Transformation Optics scheme for two-dimensional materials

Abstract

Two dimensional optical materials, such as graphene can be characterized by a surface conductivity. So far, the transformation optics schemes have focused on three dimensional properties such as permittivity $\epsilon$ and permeability $\mu$. In this paper, we use a scheme for transforming surface currents to highlight that the surface conductivity transforms in a way different from $\epsilon$ and $\mu$. We use this surface conductivity transformation to demonstrate an example problem of reducing scattering of plasmon mode from sharp protrusions in graphene.