Bandwidth Enhancement of Low-Profile Metasurface Antenna Using Nonuniform Geometries

Artificial magnetic conductor metasurface antennas are investigated using a robust, surrogate-assisted, differential evolution optimization technique. Using a uniform metasurface array configuration as a starting point, multiple array configurations are parameterized and the differential evolution optimizer yields nonuniform array geometries exhibiting wideband performance. The bandwidth improvement is attributed to the structure’s ability to support additional higher-order modes with good impedance matching. A comparison between the uniform metasurface antenna cases and their ‘evolved’ nonuniform counterparts is presented to demonstrate the advantages of the proposed technique. Two prototypes are fabricated and characterized to experimentally confirm the advantages of proposed designs. The first prototype, a 3x3 case, measured a fractional bandwidth of 36.8% with peak gain of 8.3 dBi. The second prototype, a 4x4 case, measured a fractional bandwidth of 51.8% with peak gain of 8.8 dBi. When compared to standard uniform cases, the proposed nonuniform geometries exhibit substantial impedance bandwidth enhancement.

Artificial magnetic conductor (AMC) metasurfaces have been demonstrated to enhance the impedance bandwidth of microstrip and slot antennas [8], [9], [10], [11], [12]. One distinct advantage of AMC metasurfaces is they can be compactly integrated with a feed structure or source antenna, resulting in an electrically-thin (< 0.1λ) broadband element. Wideband and low-profile antennas are highly desirable in many modern wireless links. Applications utilizing high data transfer rates or subject to environments with limited available space fundamentally rely on these types of elements. Over the years, many solutions have been proposed to achieve such antennas, including magnetoelectric dipoles [14], [15], stacked-patches [16], L-probe feed structures [17], [18], [19], and U-slot apertures [20], [21], which can achieve upward of 30% impedance bandwidth. AMC metasurface antennas are among the most competitive within this class, often exceeding 30% impedance bandwidth with an electric thickness much less than 0.1λ.
AMC metasurface structures for antenna bandwidth enhancement commonly take the form of a uniform array of identical rectangular patches patterned over a substrate. By nature, these types of AMC surfaces are resonant structures, capable of supporting and radiating excited modes. Most often, AMC surfaces are excited by a source antenna, which supports the characteristic TM 10 mode as well an additional higher order mode. The multiple adjacent radiating modes result in a wide impedance bandwidth. The location of the modes is largely determined by the unit cell width, length, and gap parameters of the AMC structure. However, due to the few degrees of freedom typically involved in uniform AMC structures, there is limited tunable range and individual control of the excited modes [9]. Adopting a nonuniform AMC metasurface with additional degrees of freedom has the potential to improve the tunability of excited modes, as well as support several higher order modes [9], [11]. However, there is limited investigation into the optimal array size, cell shapes, cell patterns and parameter selections of nonuniform AMC metasurfaces to realize wideband antennas.
The use of nonuniform geometries and patterns is common in other metasurface design contexts, such as focusing lenses [1], [2], [3], [4]. The so-called phase-gradient metasurface [22] uses an array of common unit cells with slightly different scaling in order to produce a surface which has a spatially-dependent reflection or refraction response. The phase-gradient metasurface can be used to construct a compact and planar lens for gain-enhancement and beam steering applications for narrowband antenna elements. One challenge associated with nonuniform metasurface structures is design complexity, as the number of parameters involved is substantially larger when compared to uniform cases. The most general nonuniform structure, which has independent consideration for each cell without a rigours pattern, has rapid growth in dimensionality with array size. Traditional parametric studies to design such surfaces are particularly challenging and time-consuming.
Presented here is a novel nonuniform modification of standard uniform AMC metasurfaces antennas which introduces many degrees of freedom in order to extend the impedance bandwidth while maintaining the same low-profile and compact design. The nonuniform structure is formed by multiple unique rectangular cells along with an expanded adjacent element spacing parametrization, vastly increasing the available design parameters for tuning. To address this, a robust optimization technique (surrogate-assisted differential evolution) is applied to systematically manage the large number of design parameters, and ultimately synthesize the nonuniform cases effectively and efficiently. A comparison between uniform and nonuniform metasurfaces cases is made to demonstrate bandwidth enhancement mechanism. Two nonuniform prototypes are selected to be fabricated and characterized to validate the optimization-based design procedure as well as experimentally demonstrate the advantages of nonuniform geometries. When compared to uniform low-profile metasurfaces antennas, the proposed nonuniform prototypes measured a remarkable improvement in fractional bandwidth, while possessing comparable strong broadside radiation characteristics.

