Three-dimensional field expansion in the most general rotationally symmetric anisotropic material: application to scattering by a sphere

A field expansion is described for the solution of three-dimensional electromagnetic problems in material regions characterized by the most general rotationally symmetric anisotropy. The analysis (in spherical coordinates) reveals that the angular dependence is dictated by spherical harmonics, whereas the radial functions satisfy a set of coupled second-order ordinary differential equations. Due to birefringence, four sets of radial functions (each set representing mode coupling), which are described in detail, are obtained. The expansion is applied to the problem of scattering by an anisotropic sphere, where the numerical calculations confirm the existence of integrable field singularities at the origin of coordinates