| Preface |
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xv | |
| Symbols, Operators and Coordinate Systems |
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xvii | |
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1 | (20) |
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Maxwell Equations for Dielectric Media |
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1 | (1) |
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Inhomogeneous Vector Wave Equations |
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2 | (2) |
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Homogeneous Vector Wave Equations |
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4 | (1) |
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Translation-invariant Waveguides and Propagation Modes |
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4 | (8) |
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Cylindrical Polar Components |
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5 | (3) |
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8 | (4) |
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12 | (4) |
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The case of y and z Invariant Planar Waveguides |
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12 | (2) |
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The case of a Circularly Symmetric Refractive Index Profile n(r) |
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14 | (2) |
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Concluding Remarks on TE and TM Modes |
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16 | (1) |
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Nature of the Solutions to Vector Wave Equations |
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16 | (3) |
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19 | (2) |
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19 | (2) |
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Fundamental Properties of Vector Modes |
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21 | (18) |
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21 | (3) |
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Propagation Constant, Phase Velocity, and Writing Conventions |
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24 | (1) |
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Orthonormality of Guided Modes |
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25 | (3) |
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Stored Electromagnetic Energy |
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28 | (1) |
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Poynting Vector and Power Density |
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29 | (1) |
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30 | (3) |
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32 | (1) |
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Dispersion and Pulse Spreading |
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32 | (1) |
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Expansion of the Fields onto the Basis of Guided Modes |
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33 | (1) |
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Refractive Index Profile and Effective Index |
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34 | (2) |
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Fraction of Modal Power in the Core |
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36 | (1) |
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36 | (3) |
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36 | (3) |
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Exact Vector Solutions for Waveguides |
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39 | (76) |
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One-dimensional Planar Waveguides |
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40 | (25) |
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Symmetrical Step-index Planar Waveguide |
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40 | (14) |
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Asymmetrical Step-index Planar Waveguides |
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54 | (5) |
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Multi-layered Symmetrical Planar Waveguide |
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59 | (6) |
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Exact Solutions for Two-layer Step-index Optical Fibers |
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65 | (32) |
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Choice of Solutions for Longitudinal Components ez and hz |
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66 | (2) |
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68 | (1) |
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69 | (1) |
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Hybrid Modes HE and EH (v ≠ 0) |
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70 | (1) |
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Asymptotic Limits of the TE and TM Mode Eigenvalue Equations |
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71 | (1) |
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Asymptotic Limits of the HE and EH Mode Eigenvalue Equations |
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72 | (4) |
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Numerical Solutions of U(V) |
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76 | (2) |
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Analytical Expressions for the Fields |
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78 | (5) |
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83 | (1) |
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Fraction of Power Guided in the Core |
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84 | (6) |
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90 | (1) |
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Polarization of the Transverse Electric and Magnetic Fields |
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91 | (4) |
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Modal Power Density of the Hybrid Modes |
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95 | (2) |
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Radial Distribution of the Hybrid Mode Field Components |
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97 | (1) |
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Exact Solutions for Multi-layer Step-index Optical Fibers |
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97 | (13) |
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100 | (2) |
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102 | (1) |
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The Case of the TE and TM Modes |
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103 | (1) |
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Numerical Example for the SMF28™ Fiber |
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104 | (1) |
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105 | (1) |
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Group Velocity and Intramodal Dispersion of HE11 and EH11 in the SMF28™ Fiber |
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106 | (1) |
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Fundamental Mode of Multi-layered Step-index Fibers |
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106 | (4) |
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Exact Solutions for Graded-index Optical Fibers |
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110 | (2) |
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112 | (3) |
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112 | (3) |
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115 | (30) |
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116 | (2) |
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Two-layer Step-index Fibers |
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118 | (15) |
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119 | (1) |
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120 | (2) |
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Nomenclature of the Modes |
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122 | (1) |
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Polarization of the LP Modes |
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122 | (2) |
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124 | (1) |
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Effective Index Graph neff(V) |
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125 | (1) |
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Normalization of the Modes |
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125 | (2) |
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Numerical Examples of Radial Profiles Ψ (r) |
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127 | (2) |
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Fraction of Power Guided in the Core |
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129 | (2) |
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131 | (2) |
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Multi-layer Step-index Fibers |
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133 | (6) |
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133 | (2) |
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135 | (3) |
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Normalization of the Modes |
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138 | (1) |
