Electromagnetic scattering by approximately cloaked cylindrical bodies with nonhomogeneous anisotropic cloaking material

In cloaking, a body is hidden from detection by surrounding it by 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 (3D or spherical configuration) or a line (2D or cylindrical configuration). Some components of the electrical parameters of the cloaking material ε,μ$ \left( {{\varepsilon },{\mu }} \right) $ are required to have infinite or zero value at the boundary of the hidden object. Approximate cloaking can be achieved by transforming the cylindrical bodies (dielectric and conducting) virtually into a small cylinder rather than a line, which eliminates the zero or infinite values of the electrical parameters but produces scattering. The solution is obtained by rigorously solving Maxwell equations using angular harmonics expansion. In this work, the scattering pattern and the back-scattering cross-section against the frequency for cloaked conducting and dielectric cylinders are studied for both transverse magnetic (TMz) and transverse electric (TEz) polarizations of the incident plane wave for different transformed body radii.