Nonlinear Fiber Optics - 4 ed. Agrawal

Recommendations

Info

References 225 [140] A. El Amari, N. Gisin, B. Perny, H. Zbinden, and C. W. Zimmer, J. Lightwave Technol. 16, 332 (1998). [141] B. Huttner, C. Geiser, and N. Gisin, IEEE J. Sel. Topics Quantum Electron. 6, 317 (2000). [142] Y. Li and A. Yariv, J. Opt. Soc. Am. B 17, 1821 (2000). [143] D. Wang and C. R. Menyuk, J. Lightwave Technol. 19, 487 (2001). [144] R. M. Craig, J. Lightwave Technol. 21, 432 (2003). [145] C. Xie and L. F. Mollenauer, J. Lightwave Technol. 21, 1953 (2003). [146] M. Shtaif and A. Mecozzi, IEEE Photon. Technol. Lett. 16, 671 (2004). [147] L. F. Mollenauer, K. Smith, J. P. Gordon, and C. R. Menyuk, Opt. Lett. 14, 1219 (1989). [148] S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, J. Lightwave Technol. 10, 28 (1992). [149] T. Ueda and W. L. Kath, Physica D 55, 166 (1992). [150] C. de Angelis, S. Wabnitz, and M. Haelterman, Electron. Lett. 29, 1568 (1993). [151] M. Matsumoto, Y. Akagi, and A. Hasegawa, J. Lightwave Technol. 15, 584 (1997). [152] D. Marcuse, C. R. Menyuk, and P. K. A. Wai, J. Lightwave Technol. 15, 1735 (1997). [153] T. L. Lakoba and D. J. Kaup, Phys. Rev. E 56, 6147 (1997). [154] C. de Angelis, P. Franco, and M. Romagnoli, Opt. Commun. 157, 161 (1998). [155] X. Zhang, M. Karlsson, P. A. Andrekson, and E. Kolltveit, IEEE Photon. Technol. Lett. 10, 1742 (1998). [156] S. M. Baker, J. N. Elgin, and H. J. Harvey, Opt. Commun. 165, 27 (1999). [157] C. Xie, M. Karlsson, and P. A. Andrekson, IEEE Photon. Technol. Lett. 12, 801 (2000). [158] Y. Chen and H. Haus, Chaos 10, 529 (2000); Opt. Lett. 25, 290 (2000). [159] I. Nishioka, T. Hirooka, and A. Hasegawa, IEEE Photon. Technol. Lett. 12, 1480 (2000). [160] C. Xie, M. Karlsson, P. A. Andrekson, and H. Sunnerud, IEEE Photon. Technol. Lett. 13, 121 (2001). [161] H. Sunnerud, J. Li, C. Xie, and P. A. Andrekson, J. Lightwave Technol. 19, 1453 (2001). [162] C. Xie, M. Karlsson, P. A. Andrekson, H. Sunnerud, and J. Li, IEEE J. Sel. Topics Quantum Electron. 8, 575 (2002). [163] A. Levent, S. G. Rajeev, F. Yaman, and G. P. Agrawal, Phys. Rev. Lett. 90, 013902 (2003). [164] P. Kylemark, H. Sunnerud, M. Karlsson, and P. A. Andrekson, IEEE Photon. Technol. Lett. 15, 1372 (2003). [165] A. Hasegawa, Physica D, 188, 241 (2004).
