Nonlinear Effects in Optical Fibers

by Ferreira, Mario F. S.

• ISBN13: 9780470464663
• ISBN10: 0470464666
• Edition: 1st
• Format: Hardcover
• Copyright: 2011-05-31
• Publisher: Wiley-OSA

Summary

This book will provide insight into the principles and applications of nonlinear effects in fibers for students, researchers, and developers who have a basic understanding of electromagnetic theory under their belts. It will explore the physics, limitations, applications, and research results surrounding nonlinear effects in fiber optics. In addition to communications, optical fibers are already used in medical procedures, automobiles, and aircraft and are expected to have many other applications. This will expand the range of industry workers who will find a book of this type useful.

Author Biography

Mrio F. S. Ferreira, PhD, is the leader of the Optics and Optoelectronics Group of the I3N, the Institute of Nanostructures, Nanomodelling and Nanofabrication, a national Associate Laboratory. He has written for more than 300 scientific journal and conference publications and has served as an advisor for many scientific journals and publishers. Dr. Ferreira is a well-respected leader and lecturer for the Optical Society of America and SPIE, along with the New York Academy of Sciences, the American Association for the Advancement of Science, the European Optical Society, the European Physical Society, and the Portuguese Physical Society.

Table of Contents

Preface	p. xi
Introduction	p. 1
References	p. 5
Electromagnetic Wave Propagation	p. 9
Wave Equation for Linear Media	p. 9
Electromagnetic Waves	p. 11
Energy Density and Flow	p. 13
Phase Velocity and Group Velocity	p. 14
Reflection and Transmission of Waves	p. 16
Snell's Laws	p. 16
Fresnel Equations	p. 17
The Harmonic Oscillator Model	p. 21
The Refractive Index	p. 23
The Limit of Geometrical Optics	p. 24
Problems	p. 26
References	p. 27
Optical Fibers	p. 29
Geometrical Optics Description	p. 30
Planar Waveguides	p. 30
Step-Index Fibers	p. 33
Graded-Index Fibers	p. 36
Wave Propagation in Fibers	p. 39
Fiber Modes	p. 39
Single-Mode Fibers	p. 42
Fiber Attenuation	p. 44
Modulation and Transfer of Information	p. 45
Chromatic Dispersion in Single-Mode Fibers	p. 46
Unchirped Input Pulses	p. 48
Chirped Input Pulses	p. 52
Dispersion Compensation	p. 53
Polarization Mode Dispersion	p. 54
Fiber Birefringence and the Intrinsic PMD	p. 55
PMD in Long Fiber Spans	p. 57
Problems	p. 60
References	p. 61
The Nonlinear Schrödinger Equation	p. 63
The Nonlinear Polarization	p. 63
The Nonlinear Wave Equation	p. 66
The Nonlinear Refractive Index	p. 66
Importance of Nonlinear Effects in Fibers	p. 68
Derivation of the Nonlinear Schrödinger Equation	p. 70
Propagation in the Absence of Dispersion and Nonlinearity	p. 73
Effect of Dispersion Only	p. 73
Effect of Nonlinearity Only	p. 74
Normalized Form of NLSE	p. 74
Soliton Solutions	p. 75
The Fundamental Soliton	p. 76
Solutions of the Inverse Scattering Theory	p. 77
Dark Solitons	p. 80
Numerical Solution of the NLSE	p. 81
Problems	p. 83
References	p. 84
Nonlinear Phase Modulation	p. 85
Self-Phase Modulation	p. 86
SPM-Induced Phase Shift	p. 86
The Variational Approach	p. 89
Impact on Communication Systems	p. 93
Modulation Instability	p. 94
Cross-Phase Modulation	p. 97
XPM-Induced Phase Shift	p. 97
Impact on Optical Communication Systems	p. 100
Modulation Instability	p. 103
XPM-Paired Solitons	p. 105
Problems	p. 106
References	p. 107
Four-Wave Mixing	p. 111
Wave Mixing	p. 112
Mathematical Description	p. 114
Phase Matching	p. 115
Impact and Control of FWM	p. 118
