Linear and nonlinear optical susceptibilities of Maxwell Garnett composites: Dipolar spectral theory

A theory of linear and nonlinear optical susceptibilites of disordered composites consisting of nanospheres in a dielectric host (Maxwell Garnett composites) is developed. The theory is based on a spectral representation in the dipole approximation. Numerical computations are performed in the framework of the dipolar spectral theory to obtain the linear dielectric function and third-order hypersusceptibility. For the fill factors f (from 0.001 to 0.12) considered, our spectral function agrees within the expected 10% error with the previously published function. We have introduced a material independent spectral representation for hypersusceptibilities. The third-order hypersusceptibility χc⁽³⁾ shows regions of strong enhancement (by up to four orders of magnitude for a silver composite). The mean-field theory provides a reasonable approximation only at very low fill factors (f10^-3). For f0.04, the mean-field theory fails dramatically almost everywhere, except for distant wings of the spectral contour (very far from optical resonances). A physical effect responsible for the failure of the mean-field theories and contributing to the resonant enhancement of nonlinear susceptibilities is large fluctuations of local fields in the resonant region.