AN INVERSE PROBLEM FOR TIME-HARMONIC ELECTROMAGNETIC CURRENTS IN A SMOOTHLY LAYERED MEDIUM

Abstract. In this article we study the inverse source problem for Maxwell transmission problem; i.e. we study the uniqueness of constructing the electric and magnetic currents in a body with a smoothly layered medium from electromagnetic eld measurements on the boundary of the body. We use Green's functions for Maxwell equations in this medium and the mapping properties of the operator corresponding to these Green's functions. Then the inverse problem is studied for a general class of currents belonging to the Sobolev spaces. These currents contain the currents on the surfaces of discontinuity in the medium. The uniqueness is achieved in many cases with the currents on a single surface. 1