Fiber Parametric Amplifiers	p. 123
FOPA Gain and Bandwidth	p. 123
Parametric Oscillators	p. 128
Nonlinear Phase Conjugation with FWM	p. 131
Squeezing and Photon Pair Sources	p. 133
Problems	p. 135
References	p. 135
Intrachannel Nonlinear Effects	p. 139
Mathematical Description	p. 140
Intrachannel XPM	p. 142
Intrachannel FWM	p. 147
Control of Intrachannel Nonlinear Effects	p. 149
Problems	p. 153
References	p. 153
Soliton Lightwave Systems	p. 55
Soliton Properties	p. 156
Soliton Interaction	p. 157
Perturbation of Solitons	p. 159
Perturbation Theory	p. 160
Fiber Losses	p. 160
Path-Averaged Solitons	p. 162
Lumped Amplification	p. 163
Distributed Amplification	p. 164
Timing Jitter	p. 166
Soliton Transmission Control	p. 168
Fixed-Frequency Filters	p. 169
Sliding-Frequency Filters	p. 170
Synchronous Modulators	p. 173
Amplifier with Nonlinear Gain	p. 174
Dissipative Solitons	p. 176
Analytical Results of the CGLE	p. 176
Numerical Solutions of the CGLE	p. 180
Dispersion-Managed Solitons	p. 183
The True DM Soliton	p. 183
The Variational Approach to DM Solitons	p. 185
WDM Soliton Systems	p. 189
Problems	p. 192
References	p. 193
Other Applications of Optical Solitons	p. 199
Soliton Fiber Lasers	p. 199
The First Soliton Laser	p. 200
Figure-Eight Fiber Laser	p. 201
Nonlinear Loop Mirrors	p. 201
Stretched-Pulse Fiber Lasers	p. 202
Modeling Fiber Soliton Lasers	p. 203
Pulse Compression	p. 204
Grating-Fiber Compressors	p. 204
Soliton-Effect Compressors	p. 207
Compression of Fundamental Solitons	p. 210
Fiber Bragg Gratings	p. 213
Pulse Compression Using Fiber Gratings	p. 214
Fiber Bragg Solitons	p. 216
Problems	p. 220
References	p. 220
Polarization Effects	p. 225
Coupled Nonlinear Schrödinger Equations	p. 226
Nonlinear Phase Shift	p. 227
Solitons in Fibers with Constant Birefringence	p. 229
Solitons in Fibers with Randomly Varying Birefringence	p. 234
PMD-Induced Soliton Pulse Broadening	p. 236
Dispersion-Managed Solitons and PMD	p. 240
Problems	p. 242
References	p. 242
Stimulated Raman Scattering	p. 245
Raman Scattering in the Harmonic Oscillator Model	p. 246
Raman Gain	p. 250
Raman Threshold	p. 252
Impact of Raman Scattering on Communication Systems	p. 255
Raman Amplification	p. 258
Raman Fiber Lasers	p. 264
Problems	p. 269
References	p. 270
Stimulated Brillouin Scattering	p. 273
Light Scattering at Acoustic Waves	p. 274
The Coupled Equations for Stimulated Brillouin Scattering	p. 277
Brillouin Gain and Bandwidth	p. 278
Threshold of Stimulated Brillouin Scattering	p. 280
SBS in Active Fibers	p. 282
Impact of SBS on Communication Systems	p. 284
Fiber Brillouin Amplifiers	p. 286
Amplifier Gain	p. 287
Amplifier Noise	p. 289
Other Applications of the SBS Gain	p. 290
SBS Slow Light	p. 293
Fiber Brillouin Lasers	p. 296
Problems	p. 300
References	p. 301
Highly Nonlinear and Microstructured Fibers	p. 305
The Nonlinear Parameter in Silica Fibers	p. 306
Microstructured Fibers	p. 309
Non-Silica Fibers	p. 314
Soliton Self-Frequency Shift	p. 317
Four-Wave Mixing	p. 320
Supercontinuum Generation	p. 323
Basic Physics of Supercontinuum Generation	p. 323
Modeling the Supercontinuum	p. 330
Problems	p. 332
References	p. 332
Optical Signal Processing	p. 339
Nonlinear Sources for WDM Systems	p. 340
Optical Regeneration	p. 343
Optical Pulse Train Generation	p. 349
Wavelength Conversion	p. 350
Wavelength Conversion with FWM	p. 351
Wavelength Conversion with XPM	p. 354
All-Optical Switching	p. 358
XPM-Induced Optical Switching	p. 359
Optical Switching Using FWM	p. 361
Problems	p. 363
References	p. 364
Index	p. 369
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