Author biography |
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xvii | |
Preface |
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xix | |
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1 | (26) |
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1.1 Historical perspective |
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1 | (2) |
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1.2 Fiber characteristics |
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3 | (12) |
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1.2.1 Material and fabrication |
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4 | (1) |
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5 | (1) |
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1.2.3 Chromatic dispersion |
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6 | (5) |
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1.2.4 Polarization-mode dispersion |
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11 | (4) |
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15 | (4) |
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1.3.1 Nonlinear refraction |
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15 | (1) |
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1.3.2 Stimulated inelastic scattering |
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16 | (2) |
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1.3.3 Importance of nonlinear effects |
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18 | (1) |
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19 | (8) |
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22 | (1) |
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22 | (5) |
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2 Pulse propagation in fibers |
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27 | (30) |
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27 | (2) |
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29 | (5) |
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2.2.1 Eigenvalue equation |
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30 | (2) |
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2.2.2 Characteristics of the fundamental mode |
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32 | (2) |
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2.3 Pulse-propagation equation |
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34 | (12) |
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2.3.1 Nonlinear wave equation |
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34 | (6) |
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2.3.2 Higher-order nonlinear effects |
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40 | (2) |
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2.3.3 Raman response function and its impact |
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42 | (4) |
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46 | (11) |
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2.4.1 Split-step Fourier method |
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46 | (4) |
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2.4.2 Finite-difference methods |
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50 | (2) |
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52 | (1) |
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53 | (4) |
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3 Group-velocity dispersion |
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57 | (28) |
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3.1 Different propagation regimes |
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57 | (2) |
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3.2 Dispersion-induced pulse broadening |
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59 | (10) |
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60 | (2) |
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3.2.2 Chirped Gaussian pulses |
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62 | (2) |
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3.2.3 Hyperbolic secant pulses |
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64 | (1) |
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3.2.4 Super-Gaussian pulses |
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65 | (3) |
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3.2.5 Experimental results |
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68 | (1) |
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3.3 Third-order dispersion |
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69 | (7) |
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3.3.1 Chirped Gaussian pulses |
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70 | (1) |
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71 | (3) |
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3.3.3 Ultrashort-pulse measurements |
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74 | (2) |
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3.4 Dispersion management |
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76 | (9) |
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3.4.1 Dispersion compensation |
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76 | (2) |
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3.4.2 Compensation of third-order dispersion |
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78 | (2) |
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3.4.3 Dispersion-varying fibers |
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80 | (1) |
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81 | (1) |
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82 | (3) |
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85 | (42) |
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4.1 SPM-induced spectral changes |
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85 | (10) |
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4.1.1 Nonlinear phase shift |
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85 | (3) |
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4.1.2 Changes in pulse spectra |
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88 | (2) |
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4.1.3 Effect of pulse shape and initial chirp |
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90 | (3) |
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4.1.4 Effect of partial coherence |
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93 | (2) |
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4.2 Effect of group-velocity dispersion |
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95 | (13) |
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96 | (2) |
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98 | (2) |
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4.2.3 Optical wave breaking |
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100 | (3) |
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4.2.4 Experimental results |
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103 | (1) |
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4.2.5 Effect of third-order dispersion |
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104 | (1) |
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4.2.6 SPM effects in fiber amplifiers |
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105 | (3) |
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4.3 Semianalytic techniques |
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108 | (5) |
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108 | (2) |
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110 | (1) |
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4.3.3 Specific analytic solutions |
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111 | (2) |
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4.4 Higher-order nonlinear effects |
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113 | (14) |
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114 | (3) |
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4.4.2 Effect of GVD on optical shocks |
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117 | (2) |
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4.4.3 Intrapulse Raman scattering |
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119 | (2) |
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121 | (2) |
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123 | (4) |
