Coupled Resonator-Based Metasurface Reflector With Enhanced Magnitude and Phase Coverage

A metasurface reflector unit cell is proposed for achieving a near-complete range of complex reflectance (i.e., magnitude and phase) for versatile beamforming capabilities. The unit cell is based on tunable 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 that results in an enhanced complex reflectance range at the desired frequency. To provide 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 frequency, damping coefficient, 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, sidelobe 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.

To realize a general beamforming capability for a given polarization and at a given operating frequency, an ideal metasurface reflector must achieve full complex reflectance (i.e., magnitude and phase) control on each of its unit cell elements forming the surface [10].In other words, the reflector must achieve complex reflectance, = | |e j ̸ , with full range of magnitude 0 ≤ | | ≤ 1 and phase 0 ≤ ̸ ≤ 2π variations.Various designs have been proposed in the literature to achieve control over the complex reflectance using static or dynamic implementations.For instance, a static coupled resonator metasurface reflector was proposed in [11] based on varying resonator dimensions in a multilayer printed circuit board (PCB).Another example is a single-layer metasurface reflector based on X-shaped metallic meta-atoms [12], where complex reflectance control is achieved via spatial rotation of the metallic patterns, exploiting the Pancharatnam-Berry phase effect [13].While conceptually simple, this approach generates undesired cross-polarized scattering unlike the solution of [11], for instance.Both designs in [11] and [12] were demonstrated for static beamforming, and there is no clear practical or logical path to extend the functionality to dynamic beamforming.Other examples of static metasurface implementations include a wide field-of-view metalens transmitter exploiting symmetry transformation and demonstrated for achieving wide-angle beamsteering [14], and a broadband metasurface reflector based on a unit cell with multiple closed-ring resonators demonstrated for surface cloaking and lensing applications [15].
Dynamic implementations of metasurface reflectors have also been proposed.For instance, a reconfigurable metasurface reflector based on coupled resonators and varactor diodes was proposed in [16].This dynamic surface provides a large complex reflectance range and is attractive due to its real-time reconfiguration feature.However, it suffers from design complexity and the requirement of appreciable vertical separation between the magnitude and phase modules for optimum operation, thereby making it difficult to integrate and results in a nonlow-profile solution, unlike that of [11] or [12].Another dynamic implementation based on a single-layer substrate was proposed in [17].The design provides reconfigurable beamforming capabilities based on a unit cell with two varactor diodes and a resistor.The metasurface is based on a simple single-layer dielectric however this comes at the expense of beamforming capabilities limited to a single plane.This is due to the shared dc bias lines between adjacent cells along one 0018-926X © 2023 IEEE.Personal use is permitted, but republication/redistribution requires IEEE permission.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
column, leading to those unit cells having the same electrical properties.Moreover, the biasing network is co-designed with the unit cell which is exposed to incoming radiation.This naturally forces the polarization to be linear and perpendicular to the bias lines.Another approach based on a reconfigurable electro-mechanical structure was recently proposed in [18] based on motorized vertical displacement of the unit cell for phase control, and integrated PIN diodes in the unit cell resonator for magnitude control.While this configuration provides true decoupling between magnitude and phase, and thus allows their near arbitrary combination, it suffers from low speed, the added weight and power consumption of the motors, and overall bulky and nonintegrable nature of the design requiring significant mechanical assembly of the overall system.Recently, coding metasurfaces based on discretized magnitude and phase have also been reported.A coding metasurface for independent magnitude and phase control was reported in [19], where magnitude is controlled by loaded resistors, and the fixed phase is controlled by the size of the resonator.Similarly, a magnitude-phase joint coding information metasurface was reported in [20], and while it provides a full magnitude range, it has only two discrete phases and thus has limited phase coverage.Therefore, there is a clear need to design a metasurface configuration offering maximal complex reflectance coverage (i.e., simultaneous magnitude-phase range) that features design simplicity, linear polarization operation with no spurious cross-polarization generation, integrated board implementation, and suitability for both static and dynamic implementations.
To achieve this goal, in this work, a novel subwavelength unit cell is proposed that can achieve near-full-range complex reflectance control using two coplanar coupled resonators on a single-layer substrate.The unit cell uses three lumped circuit elements, two capacitive and one resistive, which provide enhanced control over the magnitude and phase of the reflected waves.While a preliminary analysis of the unit cell was reported in [21], this article features in-depth full-wave and theoretical characterization of the unit cell, practical component modeling considerations in simulation, and full-wave and experimental demonstration of beamforming.
The novelty of this work is threefold.First, in many reported works, beam-steering is presented using 1-bit coding metasurfaces with only two phases [22], [23].Such metasurfaces generate two symmetrically deflected beams under plane-wave excitation, as is typically required in applications involving intelligent reflecting surfaces or IRSs [24], [25].For single or multiple asymmetric beam-steering, more than two discrete phase values are necessary, unless a near-field source is used as in reflectarray antennas.For more than two phases, PIN diode-based coding metasurfaces become complex and expensive to design.Moreover, when 1-bit or 2-bit metasurfaces, with two or four discrete phases, respectively, are used for beam-steering, the phase quantization error increases the sidelobe level, reduces the main lobe maximum level, and reduces the beam pointing accuracy [26].This work proposes a simple unit cell that can achieve near-full-range of magnitude and phase without any inherent discretization, and therefore avoids the discretization disadvantages of coding metasurfaces.Additionally, while traditional reflectarrays use spherical-wave feed excitation [27], especially for 1-bit coded metasurfaces to avoid generating symmetrical beams [24], the proposed unit cell can be used for both plane-and spherical-wave excitation.Second, the proposed unit cell consists of two coplanar coupled resonators utilizing a single-layer dielectric, therefore it does not add multilayer PCB complexity that results when resonators are coupled across multiple layers as is common in literature [11], [16].Moreover, this work can be seen as a single-layer implementation of [11] where instead of geometrical variations, lumped circuit elements are utilized to achieve a near-complete complex reflectance control.Consequently, as a third novelty, the proposed configuration naturally allows for both static beamforming, using passive control elements, and is extendable to dynamic beamforming using PIN and varactor diodes with an additional substrate for biasing and RF/dc isolation considerations.
The article is organized as follows.Section II presents the proposed unit cell, with full-wave simulations and detailed theoretical analysis of its complex reflectance response.Section III presents a demonstration of full-wave beamforming and design methodology.Section IV shows experimental demonstration of metasurface reflectors based on the proposed unit cell using a variety of beamforming examples, with detailed discussions on their bandwidth and gain performance.Section IV also provides a comparison between the proposed unit cell and other metasurface reflectors from recent literature.Conclusions and future work are provided in Section V.

