Limitations of the Metasurface Diluted-Slab Model

In this article, we investigate the possibility to model a metasurface, defined as a zero-thickness sheet of surface polarization currents and described by generalized sheet transition conditions (GSTCs), by a thin slab with a subwavelength thickness and usual voluminal medium parameters. First, we elaborate a general equivalence relation between the metasurface and the slab in terms of average electromagnetic fields. Then, we derive the exact relations between the metasurface and slab susceptibilities and validate them by full-wave simulations. Finally, we discuss the simple and insightful diluted-slab model, called here the average field approximation (AFA) formula, illustrate its inappropriateness for strong metasurface field transformations, and establish its range of validity. All of these developments are restricted to the simplest case of a uniform isotropic metasurface under normal plane wave incidence. We conclude, from the complexity of the exact equivalence for this simplest case and from the intrinsic limitations of the AFA, that a metasurface is generally best analyzed by computational schemes incorporating the GSTCs.