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<p>Preface xiii</p> <p>List of Abbreviations xv</p> <p><b>1 Introduction 1</b></p> <p>References 5</p> <p><b>2 Waves Called Solitons 9</b></p> <p>2.1 Linear and Nonlinear Effects of a Wave 9</p> <p>2.2 Solitary Waves and Solitons 11</p> <p>2.3 Solitons in Optical Fibers 13</p> <p>2.4 Dissipative Optical Solitons 15</p> <p>References 16</p> <p><b>3 Fiber Dispersion and Nonlinearity 19</b></p> <p>3.1 Fiber Chromatic Dispersion 19</p> <p>3.1.1 Gaussian Input Pulses 21</p> <p>3.2 Fiber Nonlinearity 25</p> <p>3.2.1 The Nonlinear Refractive Index 25</p> <p>3.2.2 Relevance of Nonlinear Effects in Fibers 26</p> <p>3.3 The Pulse Propagation Equation 28</p> <p>3.3.1 The Normalized NLSE 29</p> <p>3.3.2 Propagation in the Absence of Dispersion and Nonlinearity 30</p> <p>3.3.3 Effect of Dispersion Only 30</p> <p>3.3.4 Effect of Nonlinearity Only 32</p> <p>References 33</p> <p><b>4 Nonlinear Effects in Optical Fibers 35</b></p> <p>4.1 Self-Phase Modulation 35</p> <p>4.1.1 Modulation Instability 39</p> <p>4.2 Cross-Phase Modulation 40</p> <p>4.3 Four-Wave Mixing 42</p> <p>4.4 Stimulated Raman Scattering 45</p> <p>4.5 Stimulated Brillouin Scattering 49</p> <p>References 52</p> <p><b>5 Optical Amplification 57</b></p> <p>5.1 General Concepts on Optical Amplifiers 57</p> <p>5.2 Erbium-Doped Fiber Amplifiers 59</p> <p>5.2.1 Two-Level Model 60</p> <p>5.3 Fiber Raman Amplifiers 63</p> <p>5.4 Fiber Parametric Amplifiers 68</p> <p>5.5 Lumped versus Distributed Amplification 72</p> <p>5.6 Parabolic Pulses 74</p> <p>References 76</p> <p><b>6 Solitons in Optical Fibers 81</b></p> <p>6.1 The Fundamental Soliton Solution 81</p> <p>6.2 Higher-Order Solitons 83</p> <p>6.3 Soliton Units 86</p> <p>6.4 Dark Solitons 87</p> <p>6.5 Bistable Solitons 88</p> <p>6.6 XPM-Paired Solitons 89</p> <p>6.7 Optical Similaritons 90</p> <p>6.8 Numerical Solution of the NLSE 92</p> <p>6.9 The Variational Approach 94</p> <p>6.10 The Method of Moments 97</p> <p>References 98</p> <p><b>7 Soliton Transmission Systems 101</b></p> <p>7.1 Soliton Perturbation Theory 101</p> <p>7.2 Effect of Fiber Losses 102</p> <p>7.3 Soliton Amplification 103</p> <p>7.3.1 Lumped Amplification 104</p> <p>7.3.2 Distributed Amplification 105</p> <p>7.4 Soliton Interaction 107</p> <p>7.5 Timing Jitter 110</p> <p>7.5.1 Gordon-Haus Jitter 110</p> <p>7.5.2 Polarization-Mode Dispersion Jitter 113</p> <p>7.5.3 Acoustic Jitter 113</p> <p>7.5.4 Soliton Interaction Jitter 114</p> <p>7.6 WDM Soliton Systems 114</p> <p>7.6.1 Lossless Soliton Collisions 114</p> <p>7.6.2 Soliton Collisions in Perturbed Fiber Spans 116</p> <p>7.6.3 Timing Jitter 117</p> <p>References 117</p> <p><b>8 Soliton Transmission Control 121</b></p> <p>8.1 Fixed-Frequency Filters 121</p> <p>8.1.1 Control of Timing Jitter 122</p> <p>8.1.2 Control of Soliton Interaction 123</p> <p>8.1.3 Background Instability 125</p> <p>8.2 Sliding-Frequency Filters 125</p> <p>8.2.1 Evolution of Soliton Parameters 126</p> <p>8.2.2 Control of Timing Jitter 129</p> <p>8.2.3 Control of Soliton Interaction 131</p> <p>8.3 Synchronous Modulators 132</p> <p>8.4 Amplifiers with Nonlinear Gain 133</p> <p>8.4.1 Stationary Solutions 134</p> <p>8.4.2 Control of Soliton Interaction 137</p> <p>References 139</p> <p><b>9 Propagation of Ultrashort Solitons 141</b></p> <p>9.1 Generalized NLSE 141</p> <p>9.1.1 Third-Order Dispersion 142</p> <p>9.1.2 Self-Steepening 143</p> <p>9.1.3 Intrapulse Raman Scattering 144</p> <p>9.2 Timing Jitter of Ultrashort Solitons 145</p> <p>9.3 Bandwidth-Limited Amplification