Abstract

Chapter 5 covers beam propagation methods for the design of two- and three-dimensional (2D, 3D) optical waveguides. Discussed here are the fast Fourier transform beam propagation method (FFT-BPM), the finite-difference beam propagation method (FD-BPM), the transparent boundary conditions, the wide-angle FD-BPM using the Padé approximant operators, the 3D semivectorial analysis based on the alternate-direction implicit method, and the fully vectorial analysis. The concepts of these methods are discussed in detail and their equations are derived. Also discussed are the error factors of the FFT-BPM, the physical meaning of the Fresnel equation, the problems with the wide-angle FFT-BPM, and the stability of the FD-BPM. A problem-solving section appears at the end of the chapter.

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