Radiation from an axial electric dipole with oblate spheroidal metamaterial cloak cover

Exact analytical expressions for the electromagnetic field due to an electric dipole source located inside and along the axis of symmetry of an oblate spheroid are derived. The spheroid is made of a penetrable, linear, isotropic, homogeneous and lossless material whose propagation constant is either equal (isorefractive cloak) or of opposite sign (anti-isorefractive metamaterial cloak) to the propagation constant of the medium surrounding the spheroid. In particular, the influence of the spheroidal material on the radiation pattern of the spheroid is examined.