A scalar variational analysis of rectangular dielectric waveguides using Hermite-Gaussian modal approximations

A scalar variational analysis of rectangular dielectric waveguides using Hermite-Gaussian modal approximations is presented. The technique analyzes waveguides by finding a closed-form, approximate solution to the given problem. We begin with an assumed, closed-form field solution, with unknown parameters which can be chosen to best match the assumed 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 benefit is that this method gives best-fit, closed-form modal approximations.<
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