Finite Element Methods for Nonlinear Optical Waveguides

Series Contents......Page 1
Title......Page 2
Date-line......Page 3
CONTENTS ......Page 4
Preface ......Page 8
1.1 Introduction ......Page 14
1.2 Overview ......Page 16
1.3 Miscellaneous ......Page 21
2.1 Introduction......Page 24
2.2 Nonlinear Wave Equations and Constitutive Relations ......Page 27
2.3 Formulation of Electromagnetic Wave Equations and the Self-Adjointness of the Operator ......Page 28
2.4.2 Method of moments ......Page 32
2.5 Extended Operator ......Page 33
2.6 Spurious Mode Problem and Penalty Function Method ......Page 35
2.7 Guided Power ......Page 39
3.1 Introduction ......Page 40
3.2 Nonconventional Vector Finite Elements ......Page 42
3.3 Basis Functions and Element Matrix Equations ......Page 44
3.4 Enforcing the Interface and Boundary Conditions ......Page 50
3.4.1 Interface conditions ......Page 51
3.4.2 Boundary conditions ......Page 58
4.1 Introduction ......Page 62
4.2 Fundamentals ......Page 64
4.3 Node Generation ......Page 67
4.4 Automatic Triangulation and Smoothing ......Page 70
4.5 Automatic Node Renumbering ......Page 72
4.6 Extension to Second-Order Triangular Elements ......Page 79
5.1 Introduction ......Page 82
5.2 The Generalised Eigenvalue Problem and the Nonlinear Iteration Procedure ......Page 84
5.3 Solution Methods ......Page 86
5.3.1 Successive over-relaxation and Rayleigh Quotient ......Page 88
5.3.2 Vector iteration ......Page 89
5.3.3 Bisection and inverse iteration with shift ......Page 91
5.4 A Posteriori Error Estimates ......Page 93
5.5 Application of the Package to a Classical Linear Example ......Page 94
5.6 Nonlinear Acceleration Techniques ......Page 98
6.1 Introduction ......Page 106
6.2 The Necessity of Including Saturation in the Nonlinear Permittivity Model ......Page 108
6.3 Comparison of the Electric and the Magnetic Field Formulations, Normalisation and Other Computational Aspects ......Page 125
6.4 Novel Simulation of Bistability Phenomena in Nonlinear Optical Waveguides ......Page 138
6.5 Correct Modelling of Planar Nonlinear Optical Waveguides ......Page 153
6.5.1 E-vector quasi-3D model ......Page 154
6.5.2 Characterisation of nonlinear planar optical waveguides ......Page 157
7.1 Introduction ......Page 170
7.2 Weak-Guidance Approximation ......Page 172
7.2.1 An example ofa nonlinear strip-loaded channel structure ......Page 175
7.2.2 An example ofa symmetric planar nonlinear structure ......Page 176
7.3 Weak-Guidance Approximation for an Asymmetric Planar Nonlinear Structure ......Page 184
7.4.1 Propagation algorithm ......Page 189
7.4.2 Stability analysis of nonlinear modes ......Page 191
7.4.4 All-optical switching ......Page 196
7.4.5 Conclusions ......Page 199
8.1 Introduction ......Page 204
8.2 Principle of Optical Couplers ......Page 205
8.3 Supermode Superposition Technique ......Page 209
8.4 Coupled-Mode Theory ......Page 210
8.4.1 Application to linearcoupledwaveguides ......Page 211
8.4.2 Application to nonlinear coupledwaveguides ......Page 214
8.5.1 Computational aspects ......Page 220
8.5.2 A numerical example ......Page 221
8.5.3 Application to spatial-temporal soliton systems ......Page 224
Appendix A: ANOWS Contents ......Page 230
B.1 AMG.FOR ......Page 234
B.2 OMG.FOR ......Page 237
B.3 MEF.FOR ......Page 238
B.5 MSA.FOR ......Page 243
B.6 MTE.FOR ......Page 246
B.8 FPP.FOR ......Page 249
B.9 BMS.LIB ......Page 250
С.1 Mesh Generation and Plotting ......Page 254
C.2 Vector Modal Analysis ......Page 256
C.3 Scalar E-Field Approximation ......Page 257
C.4 Ana lysis of ТЕ Modes in Planar Structures ......Page 258
C.5 Field Plot Primer ......Page 259
Appendix D: Common Errors in Using ANOWS ......Page 262
Bibliography ......Page 264
Index ......Page 298
License Agreement ......Page 304