Abstract:
We review several approaches to optical invisibility designed using transformation optics (TO)
and optical conformal mapping (CM) techniques. TO is a general framework for solving inverse
scattering problems based on mimicking spatial coordinate transformations with distributions of
material properties. There are two essential steps in the design of TO media: first, a coordinate
transformation that achieves some desired functionality, resulting in a continuous spatial
distribution of constitutive parameters that are generally anisotropic; and, second, the reduction
of the derived continuous constitutive parameters to a metamaterial that serves as a stepwise
approximation. We focus here on the first step, discussing the merits of various TO strategies
proposed for the long-sought ‘invisibility cloak’—a structure that renders opaque objects
invisible. We also evaluate the cloaking capabilities of structures designed by the related CM
approach, which makes use of conformal mapping to achieve index-only material distributions.
The performance of the various cloaks is evaluated and compared using a universal
measure—the total (all-angle) scattering cross section.
