A uniqueness theorem for a transmission problem in inverse electromagnetic scattering

In this paper we examine an inverse problem for time-harmonic electromagnetic waves in an inhomogeneous medium. Outside of a bounded domain D we assume that the medium is dielectric and homogeneous with constant electric permittivity and constant magnetic permeability. These quantities and the electric conductivity change discontinuously across delta D and are inhomogeneous in D. We show with integral equation techniques that the resulting direct transmission problem is uniquely solvable. Then, using a method suggested by Kirsch and Kress (1993), we prove that delta D is uniquely determined by a knowledge of the far field patterns for all incoming plane waves. Finally, we give conditions so that the parameters epsilon , mu and sigma are uniquely determined in D by these far field patterns. Here we use special solutions of the Maxwell equations which were constructed by Colton and Paivarinta (1992).