On the Far Field Patterns for Electromagnetic Scattering in Two Dimensions

Abstract

We consider the problem of scattering time-harmonic electromagnetic plane waves by a dielectric infinitely long cylinder with core which may be a perfect or an imperfect conductor. The corresponding scattering problems are reduced to mixed boundary value problems for the two-dimensional Helmholtz equation . For the far field patterns of these problems, we prove a reciprocity principle and a general scattering theorem. The combination of these theorems with Herglotz wave functions leads to the proof of some properties of the far field operator, which are used in the study of inverse scattering problems. Finally, an optical theorem for the above scattering problems is proved.