Double-scale homogenized impedance models for periodically modulated metasurfaces

This paper investigates the accuracy of homogenized impedance models for the description of periodically modulated metasurfaces (MTSs) realized by printing subwavelength patches on a grounded dielectric slab. The problem is relevant to surface-wave based MTS antennas. The homogenized models are based on the local impedance synthesis of the subwavelength patch elements on the basis of a micro-periodicity assumption (that is, with a subwavelength period); the homogenized impedance is successively used in a macro-periodically modulated problem; that is, a periodic homogenized problem with a period which includes several micro-periods. Two different homogenized impedance models are compared. A first model is based on an anisotropic “impenetrable” impedance, defined by boundary conditions (BCs) at the MTS-air interface, while the second one uses a “penetrable” impedance sheet describing the homogenized BCs imposed by the metallic cladding on the grounded metallic slab. Although the presence of the grounded slab is considered in both models, they provide different results when the homogenized impedance is used to describe the macro-modulation. It is shown, through comparison with a full-wave analysis, that both the homogenized models can provide consistent results, but the penetrable impedance model is more accurate in the prediction of both the complex propagation constant and the current distribution. This is due to its capability to correctly account for the spatial dispersivity of the MTS.