Spatially Dispersive Metasurfaces—Part III: Zero-Thickness Modeling of Periodic and Finite Nonuniform Surfaces

A zero-thickness model of nonuniform spatially dispersive (SD) metasurfaces is developed and demonstrated numerically for practical structures. This is an extension of Nizer Rahmeier et al. (2022) and Smy et al. (2022), which proposed a method of modeling uniform SD metasurfaces by expressing their surface susceptibilities as rational polynomial functions in the spatial frequency domain. This led to the extended generalized sheet transition conditions (GSTCs) forming a set of differential equations relating the spatial derivatives of both difference and average fields around the surface that were then integrated into an integral equation (IE) solver. Here, the extended GSTCs are further developed to model nonuniform metasurfaces by approximating them as locally linear space-invariant (LSI). Using this model, a semianalytical Floquet method is derived to predict scattered fields from periodically varying metasurfaces. The extended GSTCs, Floquet method, and IE method are tested on several nonuniform surfaces consisting of short metal dipole cells of varying lengths exhibiting strong spatial dispersion. The physical surfaces are simulated in Ansys FEM-HFSS, while their zero-thickness equivalents, both dispersive and nondispersive, are simulated using the Floquet and IE methods. Excellent agreement is shown between the Floquet-SD and IE-GSTC-SD methods and HFSS, demonstrating the importance of spatial dispersion to model their scattered fields.