Broadband high-efficiency 3-bit coding metasurface in transmission mode based on the polarization conversion technique

The main drawback of the transmissive focusing metasurface (TFM) is its low operational bandwidth and aperture efficiency. Increasing both of these radiation characteristics simultaneously is a major challenge for these structures. This paper introduces a novel multi-state coding metasurface that utilizes system-level and element-level synthesis approaches to enhance frequency bandwidth and aperture efficiency. Unlike most of the TFMs proposed in this field, the proposed novel element consists of only two dielectric layers. The multi-frequency phase synthesis (MFPS) approach, a well-established broadband technique, is utilized for the system-level synthesis approach. An optimization algorithm is utilized to balance the phase error in the whole band in terms of gain variations and aperture efficiency. At the element design level, a PCT-based wideband technology is utilized and implemented by a subwavelength non-resonant element. The element is composed of three C-shaped metallic patterns, and the metal layers are printed on both sides of two identical dielectric layers without using any metalized via in the configuration. By simply changing the angle of arc curves in all layers, eight states of phase quantization are achieved. The amplitude of the transmitted wave with rotated polarization is larger than 0.9 from 12.3 to 16.5 GHz, except for state 4, which has an amplitude greater than 0.5 at the beginning of the band. A 25 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times $$\end{document}× 25-element TFM was designed, fabricated, and tested using the aforementioned broadband technique (MFPS along with PCT-based wideband technology). The measurement results show that the 1-dB gain bandwidth of the antenna is 12.3–16.5 GHz, which is equivalent to 29%. The maximum measured aperture efficiency is 53.6%, occurring at 12.8 GHz. The proposed metasurface is classified in the group of broadband high-efficiency TFMs.

www.nature.com/scientificreports/ supporting two orthogonally polarized waves, such as V-or Y-shaped elements, exhibit broader resonances compared to classical phasing elements, offering potential improvements in bandwidth 9 . While previous studies have focused on enhancing either the TFM bandwidth or aperture efficiency, achieving both simultaneously has received less attention. For instance, a study 9 combined multiple broadband techniques to design an ultra-wideband configuration, but the peak aperture efficiency remained below 50% due to element loss. Similarly, another study 10 introduced a linearly polarized TFM with a three-metallic phasing element, achieving a peak aperture efficiency of 55% but limiting the 1-dB gain bandwidth to 15.5%. Additionally, a highefficiency TFM based on the Huygens metasurface concept was proposed 17 , attaining 64% aperture efficiency, albeit with a challenging fabrication process, and a 1-dB gain bandwidth of only 14% 17 . Similar limitations were observed in 18 . Recently, a high-gain dual-polarized bulky 3D full metal TFM was introduced using a quadrupleridged waveguide as the unit cell 19 . This design achieved a measured peak aperture efficiency of 41.9% and a 1-dB gain bandwidth of 27.3%, representing a relatively good performance in these aspects. In reflection and transmission modes, the phase quantization scheme has been recognized as a favorable solution for metasurface design due to its simplicity and reconfigurability [20][21][22] . We have discovered that utilizing coding structures with the phase quantization scheme provides the best solution for achieving a high-efficiency broadband TFM. By using a set of multi-degree-of-freedom elements, we can individually adjust the dimensions of the elements to achieve the desired geometry for each bit response. The selection process considers two crucial factors: low insertion loss and the required phase value. These factors collectively ensure the broadband and high-efficiency behavior of the metasurface.
In this paper, our objective is to simultaneously address the two aforementioned factors and develop a compact broadband high-efficiency TFM using a 3-bit coding metasurface. The main novelty of our proposed work, in comparison to previous coding metasurfaces, lies in the incorporation of both broadband techniques at the element and system design levels. By integrating these techniques with a 3-bit metasurface that exhibits lower phase error than 1-and 2-bit configurations, we enhance the aperture efficiency. Additionally, the absence of metallized vias in the element's geometry allows for its utilization at millimeter wave frequencies and beyond, minimizing errors during the construction and assembly process in multi-layer configurations. This is particularly crucial at higher frequencies, where the use of metallized vias in structures can contribute significantly to manufacturing errors 23 .

