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While metasurfaces (MSs) are constructed from deeply subwavelength unit cells, they are generally electrically large and full-wave simulations of the complete structure are computationally expensive. Thus, to reduce this high computational cost, nonuniform MSs can be modeled as zero-thickness boundaries, with sheets of electric and magnetic polarizations related to the fields by surface susceptibilities and the generalized sheet transition conditions (GSTCs). While these two-sided boundary conditions (BCs) have been extensively studied for single sheets of resonant particles, it has not been shown if they can correctly model structures where the two sides are electrically isolated, such as a fully reflective surface. In particular, we consider in this work whether the fields scattered from a fully reflective MS can be correctly predicted for arbitrary field illuminations, with the source placed on either side of the surface. In the process, we also show the mapping of a perfect electric conductor (PEC) sheet with a dielectric cover layer to bianisoptropic susceptibilities. Finally, we demonstrate the use of the susceptibilities as compact models for use in various simulation techniques, with an illustrative example of a parabolic reflector, for which the scattered fields are correctly computed using an integral-equation (IE)-based solver.

A metasurface reflector unit cell is proposed for achieving near-complete-range of complex reflectance (i.e., magnitude and phase) for versatile beamforming capabilities. The unit cell is based on coplanar coupled resonators: a split ring resonator (SRR) with a lumped capacitor and a lumped resistor, and a dipole ring resonator (DRR) with another lumped capacitor. The DRR inserted inside the SRR creates a coupled resonance configuration which results in an enhanced complex reflectance range at the desired frequency. To provide a physical insight and explain the operation principle of the structure, the response of the unit cell is modeled as a coupled Lorentz oscillator via the effective surface susceptibilities, where a unique plasma, damping constant, and resonant frequency can be attributed to each resonator. The proposed unit cell is demonstrated in an array configuration for linear-polarized beamforming, where full-wave simulations are used to demonstrate beam-steering, gain control, side-lobe level control and dual- and triple-beam generation, as illustrative examples. Finally experimental demonstration is performed to validate the full-wave results and obtain in-depth electrical characterization of the reflectors.

A simple method is proposed to characterize metasurface unit cells using rectangular waveguide. The method maps the S-parameters obtained using a dominant-mode waveguide to the S-parameters of fundamental Floquet mode for a plane wave incident at any desired angle. The mapping between the dominant waveguide mode and the fundamental Floquet mode is executed by extracting the equivalent surface susceptibilities of the metasurface unit cell. The results obtained from the proposed method show good agreement with the full-wave simulation results of the metasurface unit cell.

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.

This work continues the development of the raytracing method of [1] for computing the scattered fields from metasurfaces characterized by locally periodic reflection and transmission coefficients. In this work, instead of describing the metasurface in terms of scattering coefficients that depend on the incidence direction, its scattering behavior is characterized by the surface susceptibility tensors that appear in the generalized sheet transition conditions (GSTCs). As the latter quantities are constitutive parameters, they do not depend on the incident field and thus enable a more compact and physically motivated description of the surface. The locally periodic susceptibility profile is expanded into a Fourier series, and the GSTCs are rewritten in a form that enables them to be numerically solved for in terms of the reflected and transmitted surface fields. The scattered field at arbitrary detector locations is constructed by evaluating critical-point contributions of the first and second kinds using a Forward Ray Tracing (FRT) scheme. The accuracy of the resulting framework has been verified with an Integral Equation based Boundary Element Method (BEM)-GSTC full-wave solver for a variety of examples such as a periodically modulated metasurface, a metasurface diffuser and a beam collimator., Comment: 12 pages, 9 figures

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.

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.

