Analysis of two-dimensional electromagnetic scattering by a perfectly conducting obstacle in a homogeneous chiral environment

Abstract

The time-harmonic electromagnetic plane waves incident on a perfectly conducting obstacle in a homogeneous chiral environment are considered. A two-dimensional direct scattering model is established and the existence and uniqueness of solutions to the problem are discussed by an integral equation approach. The inverse scattering problem to find the shape of scatterer with the given far-field data is formulated. Result on the uniqueness of the inverse problem is proved. §1 IntroductionThe phenomenon of optical activity in special materials has been known since the beginning of the last century. In recent years chiral materials have been studied intensively in electromagnetic theory literature. Chiral media are examples of media responding with both electric and magnetic polarization to either electric or magnetic excitation. They can be characterized by a set of constitutive relations in which the electric and magnetic fields are coupled. In this paper we use the Drude-Born-Fedorov constitutive equations.Scattering by an obstacle in a chiral medium-although somewhat exotic at a first glanceconstitutes an attractive problem. Some illustrative examples are the turbid chiral media [1] , the Bruggeman homogenization of chiral composites [2] , the method of moments for scattering by a chiral obstacle in a chiral environment [1] ; and the solvability of the latter scattering problem is studied in [3].In this paper, a direct and an inverse scattering problems by a perfectly conducting obstacle in a homogeneous chiral environment are discussed. We confine ourselves to the two-dimensional case.We start our consideration with time-harmonic Maxwell's equationsReceived: 2005-12-16. MR Subject Classification: 65N06.