Element design
The proposed subwavelength unit cell is demonstrated in Fig. 1, which is properly designed based on multidegree-of freedom technology such that it fulfills the phase and amplitude requirements of all eight states of the 3-bit coding metasurface. Achieving a broadband high-efficiency structure relies on using elements with multi-degree-of-freedom. These elements provide better control over the transmission coefficient of waves in terms of both amplitude and phase. An ordinary anisotropic patch (such as dog-bone unit cell) with limited control over its geometrical parameters cannot meet our expectations. This aspect is particularly important in transmissive metasurfaces compared to reflective ones, as variations in frequency have a more significant impact on the amplitude of transmitted waves in transmission mode. Therefore, it is necessary to employ a phasing element that can effectively control the electromagnetic behavior of transmitted waves across a wide frequency range. Furthermore, it is worth noting that polarization twisted surfaces offer distinct advantages over classical metasurfaces, including enhanced bandwidth and easier realization of phase states in coding metasurfaces. For instance, in a 3-bit metasurface with eight discrete phase levels, only optimizing the dimensions of four unit cells is required, while the remaining four phase states can be easily achieved by rotating the metal patch by 180 • without any additional modifications to the geometrical shape of the patches. The unit cell in our design consists of three metallic layers and is based on the transmit/receive topology, without the use of any metallic vias between the layers. The top and bottom metallic patterns are double C-shaped patches with identical dimensions, connected by a narrow strip at the middle arc positions. The thicknesses of the top and bottom patches are denoted www.nature.com/scientificreports/ as t 1 and t 2 , respectively, while the strip thickness is represented by t 3 . The opening angles of the arc sections in the C-shaped patches are given as α 1 and α 2 . The lower metallic layer of the top element is a C-shaped slot patch with slot widths of t 4 and t 5 . The optimized design parameters for the unit cell can be found in Table 1. The dimensions of the unit cell are set to be 6.5 mm × 6.5 mm, equivalent to 0.3 0 at the center frequency of 14 GHz. The bottom and top dielectric layers are made of 1.57 mm-thick Rogers 5870 material with a relative permittivity ε r = 2.33 and a loss tangent of 0.0012. Fig. 1 illustrates the bonding of the top and bottom elements using a 0.038 mm thick thermoplastic bonding film (Cuclad 6250). By adjusting the opening angles of the patches and slot in all three metallic layers, we are able to manipulate the transmissive phase. Thanks to the use of a sub-wavelength non-resonant structure, our element exhibits desirable behavior across a wide frequency range in terms of magnitude and phase responses. Figure 2 demonstrates the eight states of transmissive phase, covering a full cycle of 360 • . From Fig. 2, it is evident that the desired phases for the first four states (i.e., states of 1, 2, 3, and 4) can be achieved by tuning the parameters α 1 , α 2 , and β . The remaining four states can be obtained by simultaneously rotating the middle and bottom metal patch layers by 90 • and 180 • around the z-axis, thanks to the polarization conversion characteristic of the element in transmission mode. Consequently, in the design of our 3-bit TFM operating in polarization conversion mode, we only need to determine four states of phases for the unit cells.

Theoretical calculation of EM response of the transmitted wave
It was demonstrated that a quad-layer transmissive metasurface with three conductive layers can provide a full range of 360 • with a transmission amplitude better than − 1 dB when identical conducting layers are employed as frequency selective surfaces (FSS) 2 . However, the phase range can be extended by using conducting layers with different metal patches. This extension is applicable within a limited bandwidth, and to achieve optimal phase and amplitude responses across a wide range of frequencies, a unit cell with multi-degree-of-freedom technology is required. The electromagnetic response of the unit cell in an array environment can be described by the scattering matrix, neglecting the higher-order mode coupling effect. As a general rule, the higher-order mode Table 1. Design parameter values of the proposed unit cell. Parameter Value (mm) 6. www.nature.com/scientificreports/ coupling effect decreases as the substrate thickness and permittivity increase. Through a cascading process, the overall scattering matrix of all six layers of the proposed phasing element can be extracted by considering each layer as a two-port system (Fig. 3). If the individual conducting layers are lossless, reciprocal, and symmetrical, the scattering matrix ([S] matrix) can only be described as a function of the transmission phase 2 . The [S] matrix for the conducting layers 1, 3 and 6, along with the [S] matrix associated with dielectric layers 2, 4, and 5, are shown in Eq. (1).
In (1), ε k r , and k = 2, 4, 5 is the layer number. By cascading the [S] matrices of conducting and dielectric layers presented in (1), the overall [S] matrix will be obtained. In general, the formulation for cascading two individual layers are as follows 2 : In (2), the parameter S c 21 represents the transmission coefficient of the cascaded layers with numbers of i and i + 1 . By repeating the cascading process for all pairs consecutive layers and replacing them with the cascaded layer, the final one two-port system will be obtained which could be described in the form of A overall · e jP overall = f ∡S 1 21 , ∡S 3 21 , ∡S 6 21 assuming the electrical thickness of the dielectric layers remains fixed.