This paper presents a formulation of an eigenfunction expansion (EFE) technique for the analysis of multi-shell cylindrical metasurface configurations and tests the validity of zero thickness sheet models for simulating practical structures. The formulation homogenizes the metasurface, modeling the surface as a zero-thickness discontinuity characterized by surface susceptibilities and allows for the incorporation of Perfect Electric Conductor (PEC) cores and partial cylindrical surfaces (arcs/sectors). A primary advantage of the method is that it is a fully rigorous semi-analytical approach and is well suited for investigating the limits of the zero thickness sheet models model via the Generalized Sheet Transition Conditions (GSTCs). Comparison to full-wave simulations in commercial solvers show that, for a thin deep sub-wavelength unit cell, single shell arcs with increasing curvatures (up to at least half of a wavelength in radius) are accurately captured by the use of the model. The simulations also show that the edge diffraction off the finite length arcs are well modeled. This is an important result as it indicates that susceptibilities extracted from full-wave unit-cell simulations assuming a flat periodic infinite surface are appropriate for use in high curvature finite surfaces. A second set of simulations showed that the EFE predicted multi-shell field distributions accurately when compared to unit-cell based simulations. A final set of simulations for single and double shell configurations is used to demonstrate the limitations of the GSTC approach for unit cells of appreciable thickness. Using a relatively thick unit cell (?7% of the excitation wavelength) and two different extraction models (cell edge and center) comparison to full-wave simulation shows that for resonant structures errors in field prediction are present. This is a clear indication that the zero-thickness assumption will break down for thick cells for some surface configurations. This paper demonstrates some clear advantages of the EFE approach; it is fast, rigorous and can accommodate a large range of geometric structures.

A simple concept to perfectly decouple the reflection magnitude and phase of a reflective metasurface is proposed. For a linearly-polarized illumination, a full 2? phase is achieved in reflection by physically displacing the unit cell normal to the surface, with respect to a fixed reference and source, while the reflection magnitude is independently controlled via an integrated resistive element inside the unit cell. This proposed concept is demonstrated using full-wave simulations, which is the first step towards an electromechanical metasurface with truly independent real-time amplitude and phase control.

Novel Fabry–Perot resonator-based compound Huygens’ structure with two all-dielectric metasurface layers is proposed and experimentally demonstrated. This design consists of two dielectric layers with about a quarter-wavelength separation at the center frequency. Each layer is a 2-D lattice of dielectric resonators. To realize the structure mechanically, each dielectric resonator is connected with its neighboring resonators using four interconnections or “two bridges.” The two bridges allow for a mechanically strong design with low fabrication tolerances. The two layers are used to cancel the reflections from the bridges, and hence achieve low backscattering in a wide bandwidth. Full-wave simulations are used to realize various beam transformations in the millimeter-wave (mm-wave) band, such as refracted and difference-pattern (DP) beams. The proposed structure is also successfully demonstrated using experiments for the uniform and DP beams at the mm-waves.

An all-dielectric Fabry–Perot compound Huygens’ structure is proposed for beam-forming at the millimeter-wave (mm-wave) band for circularly polarized (CP) waves. The proposed structure is based on a symmetric unit cell in the plane of the structure, which allows for CP wave transmission, and is demonstrated in the near field of a 60 GHz right-hand CP slot array antenna. Full-wave demonstration of a uniform structure shows a negligible effect on the reflection and radiation of the antenna from 59 to 62 GHz. Full-wave simulations were further used to demonstrate a phase-gradient structure for beam-steering from 59 to 61 GHz. Finally, a difference-pattern structure was fabricated and experimentally demonstrated for operation from 61 to 62 GHz, exhibiting low reflection and good axial ratio (AR) performance across the bandwidth.

A novel millimeter-wave (mm-wave) amplitude-only direction finding (DF) antenna front-end is proposed and experimentally demonstrated based on multiport leaky-wave antennas (LWAs). The multiport LWA is realized using an array of $N$ linearly polarized slot antennas. Each slot antenna is engineered to produce a beam pointing along a specific direction, exploiting the beam scanning law of LWAs. Realizing progressively shifted beams angularly in space by controlling the slot geometry of each antenna, the multiport LWA becomes sensitive to a large finite angular sector. Using this architecture, a unique mapping between the angle of arrival (AoA) and the port locations is achieved. Using detailed full-wave simulations, the DF operation of the slot-based LWA is successfully demonstrated for several examples involving single and multiple signals illuminating the antenna. It is demonstrated that the AoA can be determined by measuring the received power at each of the ports and the known radiation patterns of the LWAs. The DF antenna front-end is demonstrated experimentally at 60 GHz using a ten-port slot array antenna fabricated using substrate integrated waveguide (SIW) technology and tested in various incoming signal scenarios.

