Giant fluctuations of local fields, failure of mean-field theory, and enhanced hypersusceptibilities of composites

Summary form only given. We consider theoretically a long-standing problem of nonlinear polarizabilities of Maxwell Garnett (MG) composites. Such a composite is a random suspension of uniform spheres in a dielectric host. Experimental studies (see e.g. 1) of third-order hyperpolarizabilities of MG composites at low-fill factors (f<10/sup -4/) have shown a good quantitative agreement with mean field theory. This implies that spatial fluctuations (from one inclusion to another) of local fields are small. In this communication, we have established that large fluctuations of local fields exist in MG composites for larger fill factors (f>10/sup -/) leading to a dramatic failure of mean-field theories. We show that along with a region of enhancement that is predicted by the mean-field theory, a completely new region appears shifted to the red of it, where the third-order polarizability may be enhanced by a factor up to /spl cong/10/sup 4/.