Approximate electromagnetic cloaking of a conducting sphere using homogeneous isotropic multi-layered materials

Cloaking refers to hiding a body from detection by surrounding it with a coating consisting of an unusual anisotropic nonhomogeneous material. The radially-dependent spherical cloaking shell can be 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. In this work, the scattering properties of cloaked perfectly conducting sphere is investigated using a combination of approximate cloaking, where the conducting sphere is transformed into a small sphere rather than to a point, together with discretizing the cloaking material using pairs of homogeneous isotropic sub-layers. 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 cloaking radius.