Efficient design of transformation optics devices based on anisotropic metasurfaces

Transformation Optics (TO) is a systematic approach that makes use of coordinate transformations to design devices capable of controlling the propagation of electromagnetic waves [1]. This control is achieved on the basis of macroscopic equivalent constitutive tensors of a volumetric anisotropic material. In practice, TO-based devices can be implemented by using metamaterials, which can be engineered to achieve electromagnetic behaviors which can not be found in nature [2]. Metamaterials can be realized by periodically arranging many small inclusions in a dielectric host environment and their use offers promising opportunities for the practical implementation of TO-based devices; there are, however, technological difficulties in controlling the variation of the macroscopic constitutive tensors of volumetric metamaterials, as well as in realizing anisotropic and extreme parameters. A significant technological simplification can be obtained by using metasurfaces (MTS) [3] instead of volumetric metamaterials. MTSs are thin metamaterial layers constituted by a periodic lattice of sub-wavelength elements. Due to the small periodicity in terms of a wavelength, they can be characterized in terms of an equivalent impedance providing the relationship between the average tangential components of the electric and magnetic fields. Indeed, effects similar to addressing waves in volumetric media may be obtained by modulating the properties of an impedance surface supporting surface waves (SW) [4-6].