An integral transform technique for analysis of planar dielectric structures

This paper presents a novel efficient technique for the study of planar dielectric waveguides for submillimeter-wave and optical applications. In an appropriate integral transform domain, which is determined by the Green´s function of the substrate structure, higher-order boundary conditions are enforced in conjunction with Taylor expansions of the fields to derive an equivalent one-dimensional integral equation for the corresponding two-dimensional waveguide geometry. This reduction in the dimensionality of the boundary-value problem can easily be extended to three-dimensional planar structures, with equivalent two-dimensional integral equations being formulated. The reduced integral equations are solved numerically by invoking the method of moments, in which the transform-domain unknowns are expanded in a smooth localized entire-domain basis. It is demonstrated that using orthogonal Hermite-Gauss functions as an expansion basis provides very satisfactory results with only a few expansion terms. For the validation of the technique, single and coupled dielectric slab waveguides are treated