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Abstract
In this paper, a single-layer wideband dual-linearly polarized reflective element is developed operating from 13GHz to 15.5GHz. The developed reflective metasurface can produce orbital angular momentum (OAM) vortex waves with required modes, beam numbers, direction, x-, y- or both x- and -y polarizations. To demonstrate this versatility, three reflectarrays with multiple modes, multiple beams, and both x- and -y polarizations are designed, and one is fabricated and measured to validate the design. The measured peak gain, aperture efficiency, divergence angle is 19dBi, 11.54%, 6°, respectively. The designed reflectarray has potential applications for high communication rate.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Over the past years, metasurfaces have been widely used to generate OAM waves due to their unique properties of low profile, easy fabrication, high efficiency, not requiring complex feed network and low cost. In 2019, A high-efficiency single-layer reflectarray with small size was proposed to obtain multi-mode OAM beam at 5.8GHz [1]. At the same year, a two-layer rhombus-shaped reflectarray was designed to transfer dual linear spherical beam to circular polarization OAM beams at 9-11GHz [2]. In addition, a variety of methods are utilized to obtain dynamic OAM beams, such as mode reconfigurable water antenna [3], frequency-adjustable metasurface [4], programmable metasurface [5], and active metasurface with reconfigurable deflected angle [6]. Several multifunction meta-microstructures have been proposed such as programmable meta-microstructure [7] functioning as polarization conversion, vortex beams, scattering control and self-feeding Janus metasurface functioning as polarization conversion of incident waves, scattering control, EM wave radiation, and radiation-beam steering [8].
Nevertheless, the above metasurfaces have the shortcomings of multilayer, large divergence angle or narrow band, and is limited in vortex communication application. As is known, multimode, multibeam, multi-polarization and wideband OAM with high aperture efficiency are important ways to expand the capacity of the communication [9]. In the meantime, small divergence angle is required due to the divergence and a central phase singularity for long distance transmission, particularly in radio frequency [10]. In addition, single layer structure is desired for compact structure and low cost. Four OAM vortex beams are generated by the single-layer reflectarray combining cross dipole with 1-bit phase quantization [11]. A reflective single-layer dual-polarized metasurface based on the cross-dipole element at 5.8GHz is developed [12]. A single-layer, dual-frequency multifunctional high aperture efficiency reflectarray is developed to generate multiple OAM beams, which has low divergence angle [13]. Broadband vortex beams with divergence angle 12° is reported by using polarization insensitive metasurface [14]. Reference [15] designed a dual-bowtie structure to form a dual-polarized reflective metasurface from 9.2 to 10.5 GHz. However, most of the above works cannot obtain the features of multimode, multibeam, multi-polarization, wideband and high aperture efficiency simultaneously. A dual-polarized cross-dipole holographic metasurface is developed, which has relatively lower aperture efficiency [16]. Although Ref. [13] proposed single-layer dual-frequency multifunction reflectarray, the operation band is narrow. Therefore, it is highly demanded to seek a single-layer multi-polarization multifunction OAM metasurface with required OAM mode, beam number, direction, high aperture efficiency and wideband for high communication capacity application.
In this paper, we develop a multifunction reflectarray with size 10.4${\lambda _0} \times 10.4{\lambda _0}$, which features single-layer, dual polarization, desired OAM mode, mode number, beam number, direction, high aperture efficiency, small divergence angle and wideband simultaneously. The proposed metasurface can achieve high gain 19dBi, high aperture efficiency 11.54% low divergence angle 6$^\circ $, and beam number high up to eight. To the knowledge of the authors, the developed reflectarray produces the most beam number (eight beam numbers). The mode order and beam number are related to the metasurface size and aperture power. However, it is about the same size as that of other published works with single beam while obtaining high gain.
2. Design of the reflectarray
2.1 Mechanism of the reflectarray
The configuration of the proposed reflectarray is depicted in Fig. 1, which consists of the horn feeder and the reflective metasurface. Excited by x- or y-polarized wave, the reflectarray can produce the x- or y-polarized vortex waves with the desired modes. Here, a horn rotated 45° around its center line is used to excite both x- and y- polarizations simultaneously under normal incidence. It’s worth mentioning that when the phase difference between x-polarization and y-polarization is 90°, the circular polarized vortex wave can be obtained. Multiple beams can be obtained when phase is compensated as follows.
2.2 Design of the unit
The model of the proposed unit cell with the size 13mm${\times} $ 13mm (0.65$\; {\lambda _0} \times 0.65\; {\lambda _0}$) is shown in Fig. 2. The element consists of four L-shaped patches surrounded with two vertical and horizontal rectangle patches, which are printed on the top side of F4B substrate with thickness 0.55mm and permittivity ${\varepsilon _r}$ = 2.25. There is an air gap between the F4B substrate and the ground plane. The four L-shaped structures provide multi-resonance to form operation bandwidth from 13GHz to 15.5GHz. The lengths of four parasitic patches ($Lx$ and $Ly$) control the phase shifting, and the phase shift can cover over 360° range at 15GHz by adjusting the length of horizontal and vertical rectangular patches for x- and y-polarizations, respectively. ${L_{m(n )}}$ is about quarter wavelength of 15 GHz. The sizes are given in Table 1.
