Material parameter equation for elliptical cylindrical cloaks

Using coordinate transformation stated earlier by Pendry et al. [Science 312, 1780 (2006)], we deduced the material parameter equation for elliptic cylinder cloaks and reported the numerical simulations as well. The theoretical and numerical results indicate that, an elliptic cylinder cloak, which is constructed with metamaterials possessing the permittivity and permeability ruled by our equation, can exclude the electromagnetic fields from the interior region without perturbing the exterior fields and therefore the objects in it can be effectively invisible to the outer region.