On a two-dimensional inverse scattering problem for a dielectric

The inverse problem under consideration is to reconstruct the shape of a homogeneous dielectric infinite cylinder from the far-field pattern for scattering of a time-harmonic E-polarized electromagnetic plane wave. We propose an inverse algorithm that extends the approach suggested by Johansson and Sleeman [T. Johansson and B. Sleeman, Reconstruction of an acoustically sound-soft obstacle from one incident field and the far-field pattern, IMA J. Appl. Math. 72 (2007), pp. 96-112] for the case of the inverse problem for a perfectly conducting scatterer. It is based on a system of nonlinear boundary integral equations associated with a single-layer potential approach to solve the forward scattering problem. We present the mathematical foundations of the method and exhibit its feasibility by numerical examples.