Double-layer broadband transmission metasurface and its application in low sidelobe antenna

This study proposes a double-layer metasurface which is capable of conducting independent amplitude and phase modulation for transmitting x-polarized waves under y-polarized incidence. The phase modulation is controlled by regulating the opening angle of the middle metal ring. Meanwhile, amplitude modulation is achieved by adjusting the rotation angle of the opening ring structure. The cross-polarized transmission response achieves complete phase and amplitude coverage and exhibits wideband characteristic with which a 3 dB gain bandwidth of 54.6% (5.4–9.5 GHz). The polarization isolation level is lower than −20 dB. In the wideband frequency range, the average sidelobe level of phase-only modulated metalens antenna is less than −20 dB with the lowest value of −22.5 dB, and the intermediate sidelobe level of amplitude-phase independent modulated metalens antenna is less than −25 dB with the lowest value of −27.4 dB. Both numerical simulated and experimental results verify that the proposed metalens antenna realizes a 4.8 dB averages of the sidelobe level suppression compared with the phase-only modulation metalens antenna. Holding strong anti-interference performance due to its superiority in polarization isolation level and side lobe level, the proposed antenna embraces broad application prospects in point-to-point communication systems in jamming environments.


Introduction
Metamaterials refer to specific artificial composite structures and materials with certain electrical or magnetic responses, which are designed by using subwavelength artificial microstructural units based on electromagnetic theory. Metasurface, as two-dimensional planar forms of metamaterials [1], has * Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. received extensive attention and rapid development because of their unprecedented ability to control the radiation characteristics of electromagnetic waves. After introducing subwavelength components, metasurfaces have been applied to many functions that are almost impossible with traditional materials to achieve, such as a series of special effects including negative refraction by manipulating reflected and refracted waves [2][3][4][5]. The results of the experiment show that the flow of photons can be regulated, and a strange beam-bending phenomenon can be generated. Cui et al applied the idea of digital signal processing in the information field to metasurfaces, proposed the concept of digitally encoded metasurfaces [6][7][8], and combined two linear gradients to achieve large-angle singular beam deflection. There are also many new applications in the innovative experiments conducted by subsequent researchers, such as focusing lenses [9,10], metasurface stealth research [11][12][13] and multitasking Janus metasurfaces [14]. In the research of beam control technology, metasurface also has a bright performance, such as Xu et al [15], using three-layer dual-mode elements of the metasurface array to achieve multibeam generation.
Although metasurfaces based on pure phase modulation can effectively control the wavefront and realize some applications, such as high-quality stealth research, highperformance antenna and holographic device application research, it requires metasurfaces to have robust manipulation of amplitude and phase. Currently, digitally programmable metasurfaces [16,17] and multi-layer resonant structures [18,19] can achieve independent control of amplitude and phase. Digital metasurfaces loaded with active devices still have a series of hidden dangers such as inaccurate control of functional device parameters, processing, welding, etc. There are certain limitations in practical applications. However, the multi-layer resonant structure generally exists problems including narrow bandwidth and complicated control of amplitude and phase. Metasurfaces with multi-layer facilities often need to adjust multiple parameters to achieve amplitude and phase control, causing inconvenience in the design and fabrication process. At present, most of the metasurfaces with independently adjustable amplitude and phase are designed without antenna theory, which brings about insufficient applications of metasurfaces in some antenna fields such as low sidelobe.
The sidelobe level is always a significant index in antenna research. Still, little research focuses on controlling the main lobe and sidelobe level in the field of metasurface antenna. In terms of applications in radar diagnosis, high-resolution images, and secure communications to reduce connection interference with other components of the final assembly system, a low sidelobe level is indispensable [20]. In order to improve the efficiency of the antenna, the design of the main lobe and the sidelobe of the antenna are essential. An adaptive method of metasurface [21] with phase and amplitude controlled by selecting polarization is proposed. The design of this method is to place the low sidelobe level emission beam on the surface wave at about −20 dB. Using selective polarization to control the radiation properties [22] and introducing the concept of Berry phase [23] is added to realize this application. This paper proposes a metasurface element consisting of a two-layer dielectric substrate and a three-layer metal structure. The amplitude and phase control are implemented by the rotation angle of the intermediate metal layer and the opening angle of the ring of the middle metal layer respectively. The advantage of this structure is that the amplitude and phase changes can be controlled, and full coverage can be achieved by controlling one parameter separately. Compared with the previous methods, this design method possesses the merits of continuous and precise control of the wavefront, broadband modulation of amplitude and phase and simple control. Especially, the amplitude can be precisely and continuously controlled. To demonstrate its practical application, the study designs and fabricates a low sidelobe metasurface antenna and conducts practical processing and testing. The simulation analysis and measurement results indicate that the proposed metasurface has low sidelobe performance and broadband characteristics. According to the sidelobe experiment designed by Taylor distribution, the average sidelobe level of the proposed metasurface antenna is less than −25 dB with the lowest of −27.4 dB, and the intermediate polarization isolation level is less than −20 dB in the working frequency band. The 3 dB gain bandwidth is 54.6% (5.4-9.5 GHz).