Unit cell simulation results
The It is evident that the x-polarized transmission coefficient is larger than 0.9 for states of 1,2,3, and larger than 0.56 for state of 4 within the working frequency band. It is worth nothing that the [S] matrix method is a semi-analytical approach since the quantity ∡S21 in matrix of Eq. (1) is calculated individually for each conducting layer using CST software, and then they are cascaded using the formulation provided in Eq. (1). Similar results are obtained for states of 5 to 8 although they are not shown here. To elucidate the phase behavior of the element when the middle and bottom layers are rotated to achieve states 5 to 8, a full-wave simulation is performed, and the electric field distribution over these surfaces is investigated. Figure 6 depicts the electric field distribution on the middle and bottom layers for states 1 and 5 at 14 GHz. A clear 180 • phase difference between states 1 and 5 is observed from the direction of the electric fields on the bottom layers, which are opposite to  www.nature.com/scientificreports/ each other. In summary, the amplitude and phase of the transmission wave for all 8 states are shown in Fig. 7 at the center and extreme frequencies of the band.

MFPS approach for 3-bit TFM
The present paper employs the MFPS approach (as introduced by 24 along with subsequent studies that aimed to design broadband RFM 3,22 ) at the system design level to achieve the maximum 1-dB gain bandwidth and aperture efficiency as much as possible. The objective is to optimize the phase distribution on the aperture using this approach to balance the overall phase error caused by 3-bit phase quantization. Initially, the frequency band is set from 12.3 to 16.5 GHz, based on the amplitude and phase behavior of all bits. To achieve this, a global search algorithm known as particle swarm optimization (PSO) is utilized to balance the phase error within the frequency band and obtain an optimal phase distribution for the TFM. In the PSO algorithm, the cost function considers the sum of phase error of all elements on the aperture, along with the gain variance, to guide the optimization process.  www.nature.com/scientificreports/ It is important to note that the objective of using the PSO in this work is not solely to obtain the best phase distribution at a specific frequency sample in order to achieve the highest gain for that sample. Pursuing such an approach would result in maximum gain and aperture efficiency at only one frequency, leading to a reduced bandwidth. This approach is commonly referred to as the "Single frequency phase synthesis approach." It is evident that achieving zero phase error across the entire frequency band is impossible. Instead, we propose considering the total phase error of all elements on the aperture, along with the gain variance, as the cost function in the PSO. This ensures that the gain variation is minimized across the entire band. Additionally, by designing the unit cell to minimize loss during the transmission of the wave, we can maximize the aperture efficiency. Also, several strategies have been implemented at the system design level during the implementation of MFPS to achieve optimal performance in terms of bandwidth and efficiency. These strategies are discussed below: • Utilizing full-wave simulation results of the amplitude and phase of the horn field across the aperture.
• Incorporating full-wave simulation results for the amplitude of the transmission coefficient from the unit cell across all frequencies involved in the optimization process. This is achieved by considering the necessary phase and the corresponding state number based on Fig. 5. • Employing a horn with a relatively stable phase center and a symmetric radiation pattern. The average of the simulated phase centers across the entire frequency band is used to determine the optimal position for the horn. • Selecting the frequency at the beginning of the band (12.3 GHz) as the reference point in the optimization routine. This frequency is given the highest weighting factor to minimize phase errors.  www.nature.com/scientificreports/ In an ideal single-frequency phase synthesis approach, the gain versus frequency curve exhibits an ascending behavior. Thus, by introducing more phase errors towards the end of the band compared to the frequencies at the beginning, a flat gain response can be achieved. The required phase to transform a spherical incident wave to a planar wave focusing on (θ b , φ b ) , is determined as follows: In (3), ϕ feed (f ) represents the phase of the electric field of the horn on the aperture which is extracted from CST software at the frequency f, ϕ 0 (f ) denotes the constant reference phase at f. The parameters x mn , and y mn indicate the position of the unit cells on the aperture plane. As stated, the cost function in MFPS approach takes into account the sum of phase errors for all unit cells, as well as the variance of the gain across all frequencies considered for optimization. The cost function is defined as follows: In (4) In (6), ϕ bit represents one of 8 states defined in Fig. 2 and ϕ o.w bit refers the phases other than ϕ bit according to Fig. 2. To demonstrate the feasibility of the proposed combined broadband technique, a proof-of-concept 25 × 25-element TFM is designed in Ku-band. A Ku-band tangential profiled smooth-wall horn with q = 6.5 , which was employed in our previous work 3

