Excitation of horizontally polarized waves in critical-coupling regions where the permittivity gradient approaches zero—Full wave solutions

Abstract

Maxwell’s equations for inhomogeneous isotropic media are transformed into coupled ordinary differential equations for the wave amplitudes. To facilitate the solutions of these equations for dielectric layers with critical coupling regions, a generalized WKB approach is used. To this end, sets of auxiliary functions that are solutions to the wave equation for homogeneous or linearly varying permittivity profiles are employed. By introducing an additional set of auxiliary, parabolic cylindrical functions, the generalized WKB approach is extended to obtain suitable solutions for critical coupling regions of the dielectric layer where the gradient of the permittivity profile also approaches zero. Expressions for the reflection and transmission coefficients and the characteristic surface impedance for an inhomogeneous dielectric layer are derived as functions of the transverse wavenumber. Realizability and reciprocity relationships are also derived.