The scattering problem of obliquely incident electromagnetic waves by an inhomogeneous infinitely long cylinder

Abstract

We study the scattering of a time-harmonic electromagnetic wave incident at an oblique angle on a dielectric, isotropic, and fully inhomogeneous cylinder. This infinitely long cylinder is oriented parallel to the z − axis in three dimensions. Our main focus is on the inverse problem, aiming to reconstruct the refractive index of the cylinder. The material parameters’ z − independence allows us to consider the scattering problem only on its horizontal cross-sections. We examine the well-posedness of the direct problem and proceed to numerically solve the corresponding inverse problem for one incident field. To achieve accurate reconstructions of the refractive index, we introduce a novel numerical scheme that yields satisfactory results.