Element design and analysis
The topology of the double-substrate supported metasurface unit cell is shown in figure 1. The designed unit consists of two dielectric layers and three metal layers. The dielectric layer has a thickness of 2 mm with relative permittivity of 2.65 and a loss tangent of 0.009. The top layer is a rectangular metal sheet with a long side along the x-axis, while the bottom layer is the same metal structure with a long side along the y-axis. The middle layer is an open metal ring with an opening angle θ 2 . Applying the overall rotation angle θ 1 to the middle metal structure, where θ 1 is 0 • , the line from the center of the circle to the middle of the opening changes along the x + direction and θ 1 along the clockwise direction. The other dimensions of the unit are as follows: L = 4 mm, p = 12 mm, r = 5 mm, w = 0.8 mm. For the x/y polarized typical incident electromagnetic wave illumination incident along the z direction, the relationship through four transmission coefficients between the forward propagating wave E t x , E t y and the incident wave E i x , E i y in the Cartesian coordinate system is as follows: For an electric field incident on the surface of a metasurface element, an induced current is generated by the influence of the upper metal structure on the middle metal, and the induced current can be decomposed along the x and y directions.
For the cell structure analysis, as shown in figure 2(a), the electric field can be decomposed into two directions, the xdirection and the y-direction: The mid-level metal structure is rotated π 2 , as shown in figure 2 From equations (2) and (3), it can be seen that when the middle metal rotation angle is different, that is, 0 • -90 • and 90 • -180 • , different current characteristics are obtained. It is the different current distribution that leads to subsequent simulation studies.
To further study the transmission characteristics of the proposed metasurface unit cell, full-wave simulation are carried  The direction of the first layer of metal is in the x direction, and the direction of the third layer of metal is in the y direction. When the y-polarized wave is incident perpendicular to the meta-surface along the z-axis, the incident wave transmits entirely at the first layer of the metal grating.
The polarization decomposition occurs at the second layer of the metal structure, and both x and y polarization components are produced. The x-polarized part will be transmitted  through the third metal gate, while the y-polarized component will be fully reflected. When the reverse x and y polarization components are transferred to the first layer of metal, the x polarization components are reflected, and a small amount of the y polarization components are transmitted. As a result, most of the y-polarized waves are converted into x-polarized waves that are transmitted through the third layer of the metal structure after multiple reflections inside the metasurface, a small amount of y-polarized waves are reflected through the first metal structure, as shown in figures 4(b), (d) and (f). On the contrary, the x-polarized incidence hardly passes through the upper metal sheet, only a small amount of induced current can be generated in the second layer of metal, and it is almost impossible to transmit to the third layer of metal. In this case, the electric field can only generate induced current in the direction perpendicular to the metal, and the first layer metal structure is in the same direction as the x-polarized electric field, so almost no induced current can be generated, as shown in figures 4(a), (c) and (e).
It can be seen from figure 5 that the current direction is not reversed on the three metal structures because the metal length is less than half the wavelength at the resonant frequency.
In order to further study the transmission characteristics of the unit cell at 7.5 GHz and provide possible support for the subsequent array design, the paper carries out more comprehensive theories and simulation. It can be seen from figures 5(c) and (d) that the phase coverage of π can be achieved by changing the opening angle (5 • -180 • ) of the opening ring of the intermediate layer, and the overall phase can be increased by π after rotating π /2. When the y-polarized incident wave is incident, the proposed metasurface element In order to further improve the structural design, a theoretical analysis of the phase shift is made. In figure 5(a), when a y-polarized incident wave is irradiated vertically along the z-direction, transmitted waves can be expressed as: Similarly, the incident and transmitted waves in figure 2(b) can be expressed as: Comparing the components of x-polarization in equations (4) and (5), it can be seen that π /2 rotation of the middle-layer metal structure produces a π phase shift while the amplitude remains unchanged, which means that the transmission phase can be extended by changing the opening direction angle γ. When θ 1 is 45 • and 135 • , with the change of θ 2 , the amplitude always remains above 0.8, and the phase shift reaches 2π. In order to achieve better experimental results, the study determines the values of θ 2 when the average transmission amplitude reaches the largest degrees, 45 • and 135 • . It can not only achieve full phase coverage of 2π but also control the high transmission. Table 1 provides the comparison data between the proposed metasurface element and other amplitude-phase independently controlled element structures. Although the proposed structure and transmission modulation are similar to those in [24][25][26], the proposed metasurface element structure features the advantages of simple design and high transmission efficiency. Besides, only by rotating the single-layer frame by 90 • can the phase be shifted by π to make the phase cover 2π, which is not achieved in other reported structures.

