Invisibility enables super-visibility in electromagnetic imaging

Abstract

This paper is concerned with the inverse electromagnetic scattering problem for anisotropic media. We use the interior resonant modes to develop an inverse scattering scheme for imaging the scatterer. The whole procedure consists of three phases. First, we determine the interior Maxwell transmission eigenvalues of the scatterer from a family of far-field data by the mechanism of the linear sampling method. Next, we determine the corresponding transmission eigenfunctions by solving a constrained optimization problem. Finally, based on both global and local geometric properties of the transmission eigenfunctions, we design an imaging functional which can be used to determine the shape of the medium scatterer. We provide rigorous theoretical basis for our method. Numerical experiments verify the effectiveness, better accuracy and super-resolution results of the proposed scheme.

Boundary localization of transmission eigenfunctions in spherically stratified media

“…In fact, in order to achieve invisibility/transparency, the wave propagates in a "smart" way which slides over the boundary surface of the scattering object while avoids the singular/highly-curved places to avoid being trapped. More intriguingly, the geometric properties have been used to produce super-resolution imaging schemes for inverse acoustic and electromagnetic scattering problems [15,25], artificial mirage [21], and pseudo surface plasmon resonance [21].…”