Approximate electromagnetic cloaking of a conducting cylinder 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. Its function is to deflect the rays that would have struck the object, guide them around the object, and return them to their original trajectory, thus no waves are scattered from the body. 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. Some components of the electrical parameters of the cloaking material (ɛ, μ) are required to have infinite or zero value at the boundary of the hidden object. Approximate cloaking can be achieved by transforming the cylindrical body (dielectric and conducting) virtually into a small cylinder rather than a line, which eliminates the zero or infinite values of the electrical parameters. The radially-dependent cylindrical cloaking shell can be approximately discretized into many homogeneous anisotropic layers; 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 cylinder is investigated using a combination of approximate cloaking, together with discretizing the cloaking material using pairs of homogeneous isotropic sub-layers. The solution is obtained by rigorously solving Maxwell equations using angular harmonics expansion. The scattering pattern, and the back scattering cross section against the frequency are studied for both transverse magnetic (TMz) and transverse electric (TEz) polarizations of the incident plane wave for different transformed body radii