Surface Susceptibility Synthesis of Spatially Dispersive Metasurfaces
for Space Compression and Spatial Signal Processing
Abstract
An analytical method is proposed to synthesize the angle-dependent
surface susceptibilities, χ of spatially dispersive or non-local
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, k∥. The suggested method
derives the rational polynomial form of χ(k∥), 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 helps establishes a way to define
fundamental operational limits of spatially dis- persive metasurfaces.
This is illustrated by considering the space- plate example, and
deriving the fundamental trade-off between operation bandwidth and the
achievable space-compression.