Uniqueness of the inverse conductive scattering problem for time-harmonic electromagnetic waves

The scattering of time-harmonic electromagnetic waves by an obstacle covered with a thin layer of high conductivity leads to conductive boundary conditions. This paper is related to the inverse obstacle problem to determine the shape of such obstacles from the knowledge of scattered waves. A variational equation for this scattering problem is established. Then, under suitable assumptions, it is shown that the obstacle is uniquely determined by the far field patterns of all incident waves with a fixed wave number. This information is also sufficient for uniqueness of the other parameters of the inverse problem.