted radiation, the so-called Stokes wave, that serves as a spectroscopic tool. It was observed in 1962 that, for intense pump fields, the nonlinear phenomenon of SRS can occur in which the Stokes wave grows rapidly inside the medium such that most of the pump energy is transferred to it [2]. Since then, SRS has been studied extensively in a variety of molecular media [3]–[7]. This section introduces the basic concepts, such as the Raman gain and the 274
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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 323 [4] W. Kaiser and M
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References 325 [75] M. Nakazawa, T.
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References 327 [144] V. I. Kruglov,
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Chapter 9 Stimulated Brillouin Scat
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9.1. Basic Concepts 331 Figure 9.1:
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9.2. Quasi-CW SBS 333 [20]. A part
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9.2. Quasi-CW SBS 335 (see Figure 8
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9.2. Quasi-CW SBS 337 pseudorandom
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9.2. Quasi-CW SBS 339 Figure 9.4: S
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9.3. Brillouin Fiber Amplifiers 341
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9.3. Brillouin Fiber Amplifiers 343
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9.4. SBS Dynamics 345 9.4.1 Coupled
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9.4. SBS Dynamics 347 Pump Power (k
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9.4. SBS Dynamics 349 Figure 9.11:
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9.4. SBS Dynamics 351 Δn SBS . If
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9.5. Brillouin Fiber Lasers 357 Fig
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9.5. Brillouin Fiber Lasers 359 Fig
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9.5. Brillouin Fiber Lasers 361 rin
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References 363 9.4 Estimate SBS thr
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References 365 [47] Y.-X. Fan, F.-Y
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References 367 [119] R. G. Harrison
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10.1. Origin of Four-Wave Mixing 36
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10.2. Theory of Four-Wave Mixing 37
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10.3. Phase-Matching Techniques 377
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10.4. Parametric Amplification 387
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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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