A method for computing nonlinear scattering and absorption of light by small arbitrarily shaped particles

A method is described for the calculation of the nonlinear scattering and absorption of light by aggregates of small particles or molecular clusters of arbitrary shape, with dimensions comparable to or smaller than the wavelength of incident and generated radiation fields. The aggregate is modeled as an array of N nonlinear polarizable elements. The nonlinear polarizability of each element can be taken as that of a given molecule, molecular bond, or component of a macroscopic particle. These polarizabilities can be determined theoretically or experimentally. The complex electric field vector amplitudes of each of the nonlinear oscillators, which are driven by both incident and generated fields are determined self consistently by an iterative procedure. Given M radiation fields, the 3M x N set of nonlinear equations for the complex polarizations can be solved self consistently to include contributions from all elements in the array. The method provides a means of determining the local field susceptibilities without the assumptions associated with isotropic or cubic media. Cross sections for absorption and scattering can then be computed for a variety of aggregate shapes and nonlinear polarizabilities. Although the approach described in this study is applicable to the general nth-order nonlinear, wave scattering problem, its application is limited to the problem of two-wave mixing and second-harmonic generation.