A. Coupled Resonator Configuration
To achieve the goal of complex reflectance control, the proposed coupled resonator metasurface unit cell is shown in Fig. 1(a).The unit cell consists of two coupled coplanar resonators: an outer SRR and an inner dipole ring resonator (DRR).The SRR consists of tunable capacitance, C 0 , and Fig. 2. Full-wave analysis of the isolated and coupled resonator unit cells using Ansys FEM-HFSS.(a) Floquet unit cell setup of the isolated and coupled resonator unit cells.The dimensions of the isolated resonator are (in mm): w 1 = 1, s 1 = 0.4572, and l 1 = 6.9.The dimensions of the coupled resonator are (in mm): resistance, R, while the DRR consists of a tunable capacitance, C 1 .The functionality of each of these controls will be explained further in this section.The proposed unit cell can be used to design a beamforming metasurface reflector, for example, to generate three beams from an incident plane-wave as shown in Fig. 1(b), where the beams can be arbitrarily placed with varying gains, utilizing the control over magnitude and phase separately, which otherwise cannot be achieved using phase-only control.Compared to [11], the proposed unit cell can achieve full-range complex reflectance coverage on a single-layer, as opposed to a multilayer configuration.Furthermore, while in [11] the dimensions of the resonators were varied to control the complex reflectance, the proposed configuration uses tunable circuit elements that can be either passive as followed here, or active using an additional substrate layer for biasing.
In Sections II-B and II-C, the details of the unit cell will be presented and its response will be compared with a unit cell based on an isolated resonator to show complex reflectance enhancement.It will be demonstrated that the coupled resonator with three controls (C 0 , R, and C 1 ) provides a wider range of complex reflectance compared to an isolated resonator with two controls (C 0 and R).Furthermore, the coupled resonator response will be analytically modeled as a coupled Lorentz oscillator to gain physical insight into its operation.

