A new method of finding the propagation constants of guided modes in slab waveguides containing lossless and absorbing media

The determination of the propagation constants of guided modes in waveguiding structures is an important topic in guided-wave optics. In integrated optics, many optical components can be modeled as step-index two-dimensional slab waveguides and thereby guided modes in such optical waveguides are discussed here. To solve this problem, the standard approach is to find the dispersion relationship in the waveguide or to use the coupled-mode theory, but the formulation and calculations become very complicated for a higher-order multi-layered waveguide and media containing absorbing materials. In this work, we use a rather simple approach to investigate the propagation constants of guided modes in step-index slab waveguides. The well-known equation for the reflection of a plane wave in layered media is used. Fundamentals of our method is briefly explained and three multiple-layered waveguides are presented as examples