  We investigate the possibility to model a metasurface, defined as a
zero-thickness sheet of surface polarization currents, by a thin slab,
characterized by 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 exact relations between the metasurface and slab susceptibilities and
validate them by full-wave simulations. Finally, we discuss the simple and
insightful Average Field Approximation (AFA) formula, illustrate its
inappropriate 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 equivalence for this case, that a
metasurface is generally best modeled in terms of Generalized Sheet Transition
Conditions (GSTCs).

Applied Physics