Approximate electromagnetic cloaking of spherical bodies using nonlinear transformation with improved total scattering

Cloaking refers to hiding a body from detection by surrounding it with a coating consisting of an unusual anisotropic nonhomogeneous material. The permittivity and permeability of such a cloak are determined by the coordinate transformation of compressing a hidden body into a point or a line. In this work, the scattering properties of cloaked spherical bodies (conducting and dielectric) are investigated using a combination of approximate cloaking, where the conducting sphere is transformed into a small sphere rather than to a point, and using two types of nonlinear transformations; concave-up and concave-down. The radially-dependent spherical cloaking shell is approximately discretized into many homogeneous anisotropic layers, provided that the thickness of each layer is much less than the wavelength, and this discretization raises the level of scattering as the number of layers decreases. Each anisotropic layer can be replaced by a pair of equivalent isotropic sub-layers, where the effective medium approximation is used to find the parameters of these two equivalent sub-layers. The effect of nonlinearity in the coordinate transformation on the scattering performance is studied. The back-scattering normalized radar cross section, the scattering pattern are studied and the total scattering cross section against the frequency for different number of layers and transformed radius.