B. Isolated SRR Versus Coupled SRR-DRR
A simple metasurface reflector unit cell for complex reflectance control could be conceptualized based on a single SRR as shown in Fig. 2(a), with a tunable capacitance, C 0 , for phase control and a tunable resistance, R, for magnitude control.As previously mentioned, the proposed coupled resonator unit cell consists of a DRR, with an additional tunable capacitance control, C 1 , inserted inside the SRR creating a coupled SRR-DRR configuration as shown in Fig. 2(a).Full-wave analysis on Ansys FEM-HFSS of both unit cells was performed using periodic boundary conditions and plane-wave excitation (normal incidence and linear x-polarization), as shown in Fig. 2(a).Ideal R and C boundaries are used to model the circuit elements.The range of values used are 0.1-0.8pF in increments of 0.1 pF for capacitance, and 0-50 in increments of 2 for resistance, based on typical values found for off-the-shelf circuit elements (both static and tunable elements).
The complex reflection coefficient (i.e., magnitude and phase) of the isolated resonator with tunable C 0 and R are shown in Fig. 2(b) and (c), respectively.Fig. 2(b) shows that the effect of changing C 0 is to change the resonant frequency, and hence the reflection phase at a fixed operating frequency.Fig. 2(c) shows that the effect of changing R is to change the reflection magnitude near resonance.At a desired operating frequency, f = 8.4 GHz (in this case), sweeping both C 0 and R gives all possible complex reflectance values as shown in the Smith chart of Fig. 2(d), where it is evident that limited complex reflectance values can be achieved for a given set of capacitance and resistance values.In other words, the isolated resonator provides limited control over the reflection magnitude and phase for the given discrete capacitance and resistance values.  , and (f) resonant frequency, ω 0,3 = 2π {11.8, 12.9, 13.9, 15} Grad/s.(g) Smith chart show achievable complex reflectance at ω = 2π(8.5)Grad/s for sweeps of ω 0,2 from 2π(8) to 2π(11) Grad/s, γ 2 from 0.25×10 9 to 12.6×10 9 , and ω 0,3 from 2π(10) to 2π(15) Grad/s.
Next, the complex reflection coefficient results of the coupled resonator with tunable C 0 , R, and C 1 are shown in Fig. 2(e)-(g), respectively.Similar to the isolated resonator, C 0 and R control the phase and magnitude, respectively, at the desired frequency.The DRR introduces another resonance at a higher frequency, controlled by C 1 as shown in Fig. 2

(g).
Tuning C 1 affects both the magnitude and phase at the lower resonance.At a desired frequency, f = 9.8 GHz (in this case), sweeping C 0 , R, and C 1 gives all possible complex reflectance values as shown in the Smith chart of Fig. 2(h).For the same ranges of capacitance and resistance, it is therefore clearly evident that the coupled resonator covers a wider range of complex reflectance compared to the isolated resonator.In summary, C 0 controls the reflection phase, R controls the reflection magnitude, and C 1 controls both the phase and magnitude to achieve a complex reflectance range beyond that obtained by only tuning C 0 and R.

C. Coupled Lorentz Oscillator Model
To gain better insight into the operation of this unit cell, its complex reflectance response will now be analyzed using a coupled Lorentz oscillator model [28].The authors elected to use the Lorentz model to obtain physical insight into the operation of the unit cell for a number of reasons.First, the Lorentz model is a simple classical microscopic approach to modeling dispersive structures and can be used to capture both resonances and their coupling.Second, it is less cumbersome than other approaches, such as an equivalent circuit model, while providing the same basic understanding of the unit cell operation.Finally, one can argue that since a metasurface unit cell is being analyzed, a Lorentz model via the effective surface susceptibilities of the homogenized structure is the most suitable modeling approach.
The unit cell response under normal plane wave incidence can be modeled using electric and magnetic surface susceptibilities, χ ee (ω) and χ mm (ω), respectively, which can be calculated from the S-parameters [29] where k 0 = ω/c is the free-space wavenumber, R(ω) = S 11 (ω), and T (ω) = S 21 (ω) = 0 for zero transmission in this case.Additionally, a frequency-dispersive electric susceptibility can be modeled as a sum of n Lorentz resonances [28] where a 0 is a constant, ω 0 is the resonant frequency, ω p is the plasma frequency, and γ is the damping coefficient.Finally, the electric and magnetic susceptibilities are related by the following equation (to satisfy zero transmission conditions): To illustrate this model, a coupled resonator unit cell was chosen to analyze with C 0 = 0.2 pF, C 1 = 0.1 pF, and R = 0 , as an example.The complex reflection coefficient, obtained from full-wave simulation results, is shown in Fig. 3(a).The calculated χ ee (ω) and χ mm (ω) are shown in Fig. 3(b) and (c), respectively.Curve fitting of χ ee (ω) with Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.(2) was done to match with the full-wave calculated results, then χ mm (ω) was calculated with (3).The fit parameters (ω 0 , ω p , and γ ) are provided in Fig. 3's caption, with the first and second resonant frequencies of the unit cell captured by ω 0,2 and ω 0,3 , respectively.The loss in the first resonance is captured by γ 2 .The complex reflectance, electric susceptibility, and magnetic susceptibility calculated from the curve-fit parameters show good agreement with full-wave results as shown in Fig. 3(a)-(c), respectively.Next, the complex reflectance was calculated from the curve fit χ ee and χ mm for variations in ω 0,2 of the first resonance (equivalent to sweeping C 0 ), γ 2 of the first resonance (equivalent to sweeping R), and ω 0,3 of the second resonance (equivalent to sweeping C 1 ).Results are shown in Fig. 3(d)-(f) for variations ω 0,2 , γ 2 , and ω 0,3 , respectively.The Smith chart in Fig. 3(g) shows achievable complex reflectance at ω = 2π(8.5)Grad/s for sweeps of ω 0,2 , γ 2 , and ω 0,3 .The resemblance between the Smith chart results in Figs.2(h) and 3(g) is clear and confirms the correct Lorentz modeling of the unit cell and demonstrates that tuning the resonant and loss parameters of the different Lorentz oscillators correctly predicts the complex reflectance coverage of the unit cell.

