Surface Susceptibility Synthesis of Spatially Dispersive Metasurfaces for Space Compression and Spatial Signal Processing

An analytical method is proposed to synthesize the angle-dependent surface susceptibilities, <inline-formula> <tex-math notation="LaTeX">$\chi $ </tex-math></inline-formula>, of spatially dispersive (SD) or nonlocal zero-thickness metasurfaces. The proposed method is based on the extended generalized sheet transition conditions (GSTCs), whereby spatially dispersive metasurfaces are modeled using angle-dependent surface susceptibilities that take the form of rational polynomial functions of the transverse wave vector, <inline-formula> <tex-math notation="LaTeX">$k_{\parallel } $ </tex-math></inline-formula>. The suggested method derives the rational polynomial form of <inline-formula> <tex-math notation="LaTeX">$\chi (k_{\parallel })$ </tex-math></inline-formula>, which can then be expressed in the space-domain using spatial derivatives of the fields, resulting in a corresponding higher order spatial boundary condition to achieve the desired field operation. The proposed synthesis method is illustrated using variety of examples such as a space plate, spatial filters, and field absorbers, which are then validated using an integral equation (IE) solver, in which the corresponding higher order boundary conditions are integrated to predict the scattered fields. The proposed method thus not only represents a simple way to synthesize ideal zero-thickness metasurfaces but also helps establishes a way to define fundamental operational limits of spatially dispersive metasurfaces. This is illustrated by considering the space plate example and deriving the fundamental tradeoff between operation bandwidth and the achievable space compression.