Abstract
Assume a time-harmonic electromagnetic wave is scattered by an infinitely long cylindrical conductor surrounded by an unknown piecewise homogenous 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 phase-shift. The proofs are based on the singularity of the Green function to a two dimensional elliptic equation with piecewise constant leading coefficients.
Highlights
The reconstruction of an obstacle from its far field pattern is of great importance in inverse scattering problems
The first half of this paper investigates uniqueness in determining the shape of a cylindrical conductor and the unknown piecewise homogeneous background medium
If the wave numbers for characterizing the piecewise homogeneous medium and the transmission coefficients on the interfaces are known, it was proved that the buried obstacle and the interfaces of the background can be uniquely determined from the measurements of far field for all incident directions at a fixed frequency; see [23, 29] for the scattering of acoustic waves and [24] for electromagnetic waves
Summary
The reconstruction of an obstacle from its far field pattern is of great importance in inverse scattering problems. If the wave numbers for characterizing the piecewise homogeneous medium and the transmission coefficients on the interfaces are known, it was proved that the buried obstacle and the interfaces of the background can be uniquely determined from the measurements of far field for all incident directions at a fixed frequency; see [23, 29] for the scattering of acoustic waves and [24] for electromagnetic waves. One aim of this paper is to prove that, in the case of TM polarization and a piecewise homogeneous background, the far field data from all incident directions at a fixed frequency can uniquely determine the cross-section of the cylindrical conductor and its layered surroundings.
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