III. FULL-WAVE DEMONSTRATION OF BEAMFORMING
To demonstrate the beamforming capabilities of the proposed unit cell, several examples will be shown for beam-steering, sidelobe level (SLL) control, and multibeam generation.A lookup table is first generated for the achievable complex reflectance from the proposed coupled resonator unit cell in the Floquet simulation of Fig. 2(a).Each unique set of C 0 , C 1 , and R corresponds to a specific complex reflection coefficient (i.e., {C 0 , C 1 , R} ↔ | |e j ̸ ).A linear N = 20 unit cell array is simulated as shown in Fig. 4, with the radiation patterns plotted in the x z-plane (i.e., beamforming plane).For each beamforming case, the desired ideal complex reflectance value for each unit cell (at each location of the array elements) is determined using array factor theory.For an array of N unit cells of periodicity oriented along the  (5) x-direction, the array factor is given by [30] a n e j(n−1)(k 0 sin θ ) where a n = | n |e j ̸ n is the complex reflectance, and θ is the angle measured from the z-axis.For each unit cell, the closest complex value in the lookup table is obtained through a minimization that considers both magnitude and phase, as where LU and ideal are the lookup table and ideal reflection coefficients, respectively, and w 1 and w 2 are weighing coefficients for the magnitude and phase, respectively.w 1 and w 2 are chosen through trial and error to give the best match between the ideal pattern and the pattern generated from the lookup table values.For instance, w 1 > w 2 is used for beamforming sensitive to magnitude, while for beamforming that is sensitive to the phase, w 2 > w 1 is used.For beamforming that is sensitive to both magnitude and phase, an optimum ratio of w 1 /w 2 is used.Values of w 1 and w 2 used in all beamforming examples to be shown here are tabulated in Table I.
Once the {C 0 , R, C 1 } set for each array element is determined, they are assigned as ideal R and C boundaries in the simulation.Radiation patterns will be compared from the ideal array factor, array factor using lookup table complex reflectance, and full-wave simulation.Additionally, the complex reflectance will be compared from ideal calculations, lookup table, and full-wave simulation near-field results.It is important to note that differences between full-wave and array factor calculations are expected due to unit cell coupling, edge diffraction, and unit cell pattern shaping, all of which are not accounted for by the simple array factor calculations.

A. Beamforming Examples
Let us consider the following beamforming examples that utilize the complex reflectance control capabilities of the proposed unit cell architecture.1) Beam-Steering With Gain Control: Fig. 5(a)-(c) show the results for beam-steering to θ des.= 30 • , θ des.= 45 • , and θ des.= 60 • , respectively.The desired ideal phase at the n th element to steer a beam at a desired angle can be calculated based on generalized Snell's law of reflection with normal incidence [31] as follows: where θ des. is the desired beam angle.In all cases in Fig. 5(a)-(c), beams are successfully steered to desired angles, and a good agreement is seen between analytical and full-wave results.Here, to achieve maximum gain, a constant maximum magnitude (| n | = 1) is used as achievable with the unit cell.An example of controlling the gain of a beam that is steered to θ des.= 30 • , for instance, is shown in Fig. 5(d), where the peak value can be varied from a strong reflection to a near-complete absorption.For gain control, a constant magnitude is used that achieves the required drop in gain.For example, to achieve a lower gain by 10 dB, a relative magnitude of | n | = 10 −10/20 = 0.32 is used across the unit cell array.
2) Sidelobe Level Control: A unit cell based on magnitude control allows for nonuniform amplitude distribution across the array which can be used to control the SLL of the reflected beam.Fig. 5(e)-(g) shows results for sidelobe level (SLL) reduction to −20, −30, and −40 dB, respectively, to illustrate this.To control the SLL without steering the beam, a constant phase was used with nonuniform amplitude at each array element determined by Dolph-Tschebyscheff polynomial method [30].Fig. 5(h) further shows the results for steering the beam to θ des.= 30 • in addition to obtaining a −20 dB SLL.In this case, the phase of each unit cell is determined using (6) and amplitude determined by Dolph-Tschebyscheff polynomial method, simultaneously.3) Asymmetric and Symmetric Beam Generation: One of the key benefits of achieving an enhanced complex reflectance control is the generation of multibeam reflection patterns with near-arbitrarily defined beam-steering angles, gains, and even beamwidths, which otherwise cannot be achieved using standard phase-only surfaces.
For multibeam generation, the magnitude and phase at each element are calculated using the direct superposition of the required beams.To generate M beams, the phase required at the nth unit cell for each beam can be calculated with (6), then the overall phase and magnitude can be obtained using A m e j ̸ n,m (7a) where A m is the relative peak gain for each beam, and |a n | is the amplitude for SLL control determined using the Dolph-Tschebyscheff method.Fig. 5(i)-(l) demonstrate these flexible beamforming capabilities using the case of dual-and triple-beams generation.For example, Fig. 5(i) shows asymmetric dual-beams in different quadrants with the same gain, Fig. 5(j) shows asymmetric dual-beams in the same quadrant and with different gains, while Fig. 5(k) and (l) show asymmetric and symmetric triple-beams, respectively.All these cases successfully demonstrate the extended beamforming capabilities utilizing the enhanced complex reflectance control of the proposed structures.

