Abstract
The design rules of transformation optics generally lead to spatially inhomogeneous and anisotropic impedance-matched magneto-dielectric material distributions for, e.g., free-space invisibility cloaks. Recently, simplified anisotropic non-magnetic free-space cloaks made of a locally uniaxial dielectric material (calcite) have been realized experimentally. In a two-dimensional setting and for in-plane polarized light propagating in this plane, the cloaking performance can still be perfect for light rays. However, for general views in three dimensions, various imperfections are expected. In this paper, we study two different purely dielectric uniaxial cylindrical free-space cloaks. For one, the optic axis is along the radial direction, for the other one it is along the azimuthal direction. The azimuthal uniaxial cloak has not been suggested previously to the best of our knowledge. We visualize the cloaking performance of both by calculating photorealistic images rendered by ray tracing. Following and complementing our previous ray-tracing work, we use an equation of motion directly derived from Fermat's principle. The rendered images generally exhibit significant imperfections. This includes the obvious fact that cloaking does not work at all for horizontal or for ordinary linear polarization of light. Moreover, more subtle effects occur such as viewing-angle-dependent aberrations. However, we still find amazingly good cloaking performance for the purely dielectric azimuthal uniaxial cloak.
Highlights
Transformation optics maps the geometry of a fictitious space onto actual material properties in the laboratory [1,2,3]
Equal magnetic and dielectric responses are required at the same time to have (i) anisotropic light propagation yet no polarization dependence of the optical response and (ii) no reflections from interfaces via matching of the relative optical impedance, which is given by the square root of the ratio of the magnetic permeability ! and the electric permittivity !
The rendered images of the preceding section have shown that the azimuthal uniaxial purely dielectric cloak performs much better than its radial counterpart
Summary
Transformation optics maps the geometry of a fictitious space onto actual material properties in the laboratory [1,2,3]. Polarized incident light impinging from the outside of the cloak (i.e., from vacuum or air) will be double refracted at the cloak’s interface into an ordinary and an extraordinary ray, which will propagate inside the cloak. It is worth briefly mentioning that in the case of an interface from a uniaxial dielectric crystal to air/vacuum, there will in general be double reflections within the crystal, into an ordinary reflected wave and an extraordinary reflected wave, irrespective of whether the incident wave is itself ordinary or extraordinary. The directions and amplitudes of all relevant fields are determined just as in the case of the air/vacuum-cloak interface, except here there are two reflections (in cloak) and one refraction (into air), instead of one reflection (in air) and two refractions (in cloak) at the interface Here it is the reflected wave vectors (ordinary and extraordinary) that, along with the optic axis, define the main sections. The intensity reflection coefficients are unity minus the transmission coefficient
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