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127 | (62) |
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5.1 Modulation instability |
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127 | (11) |
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5.1.1 Linear stability analysis |
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127 | (2) |
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129 | (2) |
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5.1.3 Experimental observation |
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131 | (1) |
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5.1.4 Ultrashort pulse generation |
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132 | (2) |
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5.1.5 Impact of loss and third-order dispersion |
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134 | (2) |
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5.1.6 Spatial modulation of fiber parameters |
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136 | (2) |
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138 | (12) |
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5.2.1 Inverse scattering method |
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139 | (2) |
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5.2.2 Fundamental soliton |
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141 | (2) |
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5.2.3 Second and higher-order solitons |
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143 | (3) |
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5.2.4 Experimental confirmation |
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146 | (1) |
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147 | (3) |
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5.3 Other types of solitons |
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150 | (9) |
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150 | (4) |
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154 | (1) |
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5.3.3 Dispersion-managed solitons |
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155 | (1) |
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5.3.4 Optical similaritons |
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156 | (3) |
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5.4 Perturbation of solitons |
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159 | (10) |
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5.4.1 Perturbation methods |
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159 | (1) |
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160 | (2) |
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5.4.3 Soliton amplification |
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162 | (3) |
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5.4.4 Soliton interaction |
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165 | (4) |
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169 | (11) |
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5.5.1 Moment equations for pulse parameters |
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169 | (2) |
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5.5.2 Third-order dispersion |
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171 | (2) |
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173 | (2) |
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5.5.4 Intrapulse Raman scattering |
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175 | (5) |
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5.6 Propagation of femtosecond pulses |
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180 | (9) |
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182 | (1) |
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183 | (6) |
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189 | (56) |
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6.1 Nonlinear birefringence |
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189 | (5) |
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6.1.1 Origin of nonlinear birefringence |
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190 | (2) |
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6.1.2 Coupled-mode equations |
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192 | (1) |
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6.1.3 Elliptically birefringent fibers |
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193 | (1) |
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6.2 Nonlinear phase shift |
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194 | (8) |
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194 | (2) |
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6.2.2 Optical Kerr effect |
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196 | (4) |
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200 | (2) |
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6.3 Evolution of polarization state |
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202 | (8) |
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202 | (2) |
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6.3.2 Poincare-sphere representation |
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204 | (3) |
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6.3.3 Polarization instability |
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207 | (3) |
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210 | (1) |
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6.4 Vector modulation instability |
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210 | (10) |
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6.4.1 Low-birefringence fibers |
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211 | (2) |
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6.4.2 High-birefringence fibers |
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213 | (2) |
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215 | (2) |
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6.4.4 Experimental results |
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217 | (3) |
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6.5 Birefringence and solitons |
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220 | (8) |
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6.5.1 Low-birefringence fibers |
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220 | (1) |
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6.5.2 High-birefringence fibers |
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221 | (4) |
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6.5.3 Soliton-dragging logic gates |
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225 | (1) |
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226 | (2) |
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228 | (8) |
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6.6.1 Extended coupled-mode equations |
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229 | (1) |
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6.6.2 Impact of TOD and Raman nonlinearity |
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230 | (3) |
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6.6.3 Interaction of two vector solitons |
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233 | (3) |
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236 | (9) |
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6.7.1 Polarization-mode dispersion |
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236 | (1) |
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6.7.2 Vector form of the NLS equation |
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237 | (2) |
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6.7.3 Effects of PMD on solitons |
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239 | (2) |
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241 | (1) |
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241 | (4) |
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245 | (52) |
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7.1 XPM-induced nonlinear coupling |
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245 | (3) |
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7.1.1 Nonlinear refractive index |
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245 | (2) |
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7.1.2 Coupled NLS equations |
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247 | (1) |
