The role of anisotropy in the Maxwell Garnett and Bruggeman formalisms for uniaxial particulate composite media

A particulate composite medium in which the host and the spherical inclusions are made of uniaxial dielectric - magnetic media with parallel crystallographic axes is considered. The polarizability dyadics of a single inclusion are obtained, showing in detail the significant role played therein by the degree of anisotropy of the host medium. The derived expressions are used to set up the Maxwell Garnett and the Bruggeman formalisms for homogenization of the particulate composite medium. Numerical results are presented to show that the degree of anisotropy of the homogenized composite medium (HCM) is a non-trivial function of the degrees of anisotropy of the constituent media. Shifts in axial and transverse Fröhlich resonances are also predicted.