OPTIMIZATION PROCEDURE BASED ON A STATISTICAL COOLING METHOD APPLIED TO SCATTERING BY BOUNDED NONLINEAR OBJECTS

This paper deals with the application of an optimization procedure bas ed on a statistical cooling algorithm to the computation of the electr omagnetic scattering by nonlinear dielectric objects. In particular, a numerical approach is developed that is aimed at determining the elec tromagnetic field distributions inside these bodies. An integral equat ion formulation for the scattering by two- and three-dimensional, nonl inear, inhomogeneous, isotropic scatterers of arbitrary shapes is cons idered. The scatterers are illuminated by time periodic, incident, ele ctric field vectors, and the nonlinear effects are taken into account by introducing equivalent sources. A system of integral equations is o btained that includes the internal electric field distribution as an u nknown. After discretization the method consists in treating the probl em as an optimization problem in which a nonlinear cost functional is to be minimized. Because of the large number of unknowns and the stron g nonlinearity, traditional minimization algorithms would fail to find the global minimum (i.e,, the solution of the electromagnetic problem ). Therefore the present approach resorts to a statistical cooling pro cedure based on one walker meandering in the solution space. Some prel iminary numerical results are reported concerning scatterers that exhi bited Kerr-like nonlinearities.