Anisotropic effective medium theories: random orientation of scatterers

Abstract

A family of mixing formulas is generalized in this paper to cover mixtures where dielectrically anisotropic spherical inclusions are embedded in isotropic host material. The usual limitations of quasistatic mixing rules apply also here that the inclusions should be small compared with wavelength. Special emphasis with numerical examples and illustrations is focused on the case where the inclusions are randomly oriented in the mixture, making the mixture isotropic. The result is a general mixing formula from which special cases can be extracted, among others the generalizations of Maxwell-Garnett, Effective Medium, and Coherent Potential formulas.