We present a rigorous semi-analytical formulation for the analysis of electromagnetic (EM) scattering from a cylinder constructed from a metasurface represented using surface susceptibilities. The formulation uses the Generalized Sheet Transition Conditions (GSTCs) to represent the surface and eigenfunction expansion (EFE) of the incident and scattered fields, by exploiting their angular periodicity. Incorporating a completely general non-uniform surface formulation of 36 susceptibility components, a matrix equation is formulated that can be solved for the field harmonic coefficients. The paper illustrates the methodology with a number of examples; including two formed from a finite sized practical unit-cell exhibiting a normally oriented magnetic resonance which is compared with commercial EM full-wave solver; other examples present surfaces that have a modulated gain/loss profile (i.e. amplitude modulation) and polarization conversion. It is found that for all cases the EFE solution very accurately captures the scattered fields in both the interior and exterior regions of the surface. Detailed convergence studies are further presented including the effect of susceptibility modulation on the number of terms needed in the EFEs, to reach a correct field solution. The proposed EFE framework is further compared with a second GSTC based simulator using an Integral Equations (IE) approach and it is found that the IE-GSTC simulated fields approach that of the EFE as the surface discretization is increased. The proposed EFE approach is thus a quick, rigorous methodology which, although limited in the geometry which it can model, has many advantages for investigation into the use of GSTCs, application development and providing a baseline for simulation studies.

A ray optical methodology based on the uniform theory of diffraction is proposed to model electromagnetic field scattering from curved metasurfaces. The problem addressed is the illumination of a purely reflective uniform cylindrical metasurface by a line source, models the surface with susceptibilities and employs a methodology previously used for cylinders coated in thin dielectric layers [1]. The approach is fundamentally based on a representation of the metasurface using the General Sheet Transition Conditions (GSTCs) which characterizes the surface in terms of susceptibility dyadics. An eigenfunction description of the metasurface problem is derived considering both tangential and normal surface susceptibilities, and used to develop a ray optics (RO) description of the scattered fields; including the specular geometrical optical field, surface diffraction described by creeping waves and a transition region over the shadow boundary. The specification of the fields in the transition region is dependent on the evaluation of the Pekeris caret function integral and the method follows [1]. The proposed RO-GSTC model is then successfully demonstrated for a variety of cases and is independently verified using a rigorous eigenfunction solution (EF-GSTC) and full-wave Integral Equation method (IE-GSTC), over the entire domain from the deep lit to deep shadow.

An all-dielectric Huygens’ transmit-array is proposed and experimentally demonstrated in the 120-GHz-band. The proposed transmit-array is fabricated using a high-precision laser-drilling process providing high fabrication precision and accuracy. A non-uniform Huygens’ surface is next placed on top of a planar high gain slot-array antenna for far-field beamforming. Full-wave simulations are first used to demonstrate the beamforming capability by generating difference-pattern beams as an example. A uniform transmit-array was then fabricated and characterized to investigate the effect of the transmit-array on the antenna performance, along with showing very low fabrication tolerances and minimal dimensional variation due to the laser drilling process. Next, a phase-gradient transmit-array for beam-tilting is experimentally demonstrated as a practical example of beamforming. The proposed all-dielectric structure is the first Huygens’ structure to be demonstrated at these frequency bands, and represents an attractive alternative to conventional metallic Huygens’ metasurfaces based on standard printed circuit board (PCB) solutions.