Chapter 7 Cross-Phase Modulation So far in this book, only a single electromagnetic wave is assumed to propagate inside optical fibers. When two or more optical fields having different wavelengths propagate simultaneously inside a fiber, they interact with each other through the fiber nonlinearity. In general, such an interaction can generate new waves under appropriate conditions through a variety of nonlinear phenomena such as stimulated Raman or Brillouin scattering, harmonic generation, and four-wave mixing; these topics are covered in Chapters 8 to 12. The Kerr-type nonlinearity can also couple two optical fields through cross-phase modulation (XPM) without inducing any energy transfer between them. In practice, XPM always accompanies self-phase modulation (SPM) when two or more optical fields are launched simultaneously into an optical fiber. From a physical perspective, XPM occurs because the effective refractive index seen by an optical beam in a nonlinear medium depends not only on the intensity of that beam but also on the intensity of other copropagating beams [1]. The XPM-induced coupling among multiple optical fields gives rise to a number of interesting nonlinear effects in optical fibers. The coupling between two fields of different wavelengths is considered in Section 7.1, where a set of two coupled nonlinear Schrödinger (NLS) equations is derived, assuming that each wave maintains its state of polarization. These equations are used in Section 7.2 to discuss how the XPM affects the phenomenon of modulation instability. Similar to the analysis in Section 6.4, this instability can occur even in the normal-dispersion regime of an optical fiber. Section 7.3 focuses on soliton pairs whose members support each other through XPM. The effects of XPM on the shape and the spectrum of copropagating ultrashort pulses are described in Section 7.4. Several applications of XPM-induced coupling in optical fibers are discussed in Section 7.5. A vector theory of XPM is developed in Section 7.6 and is used to discuss several new effects such as polarization-dependent spectral broadening, pulse trapping, and optical wave breaking. Section 7.7 extends this theory to the case of birefringent fibers. A pump–probe configuration is used to reveal that random changes in the birefringence of a fiber along its length lead to the phenomenon of intrapulse depolarization. 226
Page 4 and 5:
Preface Since the publication of th
Page 6 and 7:
Chapter 1 Introduction This introdu
Page 8 and 9:
1.2. Fiber Characteristics 3 Figure
Page 10 and 11:
Page 12 and 13:
1.2. Fiber Characteristics 7 1.49 1
Page 14 and 15:
Page 16 and 17:
1.2. Fiber Characteristics 11 faste
Page 18 and 19:
1.3. Fiber Nonlinearities 13 Figure
Page 20 and 21:
1.3. Fiber Nonlinearities 15 Sectio
Page 22 and 23:
1.3. Fiber Nonlinearities 17 1.3.3
Page 24 and 25:
1.4. Overview 19 briefly. The last
Page 26 and 27:
References 21 1.11 Equation (1.3.2)
Page 28 and 29:
References 23 [63] M. Ibanescu, Y.
Page 30 and 31:
Chapter 2 Pulse Propagation in Fibe
Page 32 and 33:
2.2. Fiber Modes 27 where Ẽ(r,ω)
Page 34 and 35:
2.2. Fiber Modes 29 across the core
Page 36 and 37:
2.3. Pulse-Propagation Equation 31
Page 38 and 39:
Page 40 and 41:
Page 42 and 43:
Page 44 and 45:
Page 46 and 47:
2.4. Numerical Methods 41 Equation
Page 48 and 49:
2.4. Numerical Methods 43 Figure 2.
Page 50 and 51:
2.4. Numerical Methods 45 the basic
Page 52 and 53:
References 47 2.5 Derive an express
Page 54 and 55:
References 49 [44] V. I. Karpman an
Page 56 and 57:
Chapter 3 Group-Velocity Dispersion
Page 58 and 59:
3.2. Dispersion-Induced Pulse Broad
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
3.3. Third-Order Dispersion 63 This
Page 70 and 71:
3.3. Third-Order Dispersion 65 Figu
Page 72 and 73:
3.3. Third-Order Dispersion 67 6 5
Page 74 and 75:
3.3. Third-Order Dispersion 69 Noti
Page 76 and 77:
3.4. Dispersion Management 71 Figur
Page 78 and 79:
3.4. Dispersion Management 73 10 3
Page 80 and 81:
3.4. Dispersion Management 75 Figur
Page 82 and 83:
References 77 3.10 An optical commu
Page 84 and 85:
Chapter 4 Self-Phase Modulation An
Page 86 and 87:
4.1. SPM-Induced Spectral Changes 8
Page 88 and 89:
Page 90 and 91:
Page 92 and 93:
Page 94 and 95:
4.2. Effect of Group-Velocity Dispe
Page 96 and 97:
Page 98 and 99:
Page 100 and 101:
Page 102 and 103:
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
4.3. Semianalytic Techniques 103 In
Page 110 and 111:
4.3. Semianalytic Techniques 105 (1
Page 112 and 113:
4.4. Higher-Order Nonlinear Effects
Page 114 and 115:
Page 116 and 117:
Page 118 and 119:
Page 120 and 121:
Problems 115 4.2 Plot the spectrum
Page 122 and 123:
References 117 [40] D. Marcuse, J.