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7.2 XPM-induced modulation instability |
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248 | (4) |
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7.2.1 Linear stability analysis |
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248 | (2) |
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7.2.2 Experimental results |
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250 | (2) |
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252 | (5) |
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7.3.1 Bright-dark soliton pair |
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252 | (1) |
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7.3.2 Bright-gray soliton pair |
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253 | (1) |
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254 | (2) |
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7.3.4 Multiple coupled NLS equations |
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256 | (1) |
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7.4 Spectral and temporal effects |
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257 | (10) |
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7.4.1 Asymmetric spectral broadening |
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258 | (5) |
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7.4.2 Asymmetric temporal changes |
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263 | (3) |
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7.4.3 Higher-order nonlinear effects |
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266 | (1) |
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267 | (5) |
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7.5.1 XPM-induced pulse compression |
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267 | (3) |
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7.5.2 XPM-induced optical switching |
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270 | (1) |
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7.5.3 XPM-induced wavelength conversion |
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271 | (1) |
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272 | (10) |
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7.6.1 Vector theory of XPM |
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272 | (1) |
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7.6.2 Polarization evolution |
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273 | (3) |
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7.6.3 Polarization-dependent spectral broadening |
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276 | (2) |
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7.6.4 Pulse trapping and compression |
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278 | (3) |
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7.6.5 XPM-induced wave breaking |
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281 | (1) |
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7.7 XPM effects in birefringent fibers |
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282 | (6) |
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7.7.1 Fibers with low birefringence |
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283 | (4) |
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7.7.2 Fibers with high birefringence |
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287 | (1) |
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7.8 Two counterpropagating waves |
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288 | (9) |
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291 | (1) |
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292 | (5) |
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8 Stimulated Raman scattering |
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297 | (58) |
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297 | (10) |
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8.1.1 Raman-gain spectrum |
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298 | (1) |
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299 | (3) |
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8.1.3 Coupled amplitude equations |
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302 | (3) |
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8.1.4 Effect of four-wave mixing |
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305 | (2) |
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307 | (12) |
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8.2.1 Single-pass Raman generation |
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307 | (2) |
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309 | (3) |
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8.2.3 Raman fiber amplifiers |
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312 | (5) |
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8.2.4 Raman-induced crosstalk |
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317 | (2) |
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8.3 SRS with short pump pulses |
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319 | (15) |
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8.3.1 Pulse-propagation equations |
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319 | (1) |
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320 | (3) |
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323 | (3) |
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8.3.4 Raman-induced index changes |
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326 | (1) |
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8.3.5 Experimental results |
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327 | (4) |
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8.3.6 Synchronously pumped Raman lasers |
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331 | (1) |
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8.3.7 Short-pulse Raman amplification |
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332 | (2) |
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334 | (8) |
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334 | (4) |
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8.4.2 Raman soliton lasers |
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338 | (3) |
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8.4.3 Soliton-effect pulse compression |
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341 | (1) |
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342 | (13) |
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8.5.1 Vector theory of Raman amplification |
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342 | (4) |
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8.5.2 PMD effects on Raman amplification |
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346 | (3) |
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349 | (1) |
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350 | (5) |
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9 Stimulated Brillouin scattering |
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355 | (46) |
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355 | (5) |
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355 | (1) |
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9.1.2 Brillouin-gain spectrum |
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356 | (4) |
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360 | (8) |
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9.2.1 Brillouin threshold |
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360 | (1) |
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9.2.2 Polarization effects |
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361 | (2) |
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9.2.3 Techniques for controlling the SBS threshold |
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363 | (2) |
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9.2.4 Experimental results |
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365 | (3) |
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9.3 Brillouin fiber amplifiers |
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368 | (4) |
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368 | (2) |
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9.3.2 Amplifier design and applications |
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370 | (2) |
