Uniqueness in Inverse Transmission Scattering Problems for Multilayered Obstacles

Assume a time-harmonic electromagnetic wave is scattered by an infinitely long cylindrical conductor surrounded by an unknown piecewise homogeneous medium remaining invariant along the cylinder axis. We prove that, in TM mode, the far field patterns for all incident and observation directions at a fixed frequency uniquely determine the unknown surrounding medium as well as the shape of the cylindrical conductor. A similar uniqueness result is obtained for the scattering by multilayered penetrable periodic structures in a piecewise homogeneous medium. The periodic interfaces and refractive indices can be uniquely identified from the near field data measured only above (or below) the structure for all quasi-periodic incident waves with a fixed phaseshift. The proofs are based on the singularity of the Green function to a two dimensional elliptic equation with piecewise constant leading coefficients.