Metalens antenna with phase-only modulation
To verify the practical application of the proposed cell structure, the study designs the array antenna according to the cell characteristics to achieve the best broadband performance and high efficiency. In this part, the study designs a metasurface metal antenna with high directivity based on phase modulation to compensate for the spherical wave emitted by the feed after passing through the metasurface array. To achieve the best transmission efficiency and beam convergence, an array  figure 7, the main beam of x-polarized incidence has a peak antenna gain of 23.6 dB, while the peak gain of the y-polarized incidence is just 3.1 dB at 7.5 GHz. Figure 7 also illustrates that the measured sidelobe level of the xoz and yoz planes are −22.5 dB and −20.3 dB, respectively. The radiation mismatch of the feed antenna leads to the difference between the results of the xoz and yoz planes. The sidelobe level of the xoz plane are better than it of the yoz plane.

Metalens antenna with phase/amplitude manipulations
The design of a low sidelobe is of great significance in practical applications. For low-side lobe antennas, the narrower the main lobe width is and the sharper the pattern is, the more concentrated the radiated energy of the antenna becomes, or the stronger the receiving ability is, the stronger the directional effect becomes. From the practical application, the study adds a side lobe design to the above-mentioned array antenna to reduce the side lobe level and make the antenna achieve the best performance.
According to the theory of array antenna, the design of the low sidelobe of the antenna pattern is based on phase compensation to adjust the amplitude of the array further. The Taylor synthesis method is used to apply a gradually decreasing amplitude distribution from the center to the edge of the array. The amplitude distribution of the designed array is determined by combining the Taylor synthesis method for linear array design and the amplitude intensity generated by the feed radiation on the array surface. The study use Taylor synthesis linear array design theory to extract the amplitude matrix of a planar array distribution from two different vectors in the x and y directions. The 1D Taylor distribution is represented as: where T is a vector in the distribution of a linear Taylor array, N is the total number of elements in T, and n is the specific sequence number of elements in T.
According to the array antenna theory, combined with the 1D Taylor distribution, an assumption can be made: where, I t is the matrix of the array target amplitude distribution. I x is The normalized radiation amplitude matrix of the feed at the metasurface. I unit is the normalized amplitude distribution matrix required for each element in the array. Taylor array design needs to follow the principle of enough cells and margin design. The number of array cells designed is 21 × 21 elements to meet the requirements. Because of the influence of sidelobe level on the main lobe width and aperture efficiency of the Taylor array which are analyzed by calculation and simulation, the study sets the sidelobe level to −30 dB. According to equations (6) and (7), the study extracts the value of the feed radiation level along the x-axis direction and combines the 2D planar array Taylor distribution theory to obtain the array amplitude distribution of the target sidelobe level, as shown in figure 8(a), and combined with the unit amplitude characteristics to calculate the required size, as shown in figures 8(b) and (c). A new metalens antenna is designed with the normalized target amplitude, as shown in figure 8(d).
