Reflectionless quasiconformal carpet cloak via parameterization strategy

Abstract

In this work the possibility of using both the parameterization function and the least squares method to achieve a quasiconformal carpet cloak via a transformation optical design is demonstrated. The parameterization strategy allows us to obtain a continuous interface around the media, and, therefore, the resulting structure is reflectionless. Polynomial series are added to the coordinate transformation functions, providing a number of degrees of freedom (DoF) without modifying the device boundary conditions. The anisotropy reduction effects over the coordinate transformation are analyzed for different numbers of DoF in the parameterization function. The method’s connection with the Riemann mapping theorem is also studied. Our results indicate that anisotropy can be reduced to very close to zero with increasing DoF without incurring edge reflections around the carpet cloak.