Approximate electromagnetic cloaking and scattering of a dielectric cylinder with nonhomogeneous anisotropic cloaking material

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 2D or cylindrical body into a line. Some components of the electrical parameters of the cloaking material (ε,μ) are required to have infinite or zero value at the boundary of the hidden object. In order to eliminate the zero or infinite values of the electrical parameters, approximate cloaking can be used by transforming the cylindrical body virtually into a small cylinder rather than a line, but this produces some scattering. In this work, the scattering pattern, and the back scattering cross section against the frequency for cloaked dielectric cylinder are studied for both transverse magnetic (TM_z) and transverse electric (TE_z) polarizations of the incident plane wave for different transformed body radii.