of Ultrashort Solitons 147</p> <p>9.4 Transmission Control Using Nonlinear Gain 151</p> <p>9.4.1 Stationary Solutions 151</p> <p>9.4.2 Linear Stability Analysis 153</p> <p>References 157</p> <p><b>10 Dispersion-Managed Solitons 161</b></p> <p>10.1 Dispersion Management 161</p> <p>10.2 Characteristics of the Dispersion-Managed Soliton 163</p> <p>10.3 The Variational Approach to DM Solitons 167</p> <p>10.3.1 Generic Ansatz 167</p> <p>10.3.2 Gaussian Pulses 168</p> <p>10.3.3 Stationary Solutions 169</p> <p>10.4 Interaction Between DM Solitons 170</p> <p>10.5 The Gordon–Haus Effect for DM Solitons 172</p> <p>10.6 Effects of a Spectral Filter 173</p> <p>10.6.1 Timing Jitter Control 174</p> <p>10.7 Effects of an Amplitude Modulator 175</p> <p>10.8 WDM with DM Solitons 177</p> <p>References 179</p> <p><b>11 Polarization Effects 183</b></p> <p>11.1 Fiber Birefringence and Polarization Mode Dispersion 183</p> <p>11.1.1 PMD in Long Fiber Spans 185</p> <p>11.1.2 PMD-Induced Pulse Broadening in Linear Systems 187</p> <p>11.1.3 PMD Compensation 188</p> <p>11.2 Coupled Nonlinear Schrödinger Equations 190</p> <p>11.3 Solitons in Fibers with Constant Birefringence 191</p> <p>11.4 Vector Solitons 195</p> <p>11.5 Solitons in Fibers with Randomly Varying Birefringence 196</p> <p>11.6 PMD-Induced Soliton Pulse Broadening 197</p> <p>11.7 Dispersion-Managed Solitons and PMD 200</p> <p>References 202</p> <p><b>12 Stationary Dissipative Solitons 207</b></p> <p>12.1 Balance Equations for the CGL Equation 207</p> <p>12.2 Exact Analytical Solutions 210</p> <p>12.2.1 Solutions of the Cubic CGLE 210</p> <p>12.2.2 Solutions of the Quintic CGLE 212</p> <p>12.3 Numerical Stationary Soliton Solutions 213</p> <p>12.4 High-Energy Dissipative Solitons 216</p> <p>12.5 Soliton Bound States 221</p> <p>12.6 Impact of Higher-Order Effects 225</p> <p>References 229</p> <p><b>13 Pulsating Dissipative Solitons 233</b></p> <p>13.1 Dynamic Models for CGLE Solitons 233</p> <p>13.1.1 The Variational Approach 234</p> <p>13.1.1.1 Sech Ansatz 235</p> <p>13.1.1.2 Gaussian Ansatz 235</p> <p>13.1.2 The Method of Moments 236</p> <p>13.2 Plain Pulsating Solitons 238</p> <p>13.2.1 Impact of Higher-Order Effects 239</p> <p>13.3 Creeping Solitons 241</p> <p>13.3.1 Impact of Higher-Order Effects 242</p> <p>13.4 Chaotic Solitons 244</p> <p>13.5 Erupting Solitons 247</p> <p>13.5.1 Impact of Higher-Order Effects 251</p> <p>13.5.2 Experimental Observation of Soliton Explosions 253</p> <p>References 256</p> <p><b>14 Soliton Fiber Lasers 259</b></p> <p>14.1 The First Soliton Laser 259</p> <p>14.2 Fundamentals of Fiber Soliton Lasers 260</p> <p>14.3 Mode-Locking Techniques 262</p> <p>14.3.1 Active Mode-Locking 262</p> <p>14.3.2 Passive Mode-Locking 262</p> <p>14.3.3 Nonlinear Optical Loop Mirrors 263</p> <p>14.3.4 Figure-Eight Laser 264</p> <p>14.3.5 Nonlinear Polarization Rotation 265</p> <p>14.3.6 Hybrid Mode-Locking 265</p> <p>14.4 High-Energy Soliton Fiber Lasers 266</p> <p>14.5 Modeling of Soliton Fiber Lasers 268</p> <p>14.6 Polarization Effects 272</p> <p>14.7 Dissipative Soliton Molecules 273</p> <p>14.8 Experimental Observation of Pulsating Solitons 274</p> <p>References 279</p> <p><b>15 Other Applications of Optical Solitons 285</b></p> <p>15.1 All-Optical Switching 285</p> <p>15.1.1 The Fiber Coupler 285</p> <p>15.1.2 The Sagnac Interferometer 286</p> <p>15.2 2R Optical Regeneration 288</p> <p>15.3 Pulse Compression 290</p> <p>15.3.1 Grating-Fiber Compression 290</p> <p>15.3.2 Higher-Order Soliton-Effect Compression 291</p> <p>15.3.3 Compression of