Designing the coordinate transformation function for non-magnetic invisibility cloaking

Abstract

An optical invisibility cloak based on a transformation approach has recently been proposed by a reduced set of material properties due to their easier implementation in reality and little need for an inhomogeneous permeability distribution, but the drawback of undesired scattering caused by the impedance mismatching at the outer boundary is unavoidable in such a cloak. By properly designing the coordinate transformation function to ensure impedance matching at the outer surface, we show that the performance of a nonmagnetic cylindrical cloak could be improved with minimized scattering fields. Using either a single high order power function or an optimized piecewise continuous power function, a cylindrical non-magnetic cloak has been designed with nearly perfect cloaking performance, which is better than those generated with a linear or a quadratic function. Due to the monotonicity of the designed power functions, the resulting cloak has no restriction on the size of the cloaking shell, therefore is suitable for both thick and thin cloaking structures.