Permittivity and Permeability Tensors for a Paraboloidal Invisibility Cloaking Shell

Invisibility or stealth in aerospace is a foremost requirement which can be achieved through various techniques such as shaping, radar absorbing materials or adaptive techniques. The constraints in all these techniques can be put together to move forward in the research of achieving the optimal version of electromagnetic (EM) stealth property. Invisibility cloaking is amongst one of them, in which, the EM waves can be controlled within the cloaking shell by introducing a prescribed spatial variation in the constitutive parameters. In this paper, analytical expressions of the permittivity and permeability tensors have been derived for General Paraboloid of Revolution (GPOR) structure and the final expressions along with simulation results are reported. These analytical expressions will help the EM designers to analyze and design of cloaking shells of paraboloidal shape and their hybrids which can lead to design of cloaking shells of arbitrary shapes.