Nonlinear Effects in Optical Fibers

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  • Format: Hardcover
  • Copyright: 2011-05-31
  • Publisher: Wiley-OSA

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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

Prefacep. xi
Introductionp. 1
Referencesp. 5
Electromagnetic Wave Propagationp. 9
Wave Equation for Linear Mediap. 9
Electromagnetic Wavesp. 11
Energy Density and Flowp. 13
Phase Velocity and Group Velocityp. 14
Reflection and Transmission of Wavesp. 16
Snell's Lawsp. 16
Fresnel Equationsp. 17
The Harmonic Oscillator Modelp. 21
The Refractive Indexp. 23
The Limit of Geometrical Opticsp. 24
Problemsp. 26
Referencesp. 27
Optical Fibersp. 29
Geometrical Optics Descriptionp. 30
Planar Waveguidesp. 30
Step-Index Fibersp. 33
Graded-Index Fibersp. 36
Wave Propagation in Fibersp. 39
Fiber Modesp. 39
Single-Mode Fibersp. 42
Fiber Attenuationp. 44
Modulation and Transfer of Informationp. 45
Chromatic Dispersion in Single-Mode Fibersp. 46
Unchirped Input Pulsesp. 48
Chirped Input Pulsesp. 52
Dispersion Compensationp. 53
Polarization Mode Dispersionp. 54
Fiber Birefringence and the Intrinsic PMDp. 55
PMD in Long Fiber Spansp. 57
Problemsp. 60
Referencesp. 61
The Nonlinear Schrödinger Equationp. 63
The Nonlinear Polarizationp. 63
The Nonlinear Wave Equationp. 66
The Nonlinear Refractive Indexp. 66
Importance of Nonlinear Effects in Fibersp. 68
Derivation of the Nonlinear Schrödinger Equationp. 70
Propagation in the Absence of Dispersion and Nonlinearityp. 73
Effect of Dispersion Onlyp. 73
Effect of Nonlinearity Onlyp. 74
Normalized Form of NLSEp. 74
Soliton Solutionsp. 75
The Fundamental Solitonp. 76
Solutions of the Inverse Scattering Theoryp. 77
Dark Solitonsp. 80
Numerical Solution of the NLSEp. 81
Problemsp. 83
Referencesp. 84
Nonlinear Phase Modulationp. 85
Self-Phase Modulationp. 86
SPM-Induced Phase Shiftp. 86
The Variational Approachp. 89
Impact on Communication Systemsp. 93
Modulation Instabilityp. 94
Cross-Phase Modulationp. 97
XPM-Induced Phase Shiftp. 97
Impact on Optical Communication Systemsp. 100
Modulation Instabilityp. 103
XPM-Paired Solitonsp. 105
Problemsp. 106
Referencesp. 107
Four-Wave Mixingp. 111
Wave Mixingp. 112
Mathematical Descriptionp. 114
Phase Matchingp. 115
Impact and Control of FWMp. 118
Fiber Parametric Amplifiersp. 123
FOPA Gain and Bandwidthp. 123
Parametric Oscillatorsp. 128
Nonlinear Phase Conjugation with FWMp. 131
Squeezing and Photon Pair Sourcesp. 133
Problemsp. 135
Referencesp. 135
Intrachannel Nonlinear Effectsp. 139
Mathematical Descriptionp. 140
Intrachannel XPMp. 142
Intrachannel FWMp. 147
Control of Intrachannel Nonlinear Effectsp. 149
Problemsp. 153
Referencesp. 153
Soliton Lightwave Systemsp. 55
Soliton Propertiesp. 156
Soliton Interactionp. 157
Perturbation of Solitonsp. 159
Perturbation Theoryp. 160
Fiber Lossesp. 160
Path-Averaged Solitonsp. 162
Lumped Amplificationp. 163
Distributed Amplificationp. 164
Timing Jitterp. 166
Soliton Transmission Controlp. 168
Fixed-Frequency Filtersp. 169
Sliding-Frequency Filtersp. 170
Synchronous Modulatorsp. 173
Amplifier with Nonlinear Gainp. 174
Dissipative Solitonsp. 176
Analytical Results of the CGLEp. 176
Numerical Solutions of the CGLEp. 180
Dispersion-Managed Solitonsp. 183
The True DM Solitonp. 183
The Variational Approach to DM Solitonsp. 185
WDM Soliton Systemsp. 189
Problemsp. 192
Referencesp. 193
Other Applications of Optical Solitonsp. 199
Soliton Fiber Lasersp. 199
The First Soliton Laserp. 200
Figure-Eight Fiber Laserp. 201
Nonlinear Loop Mirrorsp. 201
Stretched-Pulse Fiber Lasersp. 202
Modeling Fiber Soliton Lasersp. 203
Pulse Compressionp. 204
Grating-Fiber Compressorsp. 204
Soliton-Effect Compressorsp. 207
Compression of Fundamental Solitonsp. 210
Fiber Bragg Gratingsp. 213
Pulse Compression Using Fiber Gratingsp. 214
Fiber Bragg Solitonsp. 216
Problemsp. 220
Referencesp. 220
Polarization Effectsp. 225
Coupled Nonlinear Schrödinger Equationsp. 226
Nonlinear Phase Shiftp. 227
Solitons in Fibers with Constant Birefringencep. 229
Solitons in Fibers with Randomly Varying Birefringencep. 234
PMD-Induced Soliton Pulse Broadeningp. 236
Dispersion-Managed Solitons and PMDp. 240
Problemsp. 242
Referencesp. 242
Stimulated Raman Scatteringp. 245
Raman Scattering in the Harmonic Oscillator Modelp. 246
Raman Gainp. 250
Raman Thresholdp. 252
Impact of Raman Scattering on Communication Systemsp. 255
Raman Amplificationp. 258
Raman Fiber Lasersp. 264
Problemsp. 269
Referencesp. 270
Stimulated Brillouin Scatteringp. 273
Light Scattering at Acoustic Wavesp. 274
The Coupled Equations for Stimulated Brillouin Scatteringp. 277
Brillouin Gain and Bandwidthp. 278
Threshold of Stimulated Brillouin Scatteringp. 280
SBS in Active Fibersp. 282
Impact of SBS on Communication Systemsp. 284
Fiber Brillouin Amplifiersp. 286
Amplifier Gainp. 287
Amplifier Noisep. 289
Other Applications of the SBS Gainp. 290
SBS Slow Lightp. 293
Fiber Brillouin Lasersp. 296
Problemsp. 300
Referencesp. 301
Highly Nonlinear and Microstructured Fibersp. 305
The Nonlinear Parameter in Silica Fibersp. 306
Microstructured Fibersp. 309
Non-Silica Fibersp. 314
Soliton Self-Frequency Shiftp. 317
Four-Wave Mixingp. 320
Supercontinuum Generationp. 323
Basic Physics of Supercontinuum Generationp. 323
Modeling the Supercontinuump. 330
Problemsp. 332
Referencesp. 332
Optical Signal Processingp. 339
Nonlinear Sources for WDM Systemsp. 340
Optical Regenerationp. 343
Optical Pulse Train Generationp. 349
Wavelength Conversionp. 350
Wavelength Conversion with FWMp. 351
Wavelength Conversion with XPMp. 354
All-Optical Switchingp. 358
XPM-Induced Optical Switchingp. 359
Optical Switching Using FWMp. 361
Problemsp. 363
Referencesp. 364
Indexp. 369
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