Maxwell Garnett formalism for cubically nonlinear, gyrotropic, composite media

We consider the homogenization of a composite medium formed by randomly dispersing electrically small, cubically nonlinear, dielectric spheres in a homogeneous, linear, gyrotropic, dielectric host medium. The Maxwell Garnett formalism is successfully employed to estimate the effective response properties of the homogenized composite medium (HCM). As the nonlinearity of the inclusions is perturbative and the volumetric proportion of the inclusion medium is small, the linear and the nonlinear properties of the HCM can be obtained separately. Whereas our estimate of the linear polarization in the HCM depends on the gyrotropic anisotropy of the host medium but not on the nonlinearity of the isotropic inclusion medium, our estimate of the nonlinear polarization in the HCM combines the nonlinearity of the inclusion medium with the gyrotropic anistropy of the host medium. The rich structure inherent in the response properties of the HCM can be expected to lead to significant technological applications of such composite media.