II. ANTENNA PARAMETRIZATIONS
The general design used in this work is a two-board structure with three metal layers, although is illustrated as three for clarity in Figure 1. The bottom metal layer contains a microstrip transmission line. A rectangular slot is cut into the ground plane and is used to couple energy from the transmission line into the metasurface array. The bottom substrate can be miniaturized by selecting a small h 1 with little consequence, as the width of the microstrip line can be tuned to provide a good input match. The selection of the upper (middle and top layer combined in Figure 1) substrate thickness is more sensitive, as the metasurface must be positioned above the slot at a distance which has sufficient coupling.
A Uniform metasurface parametrization is fully specified by its unit cell, which contains all the element geometry and spacing information with adjacent cells. The most basic AMC metasurface uses square elements with equal spacing between all adjacent elements within the array, and so only requires two parameters: the square length and cell gap. This simple metasurface structure is shown in Figure 2a. More commonly, uniform AMC metasurfaces are designed using rectangular cells with individual gap parameters for the vertical and horizontal directions, as shown in Figure 2b.
The most general nonuniform metasurface, which is illustrated in Figure 2c, uses a unique cell instance with its own width and length parameter for every cell. Such a structure without a geometric pattern contains vastly more design parameters, as each element must have its respective parameters determined independently. This structure is investigated using the optimization-based design procedure described in the following section. The general objective for all cases is to select numeric values for all the relevant metasurface parameters along with feed dimensions which maximize the impedance bandwidth of the antenna without compromising radiation characteristics. The substrate thickness parameters are considered static for practical considerations, as commercial boards with standardized sizes will be used for prototyping. A systematic test is executed in which array sizes of 3x3, 4x4, 5x5, and 6x6 are optimized for greatest impedance bandwidth. The highest performing candidates from the solution population for each case are saved for further analysis to empirically determine any important symmetries and key parameters. Generally speaking, the larger array sizes (5x5 and 6x6) were inferior to smaller array sizes (3x3 and 4x4) in terms of impedance bandwidth. Additionally, all arrangements contained comparable realized gain. For these reasons, array sizes beyond 6x6 were not considered, as there was no indication that increasing array size further may be advantageous. One key symmetry that was discovered is solutions which shared similar-shaped cells in individual rows were high-performing with respect to impedance bandwidth. Enforcing this symmetry can considerably reduce dimensionality, as each cell in a particular row will share the same width and length parameter, as opposed to each being individually specified.
This work proposes a restricted case of the general nonuniform metasurface using information obtains from the general case study. The proposed nonuniform parametrization is shown in Figure 2d, where unique cell instances with their own width and length parameter are distinguished with different color shading. The proposed nonuniform structure is symmetric with respect to both vertical and horizontal axis, which is required to prevent distortion or tilting of the main radiated beam. The use of multiple cells along with additional spacing parameters provides the ability to create subsections of the array with increased cell density while still maintaining comparable aperture area when compared to a uniform case of the same array size. Consequently, such a structure can be used to support additional higher-order modes and sufficiently impedance match them.

III. OPTIMIZATION PROCEDURE
A robust optimization solution is developed and applied to the nonuniform metasurface antenna design problem to effectively address the complexity and large number of parameters involved. EM optimization problems typically require a global search in non-convex spaces with very little prior information available. Evolutionary algorithm (EA) optimization techniques are well-suited for these types of problems [23], [24], [25], although are bottlenecked by the high computational cost to obtain new information through EM simulation (objective function evaluations). Various techniques have been proposed to accelerate EA optimizers, although the most popular and widely used is the generation of surrogates which predicts the objective function using a learning technique [26], [27], [28], [29]. The surrogate model is then used in place of true objective function evaluations (EM simulation) within the EA, providing significant computational relief. This work employs a surrogate-assisted differential evolution optimizer and is inspired by the framework in [26], which is considered best-in-class for EM optimization. The EM simulator used in this work is a commercial finite-element solver (Ansys HFSS), which is accessed by the optimization software using a wrapper library. The optimization steps are summarized as follows:

1) Form a Solution Database
I Generate a set of initial samples (candidate solutions) using Latin hypercube sampling (LHS) that is representative of the design space. II Use EM simulation (Ansys HFSS) to analyze all candidate solutions, collect frequency response and radiation characteristics for each. III Apply simulation post-processing to evaluate EM simulation results to determine antenna performance metrics (bandwidth, peak gain, etc.) for each candidate. IV Test the objective function for each candidate to see how well it performs with respect to the optimization goals. V Format a database (training data) consisting of candidate solutions (inputs) and corresponding objective function evaluations (outputs).

