ITERATIVE NUMERICAL COMPUTATION OF THE ELECTROMAGNETIC-FIELDS INSIDE WEAKLY NONLINEAR INFINITE DIELECTRIC CYLINDERS OF ARBITRARY CROSS-SECTIONS USING THE DISTORTED-WAVE BORN APPROXIMATION

The electromagnetic scattering by weakly nonlinear infinite dielectric cylinders Is the topic dealt with in this paper. The cylinders are as sumed to be isotropic, inhomogeneous, and lossless and to have arbitra rily shaped cross sections. A time-periodic illumination of the transv erse magnetic type is considered. The nonlinearity is assumed to be ex pressed by the dependence of the dielectric permittivity on the intern al electric field, under the hypothesis that the operator responsible for the nonlinearity does not modify the scalar nature of the dielectr ic permittivity and produces a time-periodic output. The electromagnet ic scattering is then described by an integral equation formulation, a nd the electromagnetic field distributions inside and outside a scatte rer are approximated by an iterative numerical procedure starting with the application of the distorted-wave Born approximation. In a simpli fied version of the approach, the classic first-order Born approximati on is used. The convergence of the approach is discussed in several ex amples. In the computer simulations concerning cylinders with differen t cross-section shapes, the effects of the nonlinearity on the field-c omponent fundamental frequency were evaluated for different values of the nonlinear parameters in the case of a Kerr-like nonlinearity and o f a uniform incident plane wave. The generation of higher-order harmon ics was also considered.