Electromagnetic scattering by an infinite inhomogeneous dielectric cylinder: New Green’s function and integral equations

Abstract

The scattering of electromagnetic waves by an infinite dielectric cylinder with variable dielectric permeability presents, in general, certain mathematical difficulties regarding the construction of rigorous solutions. We give a new divergenceless tensor Green’s function, specially appropriate for cylindrical symmetry, and, in terms of it, present new scattering integral equations. We prove that the series for med by all successive iterations of those scattering integral equations converge under certain conditions. Suitable transformations lead to new integral equations with Hilbert–Schmidt kernels, which imply further rigorous results.