Emulating Spatial Dispersion Using Non-Spatially Dispersive Periodic Metasurfaces

Spatially dispersive (or non-local) metasurfaces are an important class of surface where the induced currents on the surface are dependent on the fields over an extended region of the surface. These surfaces can be characterized using surface susceptibilities that take the form of rational polynomial functions in the spatial frequency domain. This representation allows us to model the field scattering from the surface as a higher-order boundary condition. Recently, a method was proposed to synthesize a set of susceptibilities to achieve any given field response in the spatial frequency domain. However, realizing these susceptibilities remains an open problem. In this paper, we demonstrate that spatially dispersive metasurfaces can be implemented as non-uniform metasurfaces composed of non-spatially dispersive unit cells.