Coherent wave propagation in inhomogeneous materials: a comparison of theoretical models

Abstract

The frequency dependent behaviour of coherent wave propagation in inhomogeneous materials is studied using several theoretical models. The predictions of a ray tracing model are compared with those of a two-dimensional finite difference model, for both isotropic and anisotropic inhomogeneous materials. The effects of frequency are studied and it is shown how the ray tracing model may be modified to incorporate the low frequency regime, in addition to the usual high frequency regime for which ray tracing approximations are valid. A further comparison is made between the ray tracing solution and an analytical solution, for electromagnetic plane waves propagating in a material with a one-dimensionally varying dielectric constant. The amplitude of the reflected wave is calculated, with good agreement between the two models over a wide range of frequencies, including low frequencies.