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 ?? and ??. When these functions satisfy the condition ??² + ??² = constant on the medium contour, the medium becomes globally lossless, and when imposing ?? = 0 and ?? = 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 ?? = 0 and ?? = 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.