ABSTRACT
This chapter deals with the study of propagation characteristics of the mode of a waveguide with arbitrary refractive index profile n(x). The optical waveguide is probably the planar waveguide that consists of a thin dielectric film sandwiched between materials of slightly lower refractive indices. The chapter also deals with variational method which uses a semi-analytical tool, can be used very effectively for obtaining propagation characteristics of guided modes in planar gradient index waveguides. It describes another approximate method that is much more powerful than any other method and uses the Airy functions (MAF). The method was first suggested by Langer and is applicable to both the initial value as well as the eigenvalue problem. The chapter briefly outlines the basic ideas of beam propagation methods (BPMs). It discusses the beam propagation methods based on the paraxial approximation. The previous BPM technique used the Fresnel or paraxial approximation.