2) Train Surrogates (Regression)
VI Apply Gaussian process (GP) regression to train a surrogate model over the design space. The surrogate will interpolate objective function at known data points, and predict over unknown regimes.

4) Checking for Convergence VII Check the best DE solution's objective function via true EM simulation (steps II-IV).
If it is satisfactory, optimization is complete. Otherwise, add the new solution to the database and return to step VI. The objective function in this work translates EM simulation results into an algorithm-tangible value which is representative of how well a given antenna is performing with respect to a set of goals. For every candidate solution submitted to the EM simulator, the frequency response and radiation pattern are solved and saved. Simulation postprocessing routines extract quantities of interest from the simulation results. These results are then processed on a case-by-case basis through goal functions, which measure how well a particular goal is satisfied.
Tuning of the algorithm is conducted empirically, that is the algorithm parameters are varied, and then the average results produced (in terms of fitness) are observed. This process is functional in that in maps initial parameters to the average result at convergence, which implicitly addresses internal issues such as overfitting of the GP regressor.

IV. NONUNIFORM VS UNIFORM METASURFACE COMPARISON
To demonstrate and further explain the impedance bandwidth enhancing mechanism of the proposed nonuniform metasurface structure, a comparison study is provided in simulation between two 4x4 metasurface antennas. The first antenna is a standard uniform metasurface antenna, and the second uses the proposed nonuniform metasurface array geometry. The two antennas have identical substrate (Rogers 4003C, r = 3.55, tanδ = 0.0027) and feed structures, and only differ by the metasurface geometry used on the top metal layer. By doing so, the comparison study of the two antennas will be focused on performance gained which are attributed to alterations to the standard metasurface structure.
Identical optimization configurations are applied to each antenna design. The optimization goal is to maximize percent bandwidth while achieving realized gain above 7 dBi at the centre frequency. Both cases are allowed to form an initial solution database using 200 EM simulations. The optimization terminates after an additional 200 EM simulations, or if the best solution within the database fails to improve by a relative 1% over 5 consecutive generations. Arguably, the standard metasurface case has an advantage with respect to optimization as it contains fewer dimensions and so the initial database generated is more representative of the design space.
The input-match for both optimized designs is shown in Figure 3. The standard uniform cases is well-matched from 5.22-7.14 GHz, which is comparable to other similar solution found in the literature. The proposed nonuniform case is well-matched from 5.03-7.88 GHz, representing a significant improvement in matched impedance bandwidth, which was achieved only by altering the metasurface structure geometry. It is notable that the non-uniform case has ripples which briefly exceed the standard -10 dB match criteria at 6.5 GHz and 7.5 GHz, however considering these cases the total the matched impedance still represents a substantial improvement. The impedance bandwidth enhancing mechanism is highlighted in Figure 3, where an additional higher-order mode is tuned closer towards the standard-case modes, as well as sufficiently matched itself.

