Non singular material parameters for arbitrarily elliptical–cylindrical invisibility cloaks

Simple general expressions for an important class of invisibility cloaks with less radial symmetry are derived by using transformation optics theory. Material parameters of arbitrarily elliptical–cylindrical invisibility cloak are obtained using a transformation in the elliptical–cylindrical coordinate system. It is explicitly shown that the azimuthal terms of material parameters in ideal case, like circular-cylindrical cloaks, are infinite at the whole interior surface of the cloak which makes ideal cloak impractical. Maxwell's equations are obtained in arbitrarily elliptical–cylindrical coordinate system and then the reduced material approximation is expanded to eliminate such singularities in the cylindrical cloaks with arbitrarily elliptical cross sections. The impedance of the cloak is derived and the cloak with reduced material approximation is designed so that the cloak's impedance at outer boundary experiences no change. An approximated 8 layer practical cloak is proposed such that each layer is divided to 32 slices azimuthally. Functionality of the proposed cloaks are numerically confirmed by two-dimensional finite element simulations where we illustrated that both layered and reduced cloaks with no singularities in their material parameters and therefore much easier realization possibility, show very good cloaking performance.