Homogenization of a Dielectric mixture with anisotropic spheres in anisotropic Background

摘要

This paper treats the problem of calculating the macroscopic effective prop-erties of dielectric mixtures where both the inclusions and the background medium can be anisotropie. For this homogenization process, the Maxwell Garnett -type approach is used where the inclusions are assumed to be spher-ical and embedded in a homogeneous background medium. The anisotropy of the background medium has to be described with a symmetric permit-tivity dyadic but the inclusion may be fully anisotropie, 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 fac-tors of the spheres become different in different directions, even if the geom-etry 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 anisotropie 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.