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138 | (1) |
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Fraction of Power Guided in the Core |
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139 | (1) |
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139 | (3) |
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Solving the Scalar Wave Equation |
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140 | (1) |
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141 | (1) |
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141 | (1) |
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142 | (3) |
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143 | (2) |
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Degeneracy of the Vector Modes |
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145 | (24) |
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Degenerate Vector Modes in the Weakly Guiding Regime (Two-layer Fiber) |
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146 | (10) |
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Degenerate Forms of the Eigenvalue Equation |
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146 | (1) |
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Degenerate Forms of the Field Components |
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147 | (3) |
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150 | (2) |
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Combinations of Degenerate Modes to form LP Modes |
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152 | (4) |
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Generalization to Multi-layer and Graded-index Fibers |
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156 | (1) |
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Polarization Corrections for Two-layer Fibers |
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156 | (9) |
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157 | (2) |
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Approximation of Nearly Identical Fields |
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159 | (1) |
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Circularly Symmetric Fibers |
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159 | (6) |
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Polarization Corrections for other Circularly Symmetric Fibers |
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165 | (2) |
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The N-layer Step-index Fiber |
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165 | (1) |
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166 | (1) |
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The Composite Profile Fiber |
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166 | (1) |
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167 | (2) |
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168 | (1) |
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Mode Coupling and Bragg Gratings |
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169 | (38) |
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General Mode Coupling Equations |
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169 | (7) |
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Coupling Equation for a Forward-propagating Mode j |
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171 | (1) |
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Coupling Equation for a Backward-propagating Mode -j |
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172 | (1) |
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General Coupled Equations |
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173 | (1) |
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174 | (1) |
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Coupling between Two Modes due to a Periodic Perturbation and Bragg Grating |
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175 | (1) |
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Coupling between two Codirectional Modes |
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176 | (5) |
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Solving the Coupled Equations |
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176 | (2) |
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Frequency Response of Transmission Bragg Gratings |
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178 | (3) |
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Coupling between Two Counterdirectional Modes |
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181 | (7) |
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Solving the Coupled Equations |
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181 | (5) |
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Frequency Response of Bragg Reflectors |
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186 | (2) |
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Experimental Realization of Bragg Gratings |
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188 | (16) |
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Reflection Bragg Grating Obtained by a Stationary Wave |
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189 | (6) |
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Reflection Bragg Grating Written with a Phase Mask |
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195 | (5) |
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Long-period Bragg Gratings Obtained by Electric Discharges |
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200 | (2) |
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Long-period Bragg Grating Obtained by CO2 Laser |
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202 | (2) |
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204 | (3) |
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205 | (2) |
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207 | (38) |
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208 | (3) |
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Normal Modes of a Local Uniform Waveguide |
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208 | (1) |
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Local Modes of a Tapered Fiber |
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209 | (1) |
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Orthonormality of the Local Modes |
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209 | (1) |
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Decomposition on the Basis of Local Modes |
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210 | (1) |
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Coupled Equations for Local Modes |
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211 | (6) |
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Coupled Equations and the First Form for the Coefficients |
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211 | (1) |
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212 | (1) |
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Second Form of the Coupling Coefficients |
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213 | (2) |
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Alternate Form of the Coupled Equations |
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215 | (2) |
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Case of Circularly Symmetric Step-index Waveguides |
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217 | (12) |
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217 | (1) |
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Scalar Modes in the Weakly Guiding Regime |
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218 | (1) |
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Modal Behavior of Tapered Fibers |
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219 | (1) |
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Characteristic regions of the waveguide |
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220 | (1) |
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221 | (2) |
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Experimental Study of a Tapered Fiber |
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223 | (3) |
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Transmitted Power During the Tapering Process |
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224 | (1) |
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224 | (1) |
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Response as a Function of the Index of the External Medium |
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225 | (1) |
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Technological Applications of Tapered Fibers |
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226 | (16) |
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226 | (1) |
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Displacement and Curvature Sensor |
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226 | (2) |
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Pass(λp)/Stop(λs) Spectral Filter |
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228 | (3) |
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Pass-band Spectral Filter |
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231 | (1) |
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232 | (8) |
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Adiabaticity: Very Strong or Very Weak Slopes of Tapered Fibers |
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240 | (2) |
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242 | (3) |