B. Bandwidth Investigation
While all these metasurface reflectors are ideally designed for a given design frequency, an important parameter to be determined about these surfaces is their operational bandwidth.Since metasurfaces are typically constructed using sub-wavelength resonators which are operated near their resonances, the desired spatial complex reflectance profile may rapidly deviate from the ideal design as the operation frequency is changed, leading to limited bandwidths.In this section, the functional bandwidth of these metasurface reflectors will be defined for various beamforming cases based on their various criteria depending on the exact beamforming capability.
A useful way to define the surface bandwidth is by investigating directivity versus angle and frequency, as shown in Fig. 6, normalized with respect to the directivity of a PEC reflector of the same size as the metasurface reflector, illuminated by a normally incident source.A comparison with a PEC reflector provides an estimate of the reflection performance, and thus an approximate loss estimate of the surface.This comparison, however, must be done with caution, as a PEC reflector has no beamforming capability.
For the single beam-steering case of Fig. 6(a), the surface bandwidth is defined here as the range where the tilted beam power is ≥ −3 dB from its peak (i.e., overall ≥ −6 dB with respect to the PEC reflector) and power in other beams is ≤ −6 dB, i.e., the power in any other beam must be lower than the power in the main beam across all angles and frequencies.This defined criterion thus leads to a bandwidth of 850 MHz centered at 9.875 GHz (i.e., 8.61%).Fig. 6(b) shows the SLL reduction case bandwidth which is defined as the range where the SLL is ≤ −20 dB, which is 400 MHz centered on 9.95 GHz (i.e., 4%).Fig. 6(c) shows the dual-beam bandwidth case, whose bandwidth is defined as the range where the power in the two beams is ≥ −3 dB from their peaks (≥ −10 dB overall) and power in other beams is ≤ −10 dB, which is 300 MHz centered on 9.85 GHz (i.e., 3.01%).Finally as shown in Fig. 6(d), triple-beam bandwidth is defined as the range where the three beams are ≥ −3 dB from their peaks (≥ −12 dB overall) and power in other beams is ≤ −12 dB, Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.which is 100 MHz centered on 9.85 GHz (i.e., 1.02%).Thus, it is observed that the usable operational bandwidths of these reflectors become narrower as more beams are generated.Finally, it should be noted that there is no universal definition of the operational bandwidth of metasurface reflectors, and the provided figures here are conservative estimates to gauge their practical performance.

C. Incidence Angle Sensitivity
All the beamforming examples shown so far assume normal plane-wave incidence, where the corresponding lookup table was generated.If the incident wave angle is changed (i.e., oblique wave incidence), it will be important to evaluate if the same lookup table can be used to synthesize the beams.To investigate this aspect, the angular sensitivity of the surface will next be considered.In this section, the effect of incidence angle on an already designed unit cell is investigated in the φ = 0 • and φ = 90 • planes.Two cases of beam-steering to θ des.= 30 • and −20 dB SLL are considered as shown in Fig. 7, for sake of illustration.
The effects of changing the angle in the plane of incidence (φ = 0 • ) are shown in Fig. 7(a) and (b), where the effect of the phase gradient resulting from the nonnormal excitation causes the beam to tilt from the desired direction as expected.However, the gain and SLLs are well-maintained.The effects of changing the angle in the φ = 90 • plane are shown in Fig. 7(c) and (d), where the performance is still maintained, except with a slight increase in the sidelobe level of the beamsteering case.In summary, the unit cell can be considered relatively insensitive to variations in incidence angle in both planes, at least up to 60 • .This insensitivity can be attributed to the sub-wavelength dimensions of the unit cell.

IV. EXPERIMENTAL DEMONSTRATION OF BEAMFORMING
Next, we will demonstrate beamforming capabilities of these metasurface reflectors based on the proposed coupled resonator unit cell concept.We chose to focus on the metasurface designs using static lumped circuit elements (as opposed to dynamic elements) to avoid implementation complexities related to biasing and multilayer fabrication, while still maintaining the ability to engineer the spatial complex reflectance of various surfaces.

