Plane wave solutions to the equations of electrodynamics in an anisotropic medium

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 $\epsilon=\mathrm{diag} (\varepsilon_1,\varepsilon_1,\varepsilon_2)$, with the functions $\varepsilon_1$ and $\varepsilon_2$ equal to positive constants beyond a bounded convex domain $\Omega\subset\Bbb{R}^3$. 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 $\Omega$.