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372 | (15) |
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9.4.1 Coupled amplitude equations |
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372 | (2) |
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9.4.2 SBS with Q-switched pulses |
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374 | (4) |
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9.4.3 SBS-induced index changes |
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378 | (5) |
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9.4.4 Relaxation oscillations |
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383 | (2) |
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9.4.5 Modulation instability and chaos |
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385 | (2) |
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9.5 Brillouin fiber lasers |
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387 | (14) |
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387 | (4) |
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391 | (3) |
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394 | (1) |
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395 | (6) |
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401 | (62) |
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10.1 Origin of four-wave mixing |
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401 | (2) |
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10.2 Theory of four-wave mixing |
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403 | (6) |
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10.2.1 Coupled amplitude equations |
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404 | (1) |
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10.2.2 Approximate solution |
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405 | (1) |
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10.2.3 Effect of phase matching |
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406 | (2) |
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10.2.4 Ultrafast four-wave mixing |
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408 | (1) |
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10.3 Phase-matching techniques |
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409 | (10) |
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10.3.1 Physical mechanisms |
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410 | (1) |
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10.3.2 Nearly phase-matched four-wave mixing |
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411 | (1) |
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10.3.3 Phase matching near the zero-dispersion wavelength |
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412 | (1) |
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10.3.4 Phase matching through self-phase modulation |
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413 | (3) |
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10.3.5 Phase matching in birefringent fibers |
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416 | (3) |
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10.4 Parametric amplification |
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419 | (15) |
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10.4.1 Review of early work |
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419 | (2) |
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10.4.2 Gain spectrum and its bandwidth |
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421 | (2) |
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10.4.3 Single-pump configuration |
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423 | (4) |
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10.4.4 Dual-pump configuration |
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427 | (5) |
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10.4.5 Effects of pump depletion |
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432 | (2) |
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10.5 Polarization effects |
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434 | (12) |
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10.5.1 Vectortheory of four-wave mixing |
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435 | (2) |
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10.5.2 Polarization dependence of parametric gain |
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437 | (3) |
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10.5.3 Linearly and circularly polarized pumps" |
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440 | (3) |
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10.5.4 Effect of residual fiber birefringence |
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443 | (3) |
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10.6 Applications of four-wave mixing |
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446 | (17) |
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10.6.1 Parametric amplifiers and wavelength converters |
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446 | (2) |
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10.6.2 Tunable fiber-optic parametric oscillators |
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448 | (3) |
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10.6.3 Ultrafast signal processing |
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451 | (2) |
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10.6.4 Quantum correlation and noise squeezing |
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453 | (3) |
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10.6.5 Phase-sensitive amplification |
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456 | (1) |
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457 | (1) |
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458 | (5) |
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11 Highly nonlinear fibers |
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463 | (40) |
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463 | (11) |
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11.1.1 Units and values of n2 |
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463 | (2) |
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11.1.2 SPM-based techniques |
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465 | (3) |
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11.1.3 XPM-based technique |
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468 | (1) |
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11.1.4 FWM-based technique |
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469 | (2) |
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11.1.5 Variations in n2 values |
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471 | (3) |
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11.2 Fibers with silica cladding |
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474 | (2) |
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11.3 Tapered fibers with air cladding |
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476 | (4) |
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11.4 Microstructured fibers |
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480 | (7) |
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11.4.1 Design and fabrication |
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480 | (2) |
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11.4.2 Modal and dispersive properties |
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482 | (3) |
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11.4.3 Hollow-core photonic crystal fibers |
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485 | (1) |
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486 | (1) |
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487 | (6) |
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11.5.1 Lead-silicate fibers |
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488 | (3) |
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11.5.2 Chalcogenide fibers |
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491 | (1) |
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11.5.3 Bismuth-oxide fibers |
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492 | (1) |
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11.6 Theory of narrow-core fibers |
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493 | (10) |