A. EM-Circuit Co-Simulation and Modeling Considerations
An important design step of the unit cell is to incorporate accurate electrical models of lumped circuit elements inside commercial full-wave simulators such as Ansys FEM-HFSS.While approximate equivalent circuit models of off-the-shelf components are typically used [32], [33], these are not provided at radio frequencies (RF) by the manufacturers, and thus are not reliable for high-frequency designs.Consequently, we elected to use the high-frequency S-parameters in the form of touchstone S2P files from the manufacturers directly inside the full-wave solver to remain as accurate as possible in accounting for their frequency-dependent responses (both resistive and reactive, as well as any parasitic effects).
In our experimental reflectors designs, we use passive "0402" capacitors and resistors (size 1 × 0.5 × 0.35 mm) due to their convenient handling during the component soldering stage.As mentioned above, to account for losses and parasitics of these practical components, it is important to simulate the unit cells with the measured two-port S-parameter files (.S2P) instead of ideal R and C boundaries.Ansys FEM-HFSS allows a convenient way to perform this co-simulation, where the touchstone S2P files can be defined between two Circuit ports placed at the edges where the component will be placed.Each port is created from transmission line edge to ground (i.e., conductor back of the substrate).The widths of the ports are chosen to be the same width of the component (i.e., 0.5 mm) Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.to account for capacitive coupling between the port edges.Additionally, the length of the port (corresponding to the substrate thickness) is de-embedded to ensure any numerical inductance to ground is removed in post-processing.
The unit cell requires lumped capacitors and resistors.Discrete capacitors from Murata [34] were used in full-wave simulations as their S2P files were readily available directly from the manufacturer.However, high-frequency RF resistors are not common, and are only available in limited values.High-precision thin film resistors can be found from several manufacturers [35], [36], [37], [38], [39], however, their S2P files were not available at the time of this investigation, and thus ideal resistance values were used in full-wave simulations.Therefore, a new lookup table of the unit cell is generated taking into account the capacitors' S2P files and ideal lumped resistance boundary for the resistors.This lookup table is now used to determine the C 0 , R, and C 1 values needed for each unit cell in the experimental demonstration of beamforming.

B. Fabricated Prototype and Measurement Setup
A 20×10-unit cell metasurface reflector was next fabricated as shown in Fig. 8(a) on Rogers RO4003C with a copper ground plane and passive capacitors and resistors, chosen to achieve specific beamforming requirements.To minimize design and measurement complexity, the goal is kept to achieving beamforming along the 20 unit cells (i.e., x zplane), hence identical values are used along the 10 unit cells (i.e., uniform complex reflectance along the yz-plane).The capacitors (referenced by S2P indices) and resistors were obtained from the lookup table as required by each case being demonstrated.In some cases, the exact resistor value was not found, and so a resistor with the closest available value was used in the design.
All the reflector prototypes were measured in an in-house bi-static measurement system as shown in Fig. 8(b).It consists of a vector network analyzer (VNA), the reflector under test, a parabolic dish, and a horn antenna forming the transmitterreceiver configuration.The parabolic dish is fixed, connected to Port 1 of the VNA, and pointed at the reflector.The horn antenna is connected to Port 2 of the VNA and can be programmed to move on a circular path centered at the position of the reflector.The magnitude of the transmission coefficient, |S 21 |, is measured as a function of the angle of the horn with respect to the reflector, and at various frequencies along the scanning plane (i.e., x z-plane).Finally, to estimate an approximate loss performance of the reflectors, a copper sheet of the same size and orientation is also measured and used as a reference.More specifically, the proposed reflector measurements at any particular frequency are normalized with respect to the peak transmission coefficient measured with the copper sheet at θ = 0 • .

C. Measurement Results
To demonstrate a variety of beamforming examples using the proposed metasurface reflectors, four reflector prototypes were fabricated for experimental demonstration: 1) beamsteering; 2) absorption; 3) dual-beam with the same peak amplitudes; and 4) dual-beam with different amplitudes, both with arbitrary beam placements forming an asymmetric beam pattern.The full-wave and measured radiation patterns and frequency response of each of the cases are shown in Fig. 9.The corresponding capacitor and resistor values used for each demonstration are shown in Table II.
In all four cases, desired beam-forming characteristics are successfully observed.A beam is steered to about 30 • in reflector #1 [Fig.9(a)], reflection is suppressed in #2 [Fig.9(b)] and dual-beams are generated in #3 [Fig.9(c)] and #4 [Fig.9(d)] at prescribed beam locations.However, in all cases, a significant frequency shift is observed compared to simulations, in addition to increased sidelobes in the reflection patterns.The reasons for these discrepancies will be identified in Section IV-D in detail.
Continuing to characterize the reflectors, the operational bandwidth is highlighted in the frequency response of each beamforming demonstration, as compared to the simulated designs.Similar to the approach followed in Section III-B, beam-steering bandwidth is defined as ≥ −3 dB from the peak power (≥ −6 dB overall) and power in other beams is ≤ −6 dB.Absorption is defined as ≤ −7 dB from the peak power.For dual-beam with the same magnitude, the bandwidth  II.
is defined where the two beams are ≥ −3 dB from their peaks (≥ −9 dB overall) and the power in other beams is ≤ −9 dB.For dual-beam with different magnitudes, bandwidth is defined where the two beams are ≥ −3 dB from their respective peaks (overall ≤ −8 dB for the first beam and ≤ −10 dB for the second beam).The measured fractional bandwidths are found to be between about 1.77% and 5.41% depending on the beamforming case.In all cases, significant discrepancies between full-wave and measured results include a consistent upward frequency shift, beam angle shifts, and higher sidelobe levels.This will be discussed next.

