Controlling frequency dispersion in electromagnetic invisibility cloaks

Electromagnetic cloaking, as challenging as it may be to the physicist and the engineer has become a topical subject over the past decade. Thanks to the transformations optics (TO) invisibility devices are in sight even though quite drastic limitations remain yet to be lifted. The extreme material properties which are deduced from TO can be achieved in practice using dispersive metamaterials. However, the bandwidth over which a metamaterial cloak is efficient is drastically limited. We design and simulate a spherical cloak which takes into account the dispersive nature of relative permittivity and permeability tensors realized by plasma-like metamaterials. This spherical cloak works over a broad frequency-band even though these materials are of a highly dispersive nature. We establish two equations of state that link the eigenvalues of the permittivity and permeability tensors in every spherical cloak regardless of the geometrical transformation. Frequency dispersive properties do not disrupt cloaking as long as the equations of states are satisfied in the metamaterial cloak.