Closed-form approximate analysis of the fundamental and higher-order modes in rectangular-channel and planar-slab dielectric waveguides

Abstract

In previous work, we have addressed the problem of describing the fundamental guided mode in a dielectric waveguiding structure using variational principles. Using this method, the value of the propagation constant and a Gaussian wavefield approximation for the fundamental mode are determined using variational arguments based on the scalar wave equation. In this paper, we present the extension of this method to include higher order modes. In this extension, the higher order modes are approximated by Hermite Gaussian functions. We will present results of the higher order analysis, along with the sets of equations used to describe the higher order modes. The structures of interest are planar slab dielectric waveguides and rectangular channel dielectric waveguides. The variational method is computationally fast, and good agreement is seen with other methods of analysis. Ways to increase accuracy will also be briefly discussed.