Plane Wave Solutions to the Equations of Electrodynamics in an Anisotropic Medium

Abstract

Under examination is the system of equations of electrodynamics for a nonconducting nonmagnetic medium with the simplest anisotropy of permittivity. We assume that permittivity is characterized by the diagonal matrix ϵ = diag(ε₁, ε₁, ε₂), with the functions ε₁ and ε₂ equal to positive constants beyond a bounded convex domain Ω ⊂ ℝ³. Two modes of traveling plane waves exist in a homogeneous anisotropic medium. The structure is studied of the solutions related to the traveling plane waves incident from infinity on an inhomogeneity located in Ω.