A Finite-Difference Time-Domain (FDTD) simulation of broadband electromagnetic metasurfaces based on direct incorporation of Generalized Sheet Transition Conditions (GSTCs) into a conventional Yee-cell region has been proposed for arbitrary wave excitations. This is achieved by inserting a zero thickness metasurface inside bulk nodes of the Yee-cell region, giving rise to three distinct cell configurations - Symmetric Cell (SC), Asymmetric Cell (AC) and Tight Asymmetric Cell (TAC). In addition, the metasurface is modelled using electric and magnetic surface susceptibilities exhibiting a broadband Lorentzian response. As a result, the proposed model guarantees a physical and causal response from the metasurface. Several full-wave results are shown and compared with analytical Fourier propagation methods showing excellent results for both 1D and 2D field simulations. It is found that the TAC provides the fastest convergence among the three methods with minimum error.

A systematic approach is presented to exploit the rich field transformation capabilities of Electromagnetic (EM) metasurfaces for creating a variety of illusions using the concept of metasurface holograms. A system level approach to metasurface hologram synthesis is presented here, in which the hologram is co-designed with the desired object to be projected. A structured approach for the classification of the creation of EM illusions is proposed for better organization and tractability of the overall synthesis problem. The deliniation is in terms of the initial incident (reference) illumination of the object to be recreated (front/back-lit), the position of illusion (posterior/anterior), and the illumination used to create the illusion (front/back). Therefore the classification is based on the specific relationship between the reference object to be recreated, the observer measuring the object, the orientation and placement of the reference and illumination field, and the desired placement of the metasurface hologram creating a virtual image. In the paper a general design procedure to synthesize metasurface holograms is presented based on Integral Equations (IE) and Generalized Sheet Transition Conditions (GSTCs), where the metasurface hologram is described as zero thickness sheet with tensorial surface susceptibility densities. Several selected configurations are chosen to illustrate various aspects of the hologram creation in 2D, along with a novel numerical technique to artificially reverse propagate the scattered fields, required in the synthesis process. Finally, the impact of the metasurface size and the illumination field strength on the quality of the reconstructed scattered fields is also discussed., Comment: 15 pages, 10 figures

This article presents a method to determine the scattered electromagnetic (EM) fields in the interconnected regions with common metasurface boundaries. This method uses a boundary element method (BEM) formulation of the frequency domain version of Maxwell’s equations, which expresses the fields present in a region due to surface currents on the boundaries. Metasurface boundaries are represented in terms of surface susceptibilities which when integrated with the generalized sheet transition conditions (GSTCs) gave rise to an equivalent configuration in terms of electric and magnetic currents. These representations are then naturally incorporated into the BEM methodology. Four examples are presented for EM scattering of a Gaussian beam to illustrate the proposed method. In the first example, a metasurface is excited with a diverging Gaussian beam, and the scattered fields are validated using a semianalytical method. The second example is concerned with a nonuniform metasurface modeling a diffraction grating, whose results were confirmed with a conventional finite-difference frequency-domain (FDFD) method. To illustrate the flexibility of the method, the third example uses a metasurface that implements a polarization rotator. Finally, a fully absorbing metasurface is simulated and compared to the FDFD simulations to emphasize the advantages of BEM method.

A novel low-profile grooved-dielectric choke ring with dual-band surface impedance resonance is proposed and experimentally demonstrated. The proposed structure is designed by engineering the surface impedance of a dielectric-based choke ring to introduce two resonant frequencies around the global navigation satellite system (GNSS) bands of L2 (1227.60 MHz) and L1 (1575.42 MHz). This provides capacitive surface impedances around both bands simultaneously, which is required for efficient surface wave suppression for higher multipath rejection performance. To demonstrate the proposed principle of surface impedance engineering, an in-house choke ring prototype of the proposed design is tested with the widely used Dorne and Margolin antenna. A high multipath rejection in both GNSS bands is experimentally confirmed with comparable performances to an otherwise bulky, heavy, and expensive conventional metallic choke ring.