The two-dimensional electromagnetic inverse scattering problem for chiral media

We introduce Maxwell's equations with chiral constitutive equations in the form given by Fedorov and Bokut. In the case where the scatterer is an infinitely long cylinder we derive a two-dimensional scattering problem and discuss the existence and uniqueness of solutions via an integral equation approach. Then we formulate the inverse scattering problem to find the shape of the scatterer if the far-field data are known. We give a uniqueness result and describe a numerical reconstruction scheme.