D. Discussion
As evident from Fig. 9, there are large discrepancies between the full-wave and measured results.These discrepancies were traced to three main reasons: capacitor tolerance, resistor parasitics, and the nonfar-field nature of the experimental setup.The effects of each of these issues are now discussed in detail.
The beam-steering case of Fig. 9(a) will be used to investigate the effect of capacitor tolerance and resistor parasitics.To understand the effect of capacitor tolerances on the reflected beam, a series 0.5 pF capacitance, obtained by trial and error, was added to all capacitors' S2P files in full-wave cosimulations.This caused the frequency at which the beam is steered to the desired angle to shift up and the angle to shift down for the original desired frequency, both approaching measurements as shown in Fig. 10(a) and (b).This capacitance tolerance is thus found to be the main reason for the upward frequency shift in all the prototype cases.
Next, all the prototypes exhibited consistently higher than designed sidelobe levels.To investigate the cause for this observation, a series 0.25 nH inductance, again obtained through trial and error, was added to all resistors' S2P files in full-wave simulations, while using original capacitor S2P files with no tolerance correction to isolate the two issues.This correction caused the sidelobe levels to increase and approach measurements as shown in Fig. 10(c).[34] AND RESISTOR [35], [36], [37], [38], [39]  Finally, it is observed that the measured radiation patterns do not exhibit sharp nulls.This aspect is attributed to the nonidealities in the bi-static measurement system setup.The far-field distance based on the reflector size of 180 mm is ≥ 2.2 m at 10 GHz.However, the separation between the horn and the reflector is ≈ 1.1 m, while the separation between the dish and the reflector is ≈ 1.2 m in our bi-static measurement system.Hence, both the horn and the dish are in the near-field of the reflector.To demonstrate the effect of this non-ideal near-field distance separation, a full-wave simulation was conducted using the parabolic dish, horn antenna, and a flat copper sheet reflector in Altair FEKO, which is based on Method of Moments, with as close a configuration as possible compared to the actual measurement setup.The results are shown in Fig. 10(d), compared with ideal FEM-HFSS simulation with plane-wave excitation and measurements.An excellent match between the FEKO near-field simulation and measurements is obtained showing incomplete formation of nulls, as opposed to those in FEM-HFSS.This clearly demonstrates the effect of the near-field on the pattern shape.Furthermore, asymmetrical reflections from environment are also evident by the asymmetry in the measured copper sheet results.
Therefore, this numerical investigation strongly indicates that the discrepancies related to frequency shift, beam-tilt shift, and high sidelobe levels can be explained by considering a complex combination of capacitor tolerances, resistance parasitic inductance, and the physical near-field effects.Based on these observations, and the measurement results of all these prototypes, we remark here that the design of high-frequency reflectors with lumped circuit elements relies on accurate co-simulation of subwavelength RF structures with complex circuit elements whose exact characteristics are quite often unknown.A variety of errors ranging from fabrication tolerances in PCB designs, imperfect soldering, solder pads and traces, circuit element tolerances, numerical inaccuracies in full-wave co-simulations, EM edge effects, and measurement inaccuracies can lead to significant deviations between simulations and experimental characterization.However, in light of all these imperfections, all our experimental prototypes featured complex beamforming as intended utilizing the enhanced complex reflectance coverage offered by the proposed coupled resonator configuration.

E. Literature Comparison
A comparison between the proposed unit cell and typical dynamic and static implementations of state-of-the-art metasurface reflectors from the literature is shown in Table III.The focus was on works that can achieve continuous magnitude and phase control, as opposed to discretized magnitudes and phases typical of bit-coding metasurfaces.The proposed unit cell is based on a simple single-layer implementation in the static configuration that maximizes complex reflectance coverage and can be readily extended to a dynamic implementation with an extra substrate for biasing for a cell-by-cell control.Typical dynamic implementations of metasurface reflectors have some drawbacks.The electro-mechanical design proposed in [18], while based on a single-layer substrate, suffers from low-reconfiguration speeds and the weight and bulkiness of the motors.The dynamic implementation in [16] features a complex and bulky unit cell design to achieve both magnitude and phase control.The single-layer dynamic implementation proposed in [17] is not immediately extendable to cell-by-cell control due to the shared dc bias lines between adjacent cells along one column.In addition, the bias lines are exposed to the incoming radiation, which further forces the polarization to be linear only.Typical static implementations of metasurface reflectors, such as [11], [12], and [40] are based on changing dimensions of resonators and hence cannot be readily extended to dynamic beamforming.The proposed unit cell therefore has the key advantages of low complexity while being suitable for both static and dynamic implementations.Finally, having three controls, the proposed concept relaxes the requirements on the component values required to achieve full magnitude and phase control and proposes a solution that maximizes the complex reflectance coverage.

