Approximate solutions to the scattering by nonlinear isotropic dielectric cylinders of circular cross sections under TM illumination

Approximate solutions to the scattering by isotropic circular cylinders with weak nonlinearities are presented. The cylinders are illuminated by a transverse magnetic (TM) incident monochromatic field. Iterative numerical solutions are developed under the assumption of approximating (both by using the Born approximation and by initially approximating the internal field distribution by the linear field distribution) the solutions of inhomogeneous vector equations derived from a description of the constitutive relations in terms of Volterra series and then simplified for the case where a nonlinearity is heuristically assumed to be of the Kerr type. An efficient numerical discretization is used, and the convergence of the iterative approach is evaluated by way of some examples. The effect of a nonlinearity on the fundamental frequency is considered, and the possibility of predicting the field components at generated higher-order harmonics is explored. The bistatic scattering width is also computed, and a comparison with some previously published results is made