The method of fundamental solutions for electromagnetic scattering by a perfect conductor in chiral environment

Abstract

The electromagnetic scattering problem for a time-harmonic plane wave by a perfectly conductive body embedded in a chiral medium is considered. Potentials in terms of the fundamental solution in dyadic form for chiral media are defined. The well-posedness of the scattering problem is studied using defined potentials in terms of the fundamental solution for chiral environment and the boundary integral operators associated with them. An extension of the method of fundamental solutions for electromagnetic scattering in chiral media is applied in order to approximate the solution. The electric scattered field is approximated by a finite linear combination of the dyadic fundamental solutions of the equation governing the problem for singularities placed on an auxiliary surface outside the domain of the problem and for unknown coefficients determined by the boundary conditions. Density properties on the surface of the scatterer are proven for a defined system of functions consisting of the tangential components of the dyadic fundamental solution. These density properties together with the well-posedness of the scattering problem are used to reduce the approximation of the solution to the approximation of the known boundary data. The linear system obtained from the boundary conditions in order to determine the appropriate unknown coefficients of the finite linear combination is presented. Using these results we approximate the far-field patterns and the scattering cross section. Numerical results for the special case of a spherical scatterer and an ellipsoidal scatterer are presented.