A Cloaking Metamaterial Based on an Inhomogeneous Linear Field Transformation

A new type of bianisotropic metamaterial is theoretically investigated on the basis of a linear inhomogeneous field transformation applied to an arbitrary free-space Maxwellian field. This transformation does not include any space compression as predicted by transformation optics, and consists of a linear combination with space-dependent coefficients of the electric and magnetic incident fields. Duality conditions are applied to select an appropriate shape of the constituent dyads, thus resulting in a metamaterial completely defined by two real differentiable functions of space sigma and eta. When these functions satisfy the condition sigma(2) + eta(2) on the medium contour, the medium becomes globally lossless, and when imposing sigma = 0 and eta = 1 at the same boundary, the medium does not scatter for any arbitrary incident field, that is, it becomes invisible. When an additional internal boundary is introduced with boundary conditions sigma = 0 and eta = 0, the medium becomes a perfect cloak. Explicit analytical results are given for an invisible sphere and for a spherical cloak to provide additional physical insight.