Volume integral equations for electromagnetic scattering by an orthotropic infinite cylinder

Abstract

We investigate time-harmonic electromagnetic wave scattering by an inhomogeneous anisotropic medium. For the case of an orthotropic cylindrical obstacle and fields invariant along the axis of the cylinder, the problem can be reduced to a two-dimensional one. This 2D problem can be written equivalently in terms of two different strongly singular volume integral equations (VIEs), one is vector-valued and the other is scalar-valued. The aim of this study is to analyze the essential spectrum of the integral operators that describe these VIEs in the case where the physical parameters are piecewise valued matrix functions with some bounds on their eigenvalues. For Lipschitz interfaces, we show that the spectrum is contained in some subsets which depend on the spectral properties of the scattering parameters. The results on the spectrum will then be used to derive sufficient conditions which ensure the uniqueness of solutions to the diffraction problem.