Effective Dielectric Tensor for Electromagnetic Waves in Weakly Inhomogeneous Media

Abstract

This paper presents a study of the effect of small fluctuations of the permittivity or conductivity of an anisotropic medium on the propagation of electromagnetic waves. There is no restriction on the scale of the inhomogeneities compared with the wavelength. An equivalent homogeneous medium is defined, with a constant effective dielectric tensor, and where the fields are derived from the actual fluctuating fields by a described regularizing process. The difference between this tensor and the mean dielectric tensor is of second order in the inhomogeneity and it generally depends on the wave vector. The effective conductivity tensor calculated by Herring in dc conditions may be used only if the scale of the fluctuations is small enough and if the fluctuations are not too anisotropic. Then there is an enhancement of the damping of helicon waves. The theory shows another kind of damping due to a resonant scattering of the incident wave on inhomogeneities; this effect, which causes a damping of the wave even in a lossless medium, is attenuated when the medium becomes lossy.