Tomographic Imaging of Meta-Shells

In this article both direct and (mainly) inverse wave scattering by hollow meta-shells, that is, closed, generally semi-transparent metasurfaces (MSs), is considered. It is shown that these meta-shells can be characterized by a singular potential. For Huygens’ MSs with magneto-electric coupling, the wave scattering is described by a four-parameter family of point interactions, derived previously within 1-D quantum mechanics. The singularity of the potential is utilized here to convert the boundary value problem into a volume integral equation. The resulting far-field pattern is expressed in the form of an impact parameter model, that is, as a true Fourier transform of the profile function. Then, a linear noniterative inversion algorithm, based on the ideas of microlocal analysis, is used to recover the support of the scattering potential, and therefore, the shape of the meta-shell. Scalar 2-D simulations of a TM-polarized wave, normally incident on (a cluster of) cylindrical meta-shells, confirm the validity of the method. Under some conditions, direct analysis of the signatures, appearing in the reconstructed tomograms, allows one to identify the type of the interaction (electric/magnetic response, or magneto-electric coupling). In fact, the meta-shell model turns out to be much more general than could be initially imagined, since it describes also all physically meaningful impenetrable objects, including perfectly conducting (Dirichlet/Neumann) and impedance-type scatterers.