Surface wave dispersion for anisotropic metasurfaces constituted by elliptical patches

This paper presents an effective approach for the derivation of the two-dimensional (2-D) frequency-wavenumber dispersion surface of anisotropic metasurfaces (MTSs) consisting of elliptical patches printed over a grounded slab. These MTSs are important in the design of leaky-wave antennas and transformation optics (TO) surface-wave based devices. The formulation resorts to an analytical expression of the currents excited on the element of the periodic texture to define a reduced spectral method of moments (MoM) procedure with only three basis functions. An exact compact formula, which links the MoM matrix to the homogenized equivalent anisotropic impedance of the MTS, is derived. The formulation presented here has been found accurate and useful for designing MTS antennas and TO devices.