A SCALAR VARIATIONAL ANALYSIS OF RECTANGULAR DIELECTRIC WAVE-GUIDES USING HERMITE-GAUSSIAN MODAL APPROXIMATIONS

A scalar variational analysis of rectangular dielectric waveguides usi ng Hermite-Gaussian modal approximations is presented. The technique a nalyzes waveguides by finding a closed-form, approximate solution to t he given problem. We begin with an assumed, closed-form field solution , with unknown parameters which can be chosen to best match the assume d field to the actual field solution using variational principles. The values of the unknown parameters of the assumed field are determined by solving a set of simultaneous equations, not by a search method. As a result, this analysis method is computationally fast. Another benef it is that this method gives best-fit, closed-form modal approximation s.