A Modification of the Hybrid Projection Method for Electrodynamical Analysis of Inhomogeneous Dielectric Cylinder with Arbitrary Cross Section

The 2D problem of E-polarized plane electromagnetic wave scattering by an inhomogeneous dielectric cylinder with arbitrary cross section is considered. A modification of the hybrid projection method is developed for its solution on the basis of projection matching of the fields on the boundaries of circular cylindrical regions introduced in the consideration, projection of the Helmholtz equation for inhomogeneous region on the Fourier harmonics, and application of the one-dimensional method of finite elements in projection form to the derived ordinary differential equations for reduction of the latter to an algebraic system with block-banded matrix. Some results obtained for a homogeneous cylinder of elliptical cross section are compared to appropriate results obtained using the method of auxiliary sources, and the results obtained for a homogeneous cylinder of square cross section are compared to appropriate results available in the literature. Performance of a half-cylindrical Maxwell fish-eye lens is also calculated and discussed.