Description
Book SynopsisA complete survey of modern design and analysis techniques for optical waveguides
This volume thoroughly details modern and widely accepted methods for designing the optical waveguides used in telecommunications systems. It offers a straightforward presentation of the sophisticated techniques used in waveguide analysis and enables a quick grasp of modern numerical methods with easy mathematics. The book is intended to guide the reader to a comprehensive understanding of optical waveguide analysis through self-study. This comprehensive presentation includes:
* An extensive and exhaustive list of mathematical manipulations
* Detailed explanations of common design methods: finite element method (FEM), finite difference method (FDM), beam propagation method (BPM), and finite difference time-domain method (FD-TDM)
* Explanations for numerical solutions of optical waveguide problems with sophisticated techniques used in modern computer-aided design (CAD) software
Table of ContentsPreface xi
1 Fundamental Equations 1
1.1 Maxwell's Equations 1
1.2 Wave Equations 3
1.3 Poynting Vectors 7
1.4 Boundary Conditions for Electromagnetic Fields 9
Problems 10
Reference 12
2 Analytical Methods 13
2.1 Method for a Three-Layer Slab Optical Waveguide 13
2.2 Effective Index Method 20
2.3 Marcatili's Method 23
2.4 Method for an Optical Fiber 36
Problems 55
References 57
3 Finite-Element Methods 59
3.1 Variational Method 59
3.2 Galerkin Method 68
3.3 Area Coordinates and Triangular Elements 72
3.4 Derivation of Eigenvalue Matrix Equations 84
3.5 Matrix Elements 89
3.6 Programming 105
3.7 Boundary Conditions 110
Problems 113
References 115
4 Finite-Difference Methods 117
4.1 Finite-Difference Approximations 118
4.2 Wave Equations 120
4.3 Finite-Difference Expressions of Wave Equations 127
4.4 Programming 150
4.5 Boundary Conditions 153
4.6 Numerical Example 160
Problems 161
References 164
5 Beam Propagation Methods 165
5.1 Fast Fourier Transform Beam Propagation Method 165
5.2 Finite-Difference Beam Propagation Method 180
5.3 Wide-Angle Analysis Using Fade Approximant
Operators 204
5.4 Three-Dimensional Semivectorial Analysis 216
5.5 Three-Dimensional Fully Vectorial Analysis 222
Problems 227
References 230
6 Finite-Difference Time-Domain Method 233
6.1 Discretization of Electromagnetic Fields 233
6.2 Stability Condition 239
6.3 Absorbing Boundary Conditions 241
Problems 245
References 249
7 Schrodinger Equation 251
7.1 Time-Dependent State 251
7.2 Finite-Difference Analysis of Time-Independent State 253
7.3 Finite-Element Analysis of Time-Independent State 254
References 263
Appendix A Vectorial Formulas 265
Appendix B Integration Formula for Area Coordinates 267
Index 273
