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.

A semi-analytical technique to simulate spatially dispersive (SD) cylindrical metasurfaces is proposed and demon- strated. This method is based on the well-known Eigenfunction Expansion (EFE) method and extends the work of [1], [2] by integrating the Extended GSTCs into this pre-existing method specific to cylindrical surfaces. This method is then applied to several cylindrical metasurfaces composed of spatially dispersive wire dipole unit cells, and successfully verified against commercial full-wave simulations. Finally, using a case of a closed metasur- face shell, the usefulness of the proposed EFE-SD method is shown to illustrate the effect of metasurface thickness on the scattered fields inside and outside the shell.

A zero thickness model of non-uniform spatially dispersive (SD) metasurfaces is developed and demonstrated numerically for practical structures. This is an extension of [1], [2], which proposed a method of modeling uniform spatially dispersive 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 non-uniform metasurfaces by approximating them as locally linear space invariant (LSI). Using this model, a semi-analytical 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 non-dispersive, 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.

An Integral Equation (IE) based field solver to compute the scattered fields from spatially dispersive metasurfaces is proposed and numerically confirmed using various examples involving physical unit cells. The work is a continuation of Part- 1 [1], which proposed the basic methodology of representing spatially dispersive metasurface structure in the spatial frequency domain, k. By representing the angular dependence of the surface susceptibilities in k as a ratio of two polynomials, the standard Generalized Sheet Transition Conditions (GSTCs) have been extended to include the spatial derivatives of both the difference and average fields around the metasurface. These extended boundary conditions are successfully integrated here into a standard IE-GSTC solver, which leads to the new IEGSTC-SD simulation framework presented here. The proposed IE-GSTC-SD platform is applied to various uniform metasurfaces, including a practical short conducting wire unit cell, as a representative practical example, for various cases of finite-sized flat and curvilinear surfaces. In all cases, computed field distributions are successfully validated, either against the semi-analytical Fourier decomposition method or the brute-force full-wave simulation of volumetric metasurfaces in the commercial Ansys FEM-HFSS simulator.

A simple method to describe spatially dispersive metasurfaces is proposed where the angle-dependent surface susceptibilities are explicitly used to formulate the zero thickness sheet model of practical metasurface structures. It is shown that if the surface susceptibilities of a given metasurface are expressed as a ratio of two polynomials of tangential spatial frequencies, k||, with complex coefficients, they can be conveniently expressed as spatial derivatives of the difference and average fields around the metasurface in the space domain, leading to extended forms of the standard Generalized Sheet Transition Conditions (GSTCs) accounting for the spatial dispersion. Using two simple examples of a short electric dipole and an all-dielectric cylindrical puck unit cells, which exhibit purely tangential surface susceptibilities and reciprocal/symmetric transmission and reflection characteristics, the proposed concept is numerically confirmed in 2D. A single Lorentzian has been found to describe the spatio-temporal frequency behavior of a short dipole unit cell, while a multi-Lorentzian description is developed to capture the complex multiple angular resonances of the dielectric puck. For both cases, the appropriate spatial boundary conditions are derived.

An accelerated Integral Equations (IE) field solver for determining scattered fields from electrically large electromagnetic metasurfaces utilizing Fast Multipole Method (FMM) is proposed and demonstrated in 2D. In the proposed method, practical general metasurfaces are expressed using an equivalent zero thickness sheet model described using surface susceptibilities, and where the total fields around it satisfy the Generalized Sheet Transition Conditions (GSTCs). While the standard IE-GSTC offers fast field computation compared to other numerical methods, it is still computationally demanding when solving electrically large problems, with a large number of unknowns. Here we accelerate the IE-GSTC method using the FMM technique by dividing the current elements on the metasurface into near- and far-groups, where either the rigorous or approximated Green’s function is used, respectively, to reduce the computation time without losing solution accuracy. Using numerical examples, the speed improvement of the FMM IE-GSTC method O(N1.5) over the standard IE-GSTC O(N3) method is confirmed. Finally, the usefulness of the FMM IE-GSTC is demonstrated by applying it to solve electromagnetic propagation inside an electrically large radio environment with strategically placed metasurfaces to improve signal coverage in blind areas, where a standard IE-GSTC solver would require prohibitively large computational resources and long simulation times.