Scattering Properties of High-Permittivity Dielectric Resonators Embedded with Impedance Sheets

Scattering from small dielectric resonators has been of high interest in the recent years for many applications such as metasurfaces and antennas with frequency operation from microwaves to optics. Various dielectric resonators have been studied; however, recently it was shown that the same type of resonances, namely Mie resonances, can be excited in impedance sheets with reactive impedances. Presently, we study a configuration consisting of a high-permittivity infinitely long, circular cylinder embedded with a coaxial impedance sheet. We present the analytical solution for the evaluation of the scattering properties for both transverse electric and magnetic plane wave illuminations. We show that resonances are excited in both the dielectric medium and the impedance sheet, and furthermore, that these resonances can be effectively tailored by changing the size of the cylinder and impedance sheet. We report on several designs with interesting scattering properties including the simultaneous excitation of magnetic and electric resonances, i.e., a Huygens type of response. Our results are general and may serve as a guideline for interesting metamaterial and antenna designs as well as graphene nanotubes.