Radial anisotropy from a geometric viewpoint: Topological singularity and effective medium realization

The correspondence between curved space-times and inhomogeneous dielectrics has been recently explored as a powerful tool to understand and manipulate novel electromagnetic behaviors in complex media. Here, we present a theoretical investigation on the optics of radially anisotropicmaterial from a geometric viewpoint. Within the framework of transformation optics, we show that the optical medium with radial anisotropy is equivalent to a disclination geometry, which is a line topological defect carrying singular curvature. By introducing a geometric parameter characterizing the global topology of the disclination space, we systematically analyze the effective geometry and the topological charge associated with two typical radial anisotropies consisting of concentric multilayers or symmetric slices in both elliptical and hyperbolical regions. It is shown that elliptical and hyperbolic radial anisotropies give rise to optical Riemannian and pseudo-Riemannian geometries, respectively. Moreover, we investigate the wave optics as well as the semiclassical ray dynamics of light in the metamaterials at optical wavelengths from the perspective of coordinate transformation. It is found that the singularity acts on the light with an attractive or repulsive inverse cube force, depending on the topological charge. Our theory provides a simple and unified framework for light in optical media of various radial anisotropies and may shed new light on the dynamics of classical and quantum waves in topological nontrivial space.