PAIR CORRELATIONS, CASCADING, AND LOCAL-FIELD EFFECTS IN NONLINEAR OPTICAL SUSCEPTIBILITIES

A formalism is developed for evaluating the effects of pair correlations on cascading of the nonlinear susceptibilities of fluid dielectrics. The corresponding correlative and nonlinear alterations of the usual local-field corrections are determined. These corrections to the nonlinear susceptibilities when the polarization density is expanded in terms of the effective linear field are found to be significantly different from results previously reported in the literature. The consequences of the considerable field dependence of the susceptibility expansions on the local-field corrections and the cascading are pointed out, and a detailed comparison is made to previous work. A simple model (beta media), in which only the second-order molecular polarizabilities are nonzero, is introduced in order to isolate the roles of the pair correlations and the intermediate electromagnetic propagators on the parts of the macroscopic third-order susceptibilities that result solely from cascading. In beta media the exact macroscopic third-order susceptibilities are expressed in terms of so-called irreducible cascading coefficients, which are multidimensional multiple integrals involving known quantities. This model is extended to include intrinsic linear and third-order polarizabilities and the effects of pair correlations in the local-field-correction factors.