A complete survey of modern design and analysis techniques foroptical waveguidesThis volume thoroughly details modern and widely accepted methodsfor designing the optical waveguides used in telecommunicationssystems. It offers a straightforward presentation of thesophisticated techniques used in waveguide analysis and enables aquick grasp of modern numerical methods with easy mathematics. Thebook is intended to guide the reader to a comprehensiveunderstanding of optical waveguide analysis through self-study.This comprehensive presentation includes:* An extensive and exhaustive list of mathematicalmanipulations* Detailed explanations of common design methods: finite elementmethod (FEM), finite difference method (FDM), beam propagationmethod (BPM), and finite difference time-domain method(FD-TDM)* Explanations for numerical solutions of optical waveguideproblems with sophisticated techniques used in moderncomputer-aided design (CAD) software* Solutions to Maxwell's equations and the SchrodingerequationThe authors provide excellent self-study material forpractitioners, researchers, and students, while also presentingdetailed mathematical manipulations that can be easily understoodby readers who are unfamiliar with them. Introduction to OpticalWaveguide Analysis presents modern design methods in acomprehensive and easy-to-understand format.

Preface xi1 Fundamental Equations 11.1 Maxwell's Equations 11.2 Wave Equations 31.3 Poynting Vectors 71.4 Boundary Conditions for Electromagnetic Fields 9Problems 10Reference 122 Analytical Methods 132.1 Method for a Three-Layer Slab Optical Waveguide 132.2 Effective Index Method 202.3 Marcatili's Method 232.4 Method for an Optical Fiber 36Problems 55References 573 Finite-Element Methods 593.1 Variational Method 593.2 Galerkin Method 683.3 Area Coordinates and Triangular Elements 723.4 Derivation of Eigenvalue Matrix Equations 843.5 Matrix Elements 893.6 Programming 1053.7 Boundary Conditions 110Problems 113References 1154 Finite-Difference Methods 1174.1 Finite-Difference Approximations 1184.2 Wave Equations 1204.3 Finite-Difference Expressions of Wave Equations 1274.4 Programming 1504.5 Boundary Conditions 1534.6 Numerical Example 160Problems 161References 1645 Beam Propagation Methods 1655.1 Fast Fourier Transform Beam Propagation Method 1655.2 Finite-Difference Beam Propagation Method 1805.3 Wide-Angle Analysis Using Fade ApproximantOperators 2045.4 Three-Dimensional Semivectorial Analysis 2165.5 Three-Dimensional Fully Vectorial Analysis 222Problems 227References 2306 Finite-Difference Time-Domain Method 2336.1 Discretization of Electromagnetic Fields 2336.2 Stability Condition 2396.3 Absorbing Boundary Conditions 241Problems 245References 2497 Schrodinger Equation 2517.1 Time-Dependent State 2517.2 Finite-Difference Analysis of Time-Independent State 2537.3 Finite-Element Analysis of Time-Independent State 254References 263Appendix A Vectorial Formulas 265Appendix B Integration Formula for Area Coordinates 267Index 273