Surface Susceptibilities as Characteristic Models of Reflective Metasurfaces

While metasurfaces (MSs) are constructed from deeply subwavelength unit cells, they are generally electrically large and full-wave simulations of the complete structure are computationally expensive. Thus, to reduce this high computational cost, nonuniform MSs can be modeled as zero-thickness boundaries, with sheets of electric and magnetic polarizations related to the fields by surface susceptibilities and the generalized sheet transition conditions (GSTCs). While these two-sided boundary conditions (BCs) have been extensively studied for single sheets of resonant particles, it has not been shown if they can correctly model structures where the two sides are electrically isolated, such as a fully reflective surface. In particular, we consider in this work whether the fields scattered from a fully reflective MS can be correctly predicted for arbitrary field illuminations, with the source placed on either side of the surface. In the process, we also show the mapping of a perfect electric conductor (PEC) sheet with a dielectric cover layer to bianisoptropic susceptibilities. Finally, we demonstrate the use of the susceptibilities as compact models for use in various simulation techniques, with an illustrative example of a parabolic reflector, for which the scattered fields are correctly computed using an integral-equation (IE)-based solver.