Fundamental Solitons 293</p> <p>15.3.4 Dissipative Soliton Compression 295</p> <p>15.4 Solitons in Fiber Gratings 298</p> <p>15.4.1 Pulse Compression Using Fiber Gratings 300</p> <p>15.4.2 Fiber Bragg Solitons 302</p> <p>References 305</p> <p><b>16 Highly Nonlinear Optical Fibers 309</b></p> <p>16.1 Highly Nonlinear Silica Fibers 309</p> <p>16.1.1 Tapered Fibers 310</p> <p>16.2 Microstructured Optical Fibers 311</p> <p>16.3 Non-Silica Fibers 318</p> <p>16.4 Soliton Fission and Dispersive Waves 320</p> <p>16.5 Four-Wave Mixing 324</p> <p>16.6 Hollow-Core Microstructured Fibers 325</p> <p>References 332</p> <p><b>17 Supercontinuum Generation 337</b></p> <p>17.1 Pumping with Femtosecond Pulses 337</p> <p>17.2 Modeling the Supercontinuum 341</p> <p>17.3 Pumping with Picosecond Pulses 344</p> <p>17.4 Continuous Wave Supercontinuum Generation 347</p> <p>17.5 Mid-IR Supercontinuum Generation 350</p> <p>17.6 Supercontinuum Coherence 352</p> <p>17.6.1 Spectral Incoherent Solitons 354</p> <p>17.7 Supercontinuum Generation in Hollow-Core Kagomé Fibers 356</p> <p>References 365</p> <p>Index 369</p>

<P><B>Mário F. S. Ferreira, PhD, </B>is a Senior Member of the Optical Society of America (OSA) and SPIE - The International Society for Optical and Photonics. He is also a member of the IEEE Photonics Society and the Portuguese Physical Society. He is a Travelling Lecturer of the OSA and SPIE.</P>

<P><b>Discover a robust exploration of the main properties and behaviors of solitons in fiber systems</B></P> <P>In <I>Solitons in Optical Fiber Systems,</I> distinguished researcher Dr. Mário F. S. Ferreira delivers a thorough treatment of the main characteristics of solitons in optical fiber communication systems and fiber devices, paying special attention to stationary and pulsating dissipative soliton pulses. The book discusses the technical aspects associated with the physical background and the theoretical description of soliton characteristics under different conditions. <P>The author employs numerical analyses and variational approaches to describe soliton evolution and describes the phenomenon of supercontinuum generation and various solitonic effects observed in highly nonlinear fibers, like photonic crystal fibers. <P>Readers will learn about different applications of fiber solitons in transmission systems, fiber lasers, couplers, and pulse compression schemes, as well as complex Ginzburg-Landau equations, which are used to model different types of dissipative systems. <P>The book also includes: <UL><LI>A thorough introduction to solitons, including the linear and nonlinear effects of a wave, the discovery of solitary waves, and the discovery of solitons in optical fibers</LI> <LI>An exploration of fiber dispersion and nonlinearity, including optical fiber dispersion, the pulse propagation equation, and the impact of fiber dispersion</LI> <LI>Practical discussions of nonlinear effects in optical fibers, including self-phase modulation, cross-phase modulations, four-wave mixing, and stimulated raman scattering</LI> <LI>In-depth treatments of solitons in optical fibers, including modulation instability, dark solitons, bistable solitons, XPM-paired solitons, and the variational approach</LI></UL> <P>Perfect for senior undergraduate and graduate students in courses dealing with fiber-optics technology,<I> Solitons in Optical Fiber Systems </I>is also an ideal resource for engineers and technicians in the fiber-optics industry and researchers of nonlinear fiber optics.

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