V. EXPERIMENTAL RESULTS
Two nonuniform antenna designs are presented here for further analysis, discussion, and experimental verification of the proposed nonuniform metasurface arrangements. One 3x3 case and one 4x4 case are selected using the proposed nonuniform metasurface geometry to demonstrate the wide impedance bandwidth potential of antennas designed with such structures. Rogers 4003C ( r = 3.55, tanδ = 0.0027) is selected as the design substrate for both cases. The bottom and top substrates uses 0.78 mm and 3.00 mm board thicknesses, respectively. Both designs are synthesized using the presented optimization technique, with the primary objective to achieve 40% impedance bandwidth around a center frequency of 6 GHz while also having comparable peak realized gain to other low-profile solutions. The center frequency target selection was made such that prototypes will have features which are several millimeters in size, and therefor could be fabricated with ease. With respect to radiation characteristics, a peak gain of 7 dBi is targeted without any main beam tilt. The final design dimensions of both prototypes are tabulated in Table 1.
Both designs are fabricated in-house using a CNC circuit milling machine to pattern the metal layers into the substrate layers. For both designs, the top substrate is constructed using two sections of 1.5 mm board which are stacked to form the design 3.00 mm height. An image of the fabricated layers of both prototypes is shown in Figure 4a. The boards are fastened together using screws which help to align the metasurface above the slot aperture correctly, as well as reduce air-gaps which may be present between the boards. Plastic insulating screws (nylon) are used as opposed to metal to not disturb the currents present on the ground plane or metasurface array. Nylon is specifically selected as its dielectric constant is comparable to that of the design substrate and has very few losses involved [30]. In simulation, the introduction of nylon screws had negligible impact on performance. The top and bottom sides of fully assembled prototypes are shown in Figure 4b. Different packaging considerations were made with respect to connection of a launcher for each prototype. The 3x3 prototype extends the bottom feed layer a short distance so that the ground plane is exposed a short distance on one side. By doing so, a launcher is easily connected as both signal and ground connections are available at the board edge. The 4x4 prototype instead cuts a notch into the upper substrate to expose a small section of the ground plane. The launcher is connected in the same way as the 3x3 case, but is more compactly integrated into the antenna. Both modifications to connect a launcher connection had negligible impact in simulation, which is expected as they are far from the radiating metasurface structure.
The frequency responses were measured using a vector network analyzer (Anritsu MS4644B). The measured results are shown with the simulated responses for reference in Figure 5. In general, good agreement between simulation and measurement is observed for both prototypes. The 3x3 prototype is able to provide sufficient separation between the excited modes while still maintaining an input match below -10 dB. This prototype is well-matched from 4.43 GHz to 6.43 GHz, for a total of 2.00 GHz (36.8%) of impedance bandwidth. The 4x4 prototype has a larger impedance bandwidth, which is primarily attributed to the excitation of additional higher-order modes. The 4x4 prototype is well-matched from 4.87 GHz to 8.27 GHz, for a total of 3.40 GHz (51.8%) impedance bandwidth.
Realized gain measurements were carried out within an anechoic chamber at Queen's University. The radiation patterns are shown at their respective center frequencies in Figure 6. These patterns show the typical broadside radiation which both prototypes exhibit within their impedancematched regimes. The measured peak gain at broadside (θ = 0) over frequency for both prototypes is shown in Figure 5. Peak realized gains of 8.3 dBi and 8.7 dBi are observed for prototype 1 and 2, respectively. Throughout the impedance-matched regime, high realized gain is generally achieved for both prototypes. Some variation in gain at broadside is observed, which is attributed to the multiple radiating modes contained in each prototype's respective bandwidth.
The respective center frequencies of each are 5.43 GHz and 6.57 GHz. Therefor, prototype 1 has a total electrical thickness of 0.07λ, while prototype 2 is slightly thicker at VOLUME 4, 2023 585 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. 0.08λ. Of course, the proposed design can be scaled to realize low-profile (< 0.1λ) and extremely wideband solutions at other design center frequencies. Both prototypes successfully demonstrate the bandwidth-enhancing mechanisms of the nonuniform metasurface. The additional degrees of freedom associated with the proposed nonuniform framework allow the excited modes to be tuned and sufficiently matched into wider bandwidths than have been previously reported in uniform metasurface cases. Additionally, the 4x4 case was able to sufficiently match additional higher-order modes, resulting in substantial impedance bandwidth improvements. A key result is that neither prototype has a significant compromise in terms of radiation characteristics, as strong broadside patterns with high realized gain are measured over the matched impedance bandwidth. These results are quite remarkable, in that the low-profile two-board designs used in many uniform metasurface antennas can be enhanced by only modifying the arrangement of the metasurface cells. The aperture-coupled feed structure was selected to be used in this work as it is due to its simplicity and straightforward integration. Since the aperture-coupled feed structure is familiar, it focuses the bandwidth-enhancement mechanism to the design of the nonuniform metasurface.

VI. CONCLUSION
The class of broadband low-profile antennas featuring metasurface arrays with nonuniform geometries in multiple spatial variables is mostly unexplored. In his work, a surrogateassisted differential evolution optimizer has been developed to robustly and systematically study many of these nonuniform metasurface cases. From this process, a promising nonuniform parametrization for the purpose of improving the bandwidth of AMC metasurface antennas is proposed. Two prototypes were fabricated and characterized to demonstrate the potential performance of such nonuniform metasurfaces antennas. Compared to existing low-profile uniform metasurface antennas, the proposed work offers greater than 10% improvement in terms of fractional bandwidth. Alternative feed structures could be used instead to improve the design. Feed structures that have a full ground plane, such as the L-probe, are advantageous in terms of reducing back radiation. Additionally, alternative feed structures with their own bandwidth-enhancement mechanism may be able to be used in conjunction with the nonuniform metasurface for further bandwidth improvements.