Homogenization of a dielectric mixture with anisotropic spheres in anisotropic background

This paper treats the problem of calculating the macroscopic effective properties
of dielectric mixtures where both the inclusions and the background
medium can be anisotropic. For this homogenization process, the Maxwell
Garnett -type approach is used where the inclusions are assumed to be spherical
and embedded in a homogeneous background medium. The anisotropy of
the background medium has to be described with a symmetric permittivity
dyadic but the inclusion may be fully anisotropic, in other words the inclusion
permittivity dyadic can contain an antisymmetric component. The effect of
the anisotropy of the background is such that the depolarization factors of
the spheres become different in different directions, even if the geometry is
isotropic. This effect has to be taken into account for the calculation of the
polarizability dyadic. As an example, numerical values are calculated for the
case of gyrotropic spheres in anisotropic environment, both for the polarizability
and effective permittivity dyadics. Finally, some thoughts are raised
concerning the physical interpretation of the anisotropy effect, as well as the
reciprocity of the materials and symmetry of their permittivities.