Parameterization strategy for anisotropy reduction in the carpet cloak

In this paper a transformation optical design with anisotropy reduction via parametrization and Least Squares Method is applied to develop a reflectionless quasi-isotropic carpet cloak. We present a coordinate transformation function for the carpet cloak geometry that includes a variable number of degrees of freedom to minimize the anisotropy of the transformed media without interfering with the device boundary conditions. Effects of anisotropy reduction in the coordinate transformation and the effectiveness of our method is verified when different numbers of degrees of freedom for the parameterization function is used. The results appointing that the anisotropy can be very close to zero at cost to use an elevated number of degrees of freedom.