Page 124 and 125:
References 119 [109] J. Santhanam a
Page 126 and 127:
5.1. Modulation Instability 121 of
Page 128 and 129:
5.1. Modulation Instability 123 2 L
Page 130 and 131:
5.1. Modulation Instability 125 Fig
Page 132 and 133:
5.1. Modulation Instability 127 Fig
Page 134 and 135:
5.2. Fiber Solitons 129 Figure 5.5:
Page 136 and 137:
5.2. Fiber Solitons 131 and write i
Page 138 and 139:
5.2. Fiber Solitons 133 Physically,
Page 140 and 141:
Page 142 and 143:
Page 144 and 145:
Page 146 and 147:
5.3. Other Types of Solitons 141 1
Page 148 and 149:
5.3. Other Types of Solitons 143 pr
Page 150 and 151:
5.3. Other Types of Solitons 145 Th
Page 152 and 153:
5.4. Perturbation of Solitons 147 w
Page 154 and 155:
5.4. Perturbation of Solitons 149 w
Page 156 and 157:
5.4. Perturbation of Solitons 151 t
Page 158 and 159:
5.4. Perturbation of Solitons 153 b
Page 160 and 161:
5.4. Perturbation of Solitons 155 F
Page 162 and 163:
5.5. Higher-Order Effects 157 where
Page 164 and 165:
5.5. Higher-Order Effects 159 Figur
Page 166 and 167:
5.5. Higher-Order Effects 161 1 N =
Page 168 and 169:
5.5. Higher-Order Effects 163 Integ
Page 170 and 171:
5.5. Higher-Order Effects 165 Figur
Page 172 and 173:
5.5. Higher-Order Effects 167 that
Page 174 and 175:
Problems 169 Problems 5.1 Solve Eq.
Page 176 and 177:
References 171 [27] E. Brainis, D.
Page 178 and 179:
References 173 [93] L. F. Mollenaue
Page 180 and 181: References 175 [165] V. V. Afanasje
Page 182 and 183: Chapter 6 Polarization Effects As d
Page 184 and 185: 6.1. Nonlinear Birefringence 179 wh
Page 186 and 187: 6.1. Nonlinear Birefringence 181 re
Page 188 and 189: 6.2. Nonlinear Phase Shift 183 dA y
Page 190 and 191: 6.2. Nonlinear Phase Shift 185 wher
Page 192 and 193: 6.2. Nonlinear Phase Shift 187 side
Page 194 and 195: 6.3. Evolution of Polarization Stat
Page 202 and 203: 6.4. Vector Modulation Instability
Page 212 and 213: 6.5. Birefringence and Solitons 207
Page 218 and 219: 6.6. Random Birefringence 213 where
Page 220 and 221: 6.6. Random Birefringence 215 PMD,
Page 222 and 223: 6.6. Random Birefringence 217 As in
Page 224 and 225: 6.6. Random Birefringence 219 Figur
Page 226 and 227: References 221 6.9 Derive the dispe
Page 228 and 229: References 223 [63] P. Kockaert, M.
