Cross-section comparisons of cloaks designed by transformation optical and opticalconformal mapping approaches

Abstract

We review several approaches to optical invisibility designed using transformation optics(TO) and optical conformal mapping (CM) techniques. TO is a general framework forsolving inverse scattering problems based on mimicking spatial coordinate transformationswith distributions of material properties. There are two essential steps in the design of TOmedia: first, a coordinate transformation that achieves some desired functionality, resultingin a continuous spatial distribution of constitutive parameters that are generallyanisotropic; and, second, the reduction of the derived continuous constitutiveparameters to a metamaterial that serves as a stepwise approximation. We focushere on the first step, discussing the merits of various TO strategies proposedfor the long-sought ‘invisibility cloak’—a structure that renders opaque objectsinvisible. We also evaluate the cloaking capabilities of structures designed by therelated CM approach, which makes use of conformal mapping to achieve index-onlymaterial distributions. The performance of the various cloaks is evaluated andcompared using a universal measure—the total (all-angle) scattering cross section.