Rigorous analysis of non-magnetic cloaks

Nonmagnetic cloak offers a feasible way to achieve invisibility at optical frequencies using materials with only electric responses. In this letter, we suggest an approximation of the ideal nonmagnetic cloak and quantitatively study its electromagnetic characteristics using a full-wave scattering theory. It is demonstrated that the forward scattering of the impedance matched cloak increases dramatically as the thickness of the cloak decreases. Nevertheless, it is still possible to effectively reduce the total scattering cross section with a very thin cloak whose impedance is not matched to the surrounding material at the outer boundary. Our analysis also provides the flexibility of reducing the scattering in an arbitrary direction.