Well-conditioned T-matrix formulation for scattering by a dielectric obstacle

Abstract

: The classic formulation of the extended boundary condition method is revisited to inject the regularization operators for the unknown coefficients of the eigen-function expansions for the travelling and standing waves throughout the dielectric scatterer. It is shown that, using the new definitions, the existing algorithm of the scattering field calculation can be kept the same for its well-conditioned version. This is exemplified for scalar 2D problems for both TM and TE polarization under illumination of a line source. The condition numbers of the matrix operators in the new version of the algorithm are drastically reduced when the regularization interfaces are eigen-surfaces of the field expansions, i.e. circles on extended boundaries in the counter null-fields. The arbitrariness of the boundary interface is involved in the calculations, via parameterized contours and effects of elongation and corrugation of the interface boundary contour on the condition of the algorithm is extensively discussed in comparison with the results of the boundary integral equation formulation of the same problem.