Nonlinear response of composite systems containing spheres of arbitrary response

Abstract

We develop a microscopic multipolar theory for the nonlinear response of composite systems containing coated spheres with a core of arbitrary nonlinear response, in the quasi-static limit. This theory applies to all range of applied fields, producing both the weak- and the strong-field nonlinearities as particular limits. The nonlinear response is found to be quite sensitive to the distribution of the spheres. For a power-law nonlinear response of uniform spheres, we find very striking and unexpected results at intermediate fields between the weak and the strong nonlinear regimes: multiple solutions occur in certain frequency ranges. This reveals a new complexity and richness in the nonlinear response of composite systems.