The amplitude of the array is adjusted by Taylor distribution, and the simulation results of the xoz and yoz planes are in good agreement with the actual measurement results. Due to the defects in the measurement process and antenna fabrication, the results are slightly inaccurate. As shown in figure 9, the main beam of x-polarized incidence has a peak antenna gain of 23 dB, while the peak gain of the y-polarized incidence is just 3.0 dB at 7.5 GHz. Figure 9 also illustrates that the measured sidelobe level of the xoz and yoz planes are −27.4 dB and −25 dB, respectively. In the above theoretical analysis, the designed theoretical sidelobe level is −30 dB. Because of According to the theory of antennas, the aperture efficiency (ε ap ) can be calculated by [27]: (8) where G is the measured gain, D max = 4π A p /λ 2 is the maximum directivity in which A p is the physical aperture of the antenna, and λ is the wavelength at the working frequency. The gain of the proposed two metalens antennas fed by the corrugated horn has been measured as 23.6 dB and 23 dB, respectively. The physical aperture of the metalens is 252 × 252 mm 2 . Therefore, according to equation (8), the aperture efficiency of the two metalens antennas is illustrated in table 2.

Comparison of two metalens antennas
The following compares the designs and results of two antennas. The first antenna is a phase-only modulation metalens antenna, and the second is an amplitude-phase co-modulation metalens antenna. The two antennas have the same array size, focal diameter ratio and upper and lower metal structure, but the parameters of the middle metal structure are different. Figure 10(a) shows the simulated and measured peak gain in the 5-10 GHz band, from which it can be seen that the phase-only modulated metal antenna has a peak gain of 23.8 dB, and the 3 dB bandwidth is 49.3% (5.8-9.5 GHz) and the aperture efficiency is 48%. After amplitude modulation, the peak gain of the metal antenna is 23 dB. The bandwidth of 3 dB is 54.6% (5.4-9.5 GHz), and the aperture efficiency is 38%. For the peak sidelobe level, the amplitude-modulated metal antenna is −27.4 dB. Compared with the phase-only modulation metal antenna, the amplitude-modulated antenna decreases the peak gain by 0.6 dB on average. Still, the sidelobe level is suppressed obviously, and the sidelobe level is reduced by 4.8 dB on average in the wideband range, as shown in figure 10(b).
In addition, the proposed antenna also performed superiorly compared with other four representative works. As shown in table 2, the proposed antenna's physical structure, bandwidth and sidelobe level are compared. The data in table 2 indicates that the proposed metalens antenna possesses the characteristics of broadband, high efficiency and excellent performance in reducing the sidelobe level, and accordingly the feasibility of its practical application is verified.

Conclusion
In conclusion, the study puts forward an amplitude and phaseindependent controlled double-substrate metasurface which is designed to manipulate both the main lobe and the sidelobe levels of the antenna. The feasibility of the metasurface structure is verified by the simulation analysis and measurement of the metal antenna with only phase modulation and amplitudephase independent adjustable metalens antenna, and a broadband metalens antenna with low sidelobe performance is realized. The proposed metasurface will extend the development of the metalens antenna and be effectively applied to other frequency ranges.

Data availability statement
All data that support the findings of this study are included within the article.