Linear and nonlinear response of inhomogeneous media: exact theory and mean field approximation

We present an exact theory of the linear and nonlinear response of inhomogeneous media based on a fully multipolar approach. The theory considers parallel-plate or substrate configurations, appropriately including all image multipoles. The theory applies to inclusions of arbitrary structure and linear and nonlinear response, having introduced corresponding polarization coefficients. For disordered systems with arbitrary particle distributions, we develop a rigorous mean field theory. We show that the various orders of multipolar contributions are precisely determined by the form of the two-particle distribution. In particular, the Clausius-Mossotti relation and the Debye's result are rigorous mean field results for isotropic distributions. In the area of nonlinear composites, we have investigated the nonlinear optical response of both uniform and coated spheres. We show that the effective third-order nonlinear susceptibility can be greatly enhanced in magnitude (up to 107 factors) and tuned in frequency through the combined effect of the particle structure and distribution.