Page 232 and 233: 7.1. XPM-Induced Nonlinear Coupling
Page 234 and 235: 7.2. XPM-Induced Modulation Instabi
Page 236 and 237: 7.2. XPM-Induced Modulation Instabi
Page 238 and 239: 7.3. XPM-Paired Solitons 233 This t
Page 240 and 241: 7.3. XPM-Paired Solitons 235 The co
Page 242 and 243: 7.3. XPM-Paired Solitons 237 It is
Page 244 and 245: 7.4. Spectral and Temporal Effects
Page 254 and 255: 7.5. Applications of XPM 249 Probe
Page 256 and 257: 7.5. Applications of XPM 251 by hig
Page 258 and 259: 7.5. Applications of XPM 253 Figure
Page 260 and 261: 7.6. Polarization Effects 255 where
Page 262 and 263: 7.6. Polarization Effects 257 Figur
Page 264 and 265: 7.6. Polarization Effects 259 1 0.8
Page 266 and 267: 7.6. Polarization Effects 261 4 Pum
Page 268 and 269: 7.6. Polarization Effects 263 Figur
Page 270 and 271: 7.7. XPM Effects in Birefringent Fi
Page 272 and 273: 7.7. XPM Effects in Birefringent Fi
Page 274 and 275: Problems 269 7.2 Derive the dispers
Page 276 and 277: References 271 [33] M. Lisak, A. H
Page 278 and 279: References 273 [105] B. V. Vu, A. S
Page 280 and 281:
8.1. Basic Concepts 275 Figure 8.1:
Page 282 and 283:
8.1. Basic Concepts 277 set of two
Page 284 and 285:
8.1. Basic Concepts 279 10 mW. Howe
Page 286 and 287:
8.1. Basic Concepts 281 0.5 Raman R
Page 288 and 289:
8.2. Quasi-Continuous SRS 283 four
Page 290 and 291:
8.2. Quasi-Continuous SRS 285 Figur
Page 292 and 293:
Page 294 and 295:
Page 296 and 297:
8.2. Quasi-Continuous SRS 291 wavel
Page 298 and 299:
8.2. Quasi-Continuous SRS 293 1 0.8
Page 300 and 301:
8.3. SRS with Short Pump Pulses 295
Page 302 and 303:
Page 304 and 305:
Page 306 and 307:
Page 308 and 309:
Page 310 and 311:
Page 312 and 313:
8.4. Soliton Effects 307 Figure 8.1
Page 314 and 315:
Page 316 and 317:
Page 318 and 319:
8.4. Soliton Effects 313 ton laser
Page 320 and 321:
8.5. Polarization Effects 315 maxim
Page 322 and 323:
8.5. Polarization Effects 317 where
Page 324 and 325:
8.5. Polarization Effects 319 and s
Page 326 and 327:
Problems 321 Figure 8.25: (a) Avera
Page 328 and 329:
References 323 [4] W. Kaiser and M
Page 330 and 331:
References 325 [75] M. Nakazawa, T.
Page 332 and 333:
References 327 [144] V. I. Kruglov,
Page 334 and 335:
Chapter 9 Stimulated Brillouin Scat
Page 336 and 337:
9.1. Basic Concepts 331 Figure 9.1:
Page 338 and 339:
9.2. Quasi-CW SBS 333 [20]. A part
Page 340 and 341:
9.2. Quasi-CW SBS 335 (see Figure 8
Page 342 and 343:
9.2. Quasi-CW SBS 337 pseudorandom
Page 344 and 345:
9.2. Quasi-CW SBS 339 Figure 9.4: S
Page 346 and 347:
9.3. Brillouin Fiber Amplifiers 341
Page 348 and 349:
9.3. Brillouin Fiber Amplifiers 343
Page 350 and 351:
9.4. SBS Dynamics 345 9.4.1 Coupled
Page 352 and 353:
9.4. SBS Dynamics 347 Pump Power (k
Page 354 and 355:
9.4. SBS Dynamics 349 Figure 9.11:
Page 356 and 357:
9.4. SBS Dynamics 351 Δn SBS . If
Page 358 and 359:
Page 360 and 361:
Page 362 and 363:
9.5. Brillouin Fiber Lasers 357 Fig
Page 364 and 365:
9.5. Brillouin Fiber Lasers 359 Fig
Page 366 and 367:
9.5. Brillouin Fiber Lasers 361 rin
Page 368 and 369:
References 363 9.4 Estimate SBS thr
Page 370 and 371:
References 365 [47] Y.-X. Fan, F.-Y
Page 372 and 373:
References 367 [119] R. G. Harrison
Page 374 and 375:
10.1. Origin of Four-Wave Mixing 36
Page 376 and 377:
10.2. Theory of Four-Wave Mixing 37
Page 378 and 379:
Page 380 and 381:
Page 382 and 383:
10.3. Phase-Matching Techniques 377
Page 384 and 385:
Page 386 and 387:
Page 388 and 389:
Page 390 and 391:
Page 392 and 393:
10.4. Parametric Amplification 387
Page 394 and 395:
Page 396 and 397:
Page 398 and 399:
Page 400 and 401:
Page 402 and 403:
Page 404 and 405:
Page 406 and 407:
10.5. Polarization Effects 401 Bril
Page 408 and 409:
10.5. Polarization Effects 403 foll
Page 410 and 411:
10.5. Polarization Effects 405 Jone
Page 412 and 413:
10.5. Polarization Effects 407 to s
Page 414 and 415:
10.5. Polarization Effects 409 Figu
Page 416 and 417:
10.6. Applications of Four-Wave Mix
Page 418 and 419:
Page 420 and 421:
Page 422 and 423:
Problems 417 Figure 10.24: Output s
Page 424 and 425:
References 419 [5] R. W. Boyd, Nonl
Page 426 and 427:
References 421 [79] A. Durécu-Legr
Page 428 and 429:
References 423 [140] M. D. Levenson
Page 430 and 431:
