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 lin ear response functions of composites to the case of a polycrystalline mater ial with uniaxially anisotropic microscopic symmetry. As an application, we combine these results with a non-linear decoupling approximation as modifi ed by Ma and co-workers, to calculate the third order non-linear optical su sceptibility of a uniaxial polycrystal, assuming that the effective dielect ric function of the polycrystal can be calculated within the effective-medi um approximation.