Spectral representation for the effective macroscopic response of a polycrystal: application to third-order non-linear susceptibility

We extend the spectral theory used for the calculation of the effective linear response functions of composites to the case of a polycrystalline material with uniaxially anisotropic microscopic symmetry. As an application, we combine these results with a non-linear decoupling approximation as modified by Ma and co-workers, to calculate the third order non-linear optical susceptibility of a uniaxial polycrystal, assuming that the effective dielectric function of the polycrystal can be calculated within the effective-medium approximation.