Integral equations in electromagnetic wave scattering by two-dimensional dielectric lenses and shells

In this paper, integral equations for two-dimensional (2D) wave diffraction by a two-layer arbitrary shaped dielectric scatterer are presented for both the E- and H-polarization cases. The surface potential approach and the method of analytical regularization are used to obtain a Fredholm second-kind matrix equation. An efficient numerical algorithm based on this approach can be used for studying such physical effects as whispering-gallery (WG) mode resonances, focusing effect, beam directivity degradation due to a dielectric shell, etc., with applications to the design of cylindrical dielectric lenses and radomes.