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.

Nonlinear optical materials, such as transparent conductive oxides, have recently drawn a lot of attention when being integrated into metasurfaces and allowing full-optical control of the surface response. Although several methods for modeling the nonlinear materials have been proposed in the literature, most of them have the limitations on being non-dispersive and of instantaneous response. In this paper, we present a straightforward integration of an extended Drude-Lorentz model that captures the local intensity response of nonlinear materials while being dispersive and allowing for inertial response via a low-pass filtering process. This method is integrated into standard finite difference time-domain (FDTD) implementation of Maxwell’s equations and the auxiliary differential equations approach of the Drude-Lorentz model is extended via local intensity-dependent parameters. A numerical demonstration shows the response for a thin film of nonlinear material, where the parameters across the sample are time-varying with respect to the local intensity of the fields. Therefore, showing a direct feedback of the field profile to the nonlinear response of the material, which is critical when incorporating such films in resonating meta-atoms.

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.