V. CONCLUSION AND FUTURE WORK
A novel metasurface reflector unit cell based on coplanar coupled resonators on a single-layer dielectric has been proposed featuring enhanced range of complex reflectance.A variety of beamforming capabilities were demonstrated in full-wave simulations, including beam-steering, SLL control, gain control, and multibeam generation, without generating spurious cross-polarization reflection, which are otherwise not possible with conventional metasurface designs.Beamforming was also experimentally demonstrated using passive capacitors and resistors, for beam-steering, absorption, and dual-beam generation cases.A systematic design procedure has been followed in all cases to design these reflectors, and strict performance criteria have been applied to estimate their bandwidths and electrical performance.Finally, indepth numerical tests have been performed to successfully explain the discrepancies between simulated and measured reflector performance.Future work will involve implementation of a real-time reconfigurable prototype using varactor diodes (instead of static lumped capacitors) for capacitance control and PIN diodes (instead of static lumped resistors) for resistance control, however, this requires an additional substrate layer for biasing and RF/dc isolation at each unit cell.The proposed concept paves the way for designing optimum beamforming reconfigurable metasurface reflectors with near-complete tunable reflectance profile for diverse applications ranging from satellite communications and CubeSat missions to smart engineering of RF environments.

Fig. 1 .
Fig. 1.Proposed coupled resonator metasurface unit cell.(a) Unit cell configuration consisting of a SRR with capacitance, C 0 , and resistance, R, and a DRR with capacitance, C 1 .The unit cell size is = 9 mm = 0.3λ 0 at 10 GHz.(b) Demonstration of the proposed unit cell in a 20 × 20-unit cell metasurface reflector to generate three x-polarized reflected beams from an incident x-polarized plane-wave.The unit cell is implemented in this work on a copper-backed Rogers RO4003C substrate (ϵ r = 3.55, tan δ = 0.0027, and height, h = 32 mil).
Fig.2.Full-wave analysis of the isolated and coupled resonator unit cells using Ansys FEM-HFSS.(a) Floquet unit cell setup of the isolated and coupled resonator unit cells.The dimensions of the isolated resonator are (in mm): w 1 = 1, s 1 = 0.4572, and l 1 = 6.9.The dimensions of the coupled resonator are (in mm):w 1 = 1, w 2 = w 3 = 0.5, s 1 = 0.4572, s 2 = 1, l 1 = 6.9, l 2 = 4.45, and l 3 = 4.6.Isolated resonator S 11 magnitude and phase results are shown for: (b) three values of C 0 , (c) three values of R, and (d) Smith chart showing complex reflectance at f = 8.4 GHz for C 0 = 0.1-0.8pF in steps of 0.1 pF and R = 0-50 in steps of 2 .Coupled resonator S 11 magnitude and phase results are shown for: (e) three values of C 0 , (f) three values of R, (g) three values of C 1 , and (h) Smith chart showing complex reflectance at f = 9.8 GHz for C 0 = 0.1-0.8pF and C 1 = 0.1-0.8pF both in steps of 0.1 pF, and R = 0-50 in steps of 2 .All S-parameter results are de-embedded from the Floquet port to the top of the unit cell.

Fig. 4 .
Fig. 4. Full-wave simulation setup of a 20 × 1-unit cell array on Ansys FEM-HFSS, with a normal x-polarized plane-wave incidence, with beamforming in the x z-plane.

Fig. 8 .
Fig. 8. (a) Photograph of the 20 × 10-unit cell prototype of metasurface reflector, fabricated on Rogers RO4003C, with passive "0402" capacitors and resistors.The unit cell dimensions are the same as those provided in Fig. 2. (b) Reflector bi-static measurement setup consisting of a fixed parabolic dish and a horn antenna rotating on a circular track centered at the position of the reflector.

Fig. 9 .
Fig. 9. Radiation pattern and frequency response measurement results of four metasurface reflector prototypes for (a) beam-steering, (b) absorption, (c) dual-beam with the same magnitude, and (d) dual beam with different magnitudes.The values of capacitors and resistors used for each case are shown in TableII.

Fig. 10 .
Fig. 10.Full-wave investigation of the effect of capacitor tolerance, resistor parasitic inductance, and near-field setup on reflector performance.Effect of capacitance tolerance on (a) frequency response and (b) radiation pattern.(c) Effect of resistor parasitic inductance on the radiation pattern.(d) Effect of the near-field setup on the radiation pattern at 9 GHz.

TABLE I MINIMIZATION
WEIGHTS USED IN

TABLE III COMPARISON
BETWEEN THE PROPOSED METASURFACE REFLECTOR AND OTHER WORKS FROM THE LITERATURE