Scattering of a Plane Electromagnetic Wave by Layered Dielectric Cylinder Simulating Luneburg Lens and Dielectric Cylinder with a Graphene Coating

Abstract

We investigate the focusing effects arising in the diffraction of a plane electromagnetic wave on a piecewise homogeneous cylindrical Luneburg lens, as well as plasmon resonance in a uniform dielectric cylinder covered with a graphene layer. A numerical simulation is performed of the diffraction and scattering of a plane TE wave incident at a cylindrical stepwise uniform Luneburg lens containing six layers. A special treatment is performed for the resonance phenomena in the dielectric cylinder coated by a graphene layer. The exact classical solution is exploited for the multilayer boundary problem. For the case of a graphene coating of zero thickness, the resistive boundary conditions are applied with the conductivity of graphene introduced by Kubo equation. We show that the stratified Luneburg lens might be substituted by a uniform dielectric cylinder coated with a graphene layer operating at the plasmon resonance frequencies of graphene when it is necessary to reduce the cylinder radius to the size being equal to or even smaller than the wavelength of incident radiation.