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498 | (1) |
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499 | (4) |
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12 Novel nonlinear phenomena |
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503 | (54) |
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12.1 Soliton fission and dispersive waves |
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503 | (9) |
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12.1.1 Fission of second-and higher-order solitons |
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503 | (4) |
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12.1.2 Generation of dispersive waves |
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507 | (5) |
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12.2 Intrapulse Raman scattering |
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512 | (20) |
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12.2.1 Enhanced RIFS through soliton fission |
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512 | (4) |
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12.2.2 Cross-correlation technique |
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516 | (2) |
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12.2.3 Wavelength tuning through RIFS |
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518 | (3) |
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12.2.4 Effects of birefringence |
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521 | (2) |
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12.2.5 Suppression of Raman-induced frequency shifts |
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523 | (4) |
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12.2.6 Soliton dynamics near a zero-dispersion wavelength |
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527 | (3) |
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12.2.7 Multipeak Raman solitons |
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530 | (2) |
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12.3 Frequency combs and cavity solitons |
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532 | (6) |
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12.3.1 CW-pumped ring cavities |
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533 | (1) |
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12.3.2 Nonlinear dynamics of ring cavities |
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534 | (3) |
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12.3.3 Frequency combs without a cavity |
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537 | (1) |
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12.4 Second-harmonic generation |
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538 | (8) |
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12.4.1 Physical mechanisms |
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539 | (2) |
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12.4.2 Thermal poling and quasi-phase matching |
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541 | (3) |
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544 | (2) |
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12.5 Third-harmonic generation |
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546 | (11) |
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12.5.1 THG in highly nonlinear fibers |
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546 | (1) |
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12.5.2 Effects of group-velocity mismatch |
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547 | (2) |
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12.5.3 Effects of fiber birefringence |
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549 | (2) |
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551 | (1) |
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552 | (5) |
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13 Supercontinuum generation |
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557 | (64) |
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13.1 Pumping with picosecond pulses |
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557 | (6) |
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13.1.1 Nonlinear mechanisms |
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558 | (2) |
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13.1.2 Experimental progress after 2000 |
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560 | (3) |
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13.2 Pumping with femtosecond pulses |
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563 | (5) |
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13.3 Temporal and spectral evolution of pulses |
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568 | (13) |
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13.3.1 Numerical modeling of supercontinuum |
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569 | (3) |
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13.3.2 Role of cross-phase modulation |
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572 | (3) |
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13.3.3 XPM-induced trapping |
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575 | (5) |
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13.3.4 Role of four-wave mixing |
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580 | (1) |
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13.4 CW or quasi-CW pumping |
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581 | (7) |
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13.4.1 Nonlinear mechanisms |
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582 | (3) |
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13.4.2 Experimental results |
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585 | (3) |
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13.5 Polarization effects |
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588 | (5) |
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13.6 Coherence properties |
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593 | (8) |
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13.6.1 Effect of pump coherence |
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593 | (3) |
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13.6.2 Spectral incoherent solitons |
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596 | (3) |
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13.6.3 Techniques for improving spectral coherence |
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599 | (2) |
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13.7 Ultraviolet and mid-infrared supercontinua |
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601 | (6) |
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13.7.1 Extension into ultraviolet region |
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602 | (2) |
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13.7.2 Extension into mid-infrared region |
|
|
604 | (3) |
|
|
607 | (14) |
|
13.8.1 L-shaped statistics of pulse-to-pulse fluctuations |
|
|
607 | (1) |
|
13.8.2 Techniques for controlling rogue-wave statistics |
|
|
608 | (3) |
|
13.8.3 Modulation instability revisited |
|
|
611 | (3) |
|
|
614 | (1) |
|
|
615 | (6) |
|
|
621 | (64) |
|
14.1 Modes of optical fibers |
|
|
621 | (10) |
|
|
621 | (4) |
|
14.1.2 Graded-index fibers |
|
|
625 | (2) |
|
|
627 | (3) |
|
14.1.4 Excitation of fiber modes |
|
|
630 | (1) |
|
14.2 Nonlinear pulse propagation |
|
|
631 | (9) |
|
14.2.1 Multimode propagation equations |
|
|
631 | (2) |
|
|
633 | (2) |
|
14.2.3 Random linear mode coupling |
|
|
635 | (3) |
|
14.2.4 Graded-index fibers |
|
|
638 | (2) |
|
14.3 Modulation instability and solitons |
|
|
640 | (11) |
|
14.3.1 Modulation instability |
|
|
641 | (3) |
|
14.3.2 Multimode solitons |
|
|
644 | (5) |
|
14.3.3 Solitons in specific fiber modes |
|
|
649 | (2) |
|
14.4 Intermodal nonlinear phenomena |
|
|
651 | (14) |
|
|
651 | (6) |
|
|
657 | (5) |
|
|
662 | (3) |
|
14.5 Spatio-temporal dynamics |
|
|
665 | (9) |
|
14.5.1 Spatial beam cleanup |
|
|
666 | (2) |
|
14.5.2 Supercontinuum generation |
|
|
668 | (6) |
|
|
674 | (11) |
|
|
678 | (1) |
|
|
679 | (6) |
|
|
685 | (2) |
|
B Nonlinear response of fibers |
|
|
687 | (2) |
|
|
688 | (1) |
|
C Derivation of the generalized NLS equation |
|
|
689 | (4) |
|
D Numerical code for the NLS equation |
|
|
693 | (2) |
|
|
695 | (2) |
Index |
|
697 | |