Results and discussion
Based on the criteria outlined in the previous section, the optimal phase distribution of the TFM is obtained and illustrated in Fig. 8a. The main beam direction is considered as (θ b , ϕ b ) = (0 • , 0 • ) . By mapping the 8 phase states of the element represented in Fig. 2 to the phase distribution of Fig. 8a, the final arrangement of the elements in array environment is obtained for all three layers. Subsequently, the designed TFM and the previously described feeding source (a smooth-wall conical horn antenna) are simulated using the time domain solver of the CST software. The simulations are performed on a computer system with 64 GB of RAM. The feeding source is positioned in front of the TFM, taking into account the average phase center value relative to the frequency range of operation. The simulation of the designed TFM, with dimensions of 16.5 mm × 165.5 mm, takes approximately 8 h to complete. The simulation results, including the S11 parameter and the 3D radiation pattern of the TFM at 14 GHz, are presented in Fig. 8b,c, respectively. The simulated 3D pattern demonstrates the satisfactory performance of the designed TFM in focusing the emitted waves from the horn. The peak gain achieved at 14 GHz is 25.8 dBi, corresponding to an aperture efficiency of 52.6%. Moreover, the S11 of the structure defined from the input port of the horn as the feeding source remains below − 20 dB which is considered acceptable. This indicates that the majority of the wave energy passes through the TFM, aligning with the predictions derived from the simulation results presented in Fig. 4.
To experimentally validate the designed broadband high-efficiency TFM, a prototype was fabricated using printed circuit board (PCB) technology. The fabricated metasurface and measurement setup are illustrated in Figs. 9 and 10. In order to fix the position of the feed relative to the TFM, a setup made of plexiglass with a flexible focal length was utilized with. The TFM was enclosed by a sturdy frame and secured with plastic screws. The farfield radiation patterns are measured at the center and extreme frequencies of the band in an anechoic chamber. Figure 11 compares the simulated and measured far-field patterns in the E-and H-planes, demonstrating good  www.nature.com/scientificreports/ consistency between them. The measurement results indicate that the side lobe levels remain below − 20 dB for all three frequency points in both planes and the cross-polarization component of the pattern remain below − 28 dB at all angles. It is worth mentioning that the designed unit cell element has a similar electromagnetic behavior when the wave is illuminated to the aperture in the opposite direction (-z-direction) with orthogonal polarization. Therefore, if the horn is positioned on another side of the TA with the same f/D, and rotated by 90 • around its longitudinal axis, it is expected that the transmitted wave would exhibit similar characteristics as the results shown in Fig. 11. The measured 1-dB gain bandwidth and the corresponding aperture efficiency of the proposed metasurface are depicted in Fig. 12. The results reveal a maximum realized gain of 25.8 dB and a maximum aperture efficiency measured at 12.8 GHz, which corresponds to 53.6%. To highlight the advantage of using the MFPS approach integrated with multi-bit coding metasurface concept to simultaneously improve the bandwidth and efficiency of TFM, two additional TFMs were designed. The first one follows the classic singlefrequency phase synthesis approach, in which the phase error is minimized at a single frequency referred to as the design frequency. The second one is a single-bit TFM with two states for the phase distribution, (state of 3 and 6 in Fig. 2), in which the MFPS approach is also employed. The Simulation results comparing the peak gain versus frequency for all three configurations are presented in Fig. 12.
The comparison of the peak gains shows that the use of single-bit TFM has a wider 1-dB bandwidth from 12.7 GHz to 17.5 GHz compared to the other two radiators. However, the maximum gain of this metasurface is nearly 2 dB lower than the 3-bit configuration which in turn causes to lower aperture efficiency.
Additionally, the side lobe levels in single-bit coding TFM are obtained at approximately − 17 dB for all frequencies of optimizations, which are higher than side lobe levels in 3-bit TFM. This difference can be attributed to the fact that the phase distribution in multi-bit configurations is closer to the ideal phase distribution dictated by the ray tracing theory in space-fed metasurfaces. In the second simulation, the design frequency is set to 15 GHz. As shown in Fig. 12, it is evident that the minimum phase error occurs at 15 GHz. The maximum peak gain of singe-frequency TFM is obtained to be 26.9 dB, which is approximately 1.2 dB higher than the 3-bit TFM. This demonstrates that in the MFPS approach, the phase error is balanced rather than minimized within the frequency band to achieve a smoother gain response. A comparison is conducted between the performance of the presented work and the previously published studies which are summarized in Table 2. The comparison highlights that the presented TFM achieves both high aperture efficiency and a wide 1-dB gain bandwidth by leveraging the combined broadband technique integrated with multi-bit coding metasurface.

Conclusion
This paper presents the design, fabrication, and testing of a novel broadband high-efficiency coding metasurface operating in transmissive mode. The integration of a multi-bit configuration and the MFPS approach allows for minimizing the phase error within the frequency band, resulting in a flat gain response. The main objective is to reduce phase errors at the lower frequencies of the band, considering the ascending gain curve versus frequency. This approach enables the achievement of a gentle gain response, with more phase errors forced at the higher   Comparison between different scenarios to design a TFM along with the measured aperture efficiency. "opt" and "unopt" stands for the optimized and unoptimized model, respectively. www.nature.com/scientificreports/

Data availability
All data required to evaluate the findings of this work is available in the presented paper. Additional data related to this work may be requested from the corresponding author.