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.
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