Singular electromagnetic modes in an anisotropic medium

We construct the singular mode corresponding to a spatial essential spectrum of the integral operator for the scattering of electromagnetic waves by a three-dimensional body of finite size with inhomogeneous and anisotropic dielectric permittivity tensor. The permittivity tensor field is assumed to be Hölder continuous throughout the whole space. The singular volume integral equation, transformed from Maxwell's equations, makes it feasible to deduce explicit forms of both the continuous essential spectrum and the corresponding singular modes. The obtained singular mode is a natural extension of the previously obtained one for the isotropic case and is applicable to a much wider class of dielectric scattering bodies. A discussion is made of the possibility for realizability of electromagnetic waves, with finite energy, concentrated at a point in the body.