Scattering Problems For Coated Obstacles

In this paper, we consider the scattering of an time harmonic electromagnetic plane wave by a perfectly conducting infinite cylinder, that is partially coated by material with surface impedance λ. The cross section is a two-dimensional bounded region D, and the boundary Γ of the region D is divided into three parts. Finally, this problem can be formulated as the exterior mixed boundary value problem in R2of Helmholtz equations, i.e.The direct scattering problem can be transformed into a boundary integral equation by using the potential theory. Then we use the Fredholm theory to prove the existence and uniqueness of solutions to the integral equations, then we can obtain the existence and uniqueness of solutions to the problem (*). The inverse scattering problem is that we want to determine the shape of the obstacle from a knowledge of the far-field pattern of the scattered field. To solve this problem, we use the linear sampling method to reconstruct the shape of the obstacle. In this article, I just analyze the relevant properties of the far-field operator and give a theoretical conclusion. We don’t reconstruct the shape of the obstacle by using the numerical method.