Solutions of the 2-D Helmoholtz equation for optical waveguides

In both optical fibers and integrated optical devices, the basic phenomenon is that of waveguidance, and in order to effectively analyse and design these waveguides, it is necessary to understand the phenomenon of guidance through them. in the most basic form, this requires the solutions of Maxwell's equations for the boundary conditions represented by the waveguiding structure. Fortunately, for optical waveguides, in most cases of practical importance, it suffices to solve the much simpler Helmholtz equation. However, is still difficult to solve this equation for those integrated optical structures which provide two-dimensional confinement to optical waves. In this case the Helmholtz equation is a partial differential equation and one has to use approximate and/or numerical techniques to obtain its solutions. The present report is concerned with some of such techniques developed recently. 40 refs, 10 figs, 4 tabs