Cloaking formulated in terms of equivalent volumetric sources

This paper presents conditions on the constitutive dyads of a bianisotropic linear metamaterial that are sufficient to ensure cloaking for arbitrary shapes and arbitrary illumination. The volumetric equivalence theorem is first formulated for a bianisotropic metamaterial scatterer. By assuming that the volumetric equivalent currents do not radiate outside the cloak, and radiate the negative of the incident field in the internal cavity of the cloak, the material constituent dyads are written as a function of two vector potentials respecting simple boundary conditions. The special known cases of transformation optics are derived in terms of a particular choice of the vector potentials as a coordinate transformation of the incident field space.