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242 | (3) |
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245 | (16) |
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Reflection and Transmission at a Splice |
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245 | (5) |
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Calculation of the Amplitudes of the Reflected and Transmitted Modes |
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246 | (2) |
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Calculation of the Overlap Integrals Ijk |
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248 | (1) |
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249 | (1) |
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Reflection Modal Interferometer |
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250 | (3) |
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Transmission Bi-modal Interferometer |
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253 | (2) |
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Reflection and Transmission on the Fiber Endface |
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255 | (5) |
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258 | (2) |
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260 | (1) |
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260 | (1) |
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261 | (56) |
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Coupling via the Field Overlap Between the Fibers |
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265 | (19) |
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Coupled Equations and Coupling Coefficients |
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267 | (2) |
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Single-mode Fibers and the Adiabatic Coupler |
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269 | (1) |
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Physical Interpretation of the Quantity n2(x, y, z) - n2(%, y, z) |
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270 | (1) |
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Expression for C12 in the Case of Two Identical Step-index Fibers with nco and ncl |
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271 | (2) |
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Expression of C11, Correction of β of the LP01 Mode of Fiber 1 |
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273 | (1) |
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Numerical Calculation of C12 and C11 |
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274 | (1) |
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Solving the Coupled Equations in the case of an Adiabatic Coupler with Identical Fibers |
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274 | (2) |
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276 | (1) |
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Coupler with b2 (0) = 0 and b1 (0) = 1 |
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277 | (1) |
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Modeling of a Coupler and Numerical Examples |
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277 | (4) |
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Expression of the Coupling Coefficient C12 in the Case of Two Different Fibers |
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281 | (3) |
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Phase Mismatch and Coupling Between Non-codirectional Modes |
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284 | (1) |
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Coupling via Beating Between Supermodes |
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284 | (10) |
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Illustration of the First Two Supermodes of a 2 x 2 Coupler of Identical Fibers |
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285 | (1) |
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Coupling via the Beating of the First Two Supermodes |
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286 | (3) |
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Calculation of the Supermodes |
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289 | (2) |
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Modeling a Partially Fused Structure |
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291 | (1) |
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292 | (2) |
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Numerical Comparison of the Two Methods |
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294 | (2) |
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296 | (5) |
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Presentation and Analysis of the Results |
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296 | (4) |
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Modeling the Effects of Polarization |
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300 | (1) |
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301 | (13) |
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Wavelength Independent Power Dividing Couplers |
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301 | (3) |
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Couplers with Abrupt Slopes in the Wavelength Response |
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304 | (2) |
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Couplers with a Broadened Wavelength Response |
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306 | (1) |
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307 | (5) |
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312 | (2) |
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314 | (3) |
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314 | (3) |
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Appendix A: Bessel Functions and Modified Bessel Functions of Integer Order |
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317 | (8) |
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Differential Equations of the Bessel and Modified Bessel Functions |
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317 | (1) |
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Graphs of the First Three Orders of Bessel and Modified Bessel Functions |
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318 | (1) |
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Expansion Series of the Bessel and Modified Bessel Functions |
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318 | (1) |
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319 | (1) |
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320 | (1) |
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320 | (1) |
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320 | (1) |
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First Terms of the Asymptotic Forms when x → 0 |
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321 | (1) |
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First Terms of the Asymptotic Forms when x → ∞ |
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321 | (1) |
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Integrals of Bessel and Modified Bessel Functions |
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322 | (1) |
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323 | (1) |
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Roots of both Je(x) and its Derivatives J'e(x) |
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324 | (1) |
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Appendix B: Proof of the Identity used to Establish the Group Velocity Formula |
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325 | (4) |
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327 | (2) |
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Appendix C: Distinguishing between the HE and EH Vector Modes of a Multi-layered Fiber |
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329 | (8) |
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Effective Index Curves and the Inversion of Correspondences |
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330 | (1) |
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Polarization of Electric and Magnetic Fields as a Function of the Reduction Ratio R |
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330 | (2) |
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Method for Distinguishing between the EHvm and HEvm+1 Modes |
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332 | (5) |
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335 | (2) |
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Appendix D: Definitions of the Refractive Indices |
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337 | (4) |
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337 | (1) |
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Relative and Absolute Indices of Silica |
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337 | (1) |
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Relative and Absolute Refractive Indices of GaAs between λ = 0.8 and 1.65 μm |
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338 | (1) |
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Relative and Absolute Refractive Indices of AlAs between λ = 0.65 and μm |
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338 | (1) |
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Relative Index Curves of AlAs and GaAs |
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339 | (2) |
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339 | (2) |
| Index |
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341 | |
