Calculation of material properties and ray tracing in transformation media

TLDR

Electromagnetic behavior in non‑flat topologies can be reinterpreted as material property tensors in flat Cartesian space via coordinate transformations. The study aims to compute material property tensors for coordinate transformations that model spaces containing spherical or cylindrical voids. The authors compute these tensors and present a geometric ray‑tracing method for the resulting inhomogeneous, anisotropic media. The derived material properties enable implementation of invisibility cloaks in flat space.

Abstract

Complex and interesting electromagnetic behavior can be found in spaces with non-flat topology. When considering the properties of an electromagnetic medium under an arbitrary coordinate transformation an alternative interpretation presents itself. The transformed material property tensors may be interpreted as a different set of material properties in a flat, Cartesian space. We describe the calculation of these material properties for coordinate transformations that describe spaces with spherical or cylindrical holes in them. The resulting material properties can then implement invisibility cloaks in flat space. We also describe a method for performing geometric ray tracing in these materials which are both inhomogeneous and anisotropic in their electric permittivity and magnetic permeability.