Introduction to Optical Waveguide Analysis

KENJI KAWANO, PhD, is Senior Research Engineer and Director of the Research Laboratory at the Anritsu Corporation.TSUTOMU KITOH, PhD, is Senior Research Engineer at the Photonics Laboratories of the Nippon Telegraph and Telephone Corporation.

• 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