Low-frequency interaction of EM waves with an anisotropic ellipsoid in an anisotropic medium

This paper presents a rigorous analytic solution for the interior EM field and the polarizability of a homogeneous anisotropic ellipsoid immersed into an unbounded homogeneous anisotropic medium. It is assumed that the wavelength is large compared to maximum dimension of the ellipsoid. The principal axes of the ellipsoid and of the dielectric matrices involved may all have different orientations. The permittivity matrix of the ellipsoid may be quite arbitrary. As regards the ambient medium it is presumed that the symmetric part of relevant permittivity matrix is real and positive definite or negative definite; the permittivity matrix itself may be neither real nor definite. The solution is achieved in the lowest order of the low-frequency scattering approximation using a theory of Newton´s potentials of an ellipsoid. Our solution generalizes previous results by other authors referring to specific models of anisotropic host media, and seems especially useful for predicting effective properties of particle-laden media such as artificial dielectrics, polymer composites and sea ice.