The linear method for solving the scattering problem in an inhomegeneous medium: the case of TE polarized

Abstract

In this article, the electromagnetic waves scattered from an inhomogeneous medium are considered when the electromagnetic waves are polarized in the case of transverse electric. Using the Rellich lemma, the uniqueness of the solution of the direct scattering problem is proved. In order to show the existence of the solution of this problem, the operator equations are constructed and the Riesz theory which provides the existence of the inverse operator is used. Furthermore, for solution of the invers scattering problems, an interior boundary value problem is considered. Finally, a linear integral equation is obtained whose the solution yield the support of the scattering object.