11.1. Nonlinear Parameter 425 11.1.
Page 432 and 433:
11.1. Nonlinear Parameter 427 Figur
Page 434 and 435:
Page 436 and 437:
Page 438 and 439:
11.1. Nonlinear Parameter 433 when
Page 440 and 441:
11.2. Fibers with Silica Cladding 4
Page 442 and 443:
11.3. Tapered Fibers with Air Cladd
Page 444 and 445:
11.3. Tapered Fibers with Air Cladd
Page 446 and 447:
11.4. Microstructured Fibers 441 he
Page 448 and 449:
11.4. Microstructured Fibers 443 Ef
Page 450 and 451:
11.5. Non-Silica Fibers 445 0.05 0.
Page 452 and 453:
11.5. Non-Silica Fibers 447 Figure
Page 454 and 455:
References 449 wavelength range of
Page 456 and 457:
References 451 [57] H. Yokota, E. S
Page 458 and 459:
Chapter 12 Novel Nonlinear Phenomen
Page 460 and 461:
12.1. Intrapulse Raman Scattering 4
Page 462 and 463:
Page 464 and 465:
Page 466 and 467:
Page 468 and 469:
Page 470 and 471:
12.2. Four-Wave Mixing 465 Figure 1
Page 472 and 473:
12.2. Four-Wave Mixing 467 Figure 1
Page 474 and 475:
12.3. Supercontinuum Generation 469
Page 476 and 477:
Page 478 and 479:
Page 480 and 481:
Page 482 and 483:
12.4. Temporal and Spectral Evoluti
Page 484 and 485:
Page 486 and 487:
Page 488 and 489:
Page 490 and 491:
Page 492 and 493:
Page 494 and 495:
Page 496 and 497:
Page 498 and 499:
Page 500 and 501:
12.5. Harmonic Generation 495 Figur
Page 502 and 503:
12.5. Harmonic Generation 497 traps
Page 504 and 505:
Page 506 and 507:
12.5. Harmonic Generation 501 analy
Page 508 and 509:
Page 510 and 511:
12.5. Harmonic Generation 505 The p
Page 512 and 513:
References 507 12.6 Derive an expre
Page 514 and 515:
References 509 [45] J. E. Sharping,
Page 516 and 517:
References 511 [111] J. Y. Y. Leong
Page 518 and 519:
References 513 [180] A. L. Calvez,
Page 520 and 521:
Appendix A 515 converted into decib
Page 522 and 523:
Appendix B 517 % This code solves t
Page 524 and 525:
Appendix C List of Acronyms Each sc
Page 526 and 527:
Index acoustic response function, 4
Page 528 and 529:
Index 523 distributed fiber sensors
Page 530 and 531:
Index 525 four-photon, 412 gain-swi
Page 532 and 533:
Index 527 Raman amplification with,
Page 534:
Index 529 spectral hole burning, 36
show all

Nonlinear Fiber Optics - 4 ed. Agrawal

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?