Generalized Sheet Transition Conditions (GSTCs) in Electromagnetic Metasurface Modeling

We present a modeling framework for metasurfaces illuminated by a plane wave based on the Generalized Sheet Transition Conditions (GSTCs). This framework describes how conventional boundary conditions are converted to GSTCs. In order to provide a physical insight into the induced dipole moments of simple small scatters, different snapshots are used when the maximum electric or maximum magnetic field touches the metasurface. The spatial derivatives of the normal components of the induced surface polarization densities are physically justified by considering all possible cases. It is shown that both the normal and transverse components of the electric surface polarization density and surface magnetization (magnetic polarization) density should be included in studying the most general case in the metasurface. In addition, we have reviewed three different modeling approaches for describing the GSTCs, which are polarizability, susceptibility, and impedance/admittance models. The interrelations between these approaches are also discussed. Finally, we have reviewed the generalized modeling approaches of GSTCs for synthesizing bianisotropic metasurfaces via all three mentioned models. This review provides several examples to demonstrate how to design a desired metasurface using GSTCs. This tutorial study may open new paradigms for a better modeling and conceptual understanding of GSTCs.