Spatially Dispersive Zero Thickness Sheet Model of All-Dielectric Metasurfaces

A general polynomial expansion of the tangential susceptibilities with respect to the transverse wave-vector, k
||
is presented to properly describe a spatially dispersive zero thickness model of an all-dielectric metasurface via an extended form of the generalized sheet transition conditions. Tangential susceptibilities of a typical cylindrical dielectric puck are extracted from commercial full-wave simulators and expanded into multi-Lorentz spatial resonances. Results are validated using integral equations solvers and show that ignoring spatial dispersion deprecates the metasurface field scattering response under oblique incidence.