Efficient design of electromagnetic devices using modulated elliptical patch metasurfaces

Metasurfaces (MTS´s) are thin metamaterial layers constituted by a periodic lattice of sub-wavelength elements. They have been recently employed to design leaky-wave antennas or to control the propagation path of guided or surface waves (S. Maci et al., “Metasurfing: addressing waves on impenetrable metasurfaces,” IEEE Antennas Wireless Propag. Lett., vol. 10, pp. 1499-1502, 2011). These applications rely on a proper modulation of the MTS equivalent impedance; for this reason, the capability to efficiently and accurately characterize the MTS impedance is a key step for the design. For same particular geometries of the constituent elements, approximate closed-form expressions are available for the MTS equivalent impedance. This is the case for MTS consisting of square patches, inductive grids or circular patches. However, all these elements provide a quite isotropic equivalent impedance and are therefore limited in their use only to particular applications. Introducing some anisotropy in the MTS behavior leads to a tensorial equivalent impedance and, by providing polarization control, allows one to enlarge the class of synthesizable devices. Application examples are provided by transformation-optics inspired devices (E. Martini and S. Maci, “Metasurface Transformation Theory,” in Transformation Electromagnetics and Metamaterials: Fundamental Principles and Applications, eds. Douglas. H. Werner and Do-Hoon Kwon, Springer, 2013).