Table 1. Dimensions of the element (Unit: mm)
Figure 3 shows the simulated phase-shift and S parameter as function of $Lx(y )$ for x(y) polarization at four frequency points 13GHz, 14GHz, 15GHz and 15.5GHz. The change of $Lx(y )$ has slight influence on the magnitude of S11, with |S11| near to 1. The curves for x and y polarizations are coincident, so the unit is polarization-insensitive. The phase-shift curves are nearly parallel at 13GHz, 14GHz, 15GHz and 15.5GHz, which means the element has wideband characteristic.
Fig. 3. The simulated phase shift and S parameter at different frequencies as function of: Lx for different Ly(a), Ly for different Lx (b).
2.3 Design and simulation of the reflectarray
Based on the above proposed unit cell, the reflectarray can be designed to generate multifunctional vortex wave with required OAM modes, beam numbers, and beam directions in the frequency range of 13GHz-15.5GHz. The phase distributions on the metasurfaces are calculated by MATLAB. As examples, three reflectarrays with the size 208mm ${\times} $ 208mm (10.4$\lambda \times $ 10.4$\lambda$) composed of 16 ${\times} $ 16 elements are designed in Table 2, where ${l_{x(y )}}$ represents OAM mode for x(y)-polarization, and (${\theta _{x(y )}}$, ${\varphi _{x(y )}}$) represents the beam direction for x(y)polarization. The related phase distributions within 13–15.5GHz are shown in Fig. 4. The simulation model of the proposed reflectarray built in CST studio is to verify the multiple beams with vortex nature. The distance between the feeding horn and the metasurface is 220mm.
Fig. 4. Phase distribution of single-beam, dual-beam and quad-beam, (a-c) for x-polarized component and (d-f) for y-polarized component within 13–15.5 GHz. (a) x-polarized and (d) y-polarized OAM beam generated by reflectarray 1, (b) x-polarized and (e) y-polarized OAM beams generated by reflectarray 2, (c) x-polarized and (f) y-polarized OAM beams generated by reflectarray 3.
Table 2. The details of beams generated by the reflectarray
The simulated far-field radiation patterns for the three reflectarrays at 13GHz, 14GHz, 15GHz and 15.5GHz are presented in Fig. 5–7, respectively. For every reflectarray, there is a clear vortex center at the axial direction of every OAM beam at four frequency points. The simulation results are consistent with the predesign, and it shows that the design method is correct. It’s obvious that sidelobe exists near the direction of θ=0°, especially at 13GHz and15.5GHz. According to the Ref. [17], the distance from the horn to each element is different, which will cause the phase error. When the element number is fixed, the more beam numbers are generated, the greater impact on sidelobe is. Increasing element number can reduce the phase error for low-sidelobe beams [18] [19].
Fig. 5. Dual-beam carried with OAM at different frequency. (a)13 GHz, (b)14 GHz, (c)15 GHz, (d)15.5 GHz.
Fig. 6. Quad-beam carried with OAM at different frequency. (a)13 GHz, (b)14 GHz, (c)15 GHz, (d)15.5 GHz.
Fig. 7. Eight-beam carried with OAM at different frequency. (a)13 GHz, (b)14 GHz, (c)15 GHz, (d)15.5 GHz.
The decomposition beams of x- and y-polarization components for Fig. 5 (two beams), Fig. 6(four beams) and Fig. 7(eight beams) are shown in Figure (8–10), respectively. As shown in Fig. 8, one x-polarized beam (l_x=−1, θ_x=30°, φ_x=0°) and one y-polarized beam (l_y=1, θ_y=30°, φ_x=180°) can obtain high gain 18.8dBi and 19.3dBi, respectively. The aperture efficiency formulas of multiple beams are as follows.
${D_i}$ refers to the gain of the nth beam, ${A_0}$ is the aperture size of the reflectarray.Fig. 8. The dual-beam composed of components in horizontal polarization and vertical polarization at 15 GHz. (a)x-polarized OAM beam, (b)y-polarized OAM beam.
Two vortex beams have low sidelobe, and obtain high aperture efficiency 11.84%. Figure 9 suggests that although there exists a little sidelobe along z axis, two x(y)- beams can still obtain high gain 15.8dBi, and high aperture efficiency 11.15%. Figure 10(a, b) are the decomposed four x- and y-polarization beams for eight beams, respectively, and the related aperture efficiency is 11.48%.
Fig. 9. The quad-beam composed of components toward the horizontal polarization and vertical polarization at 15 GHz. (a)x-polarized OAM beams, (b)y-polarized OAM beams.
Fig. 10. The eight-beam composed of components toward the horizontal polarization and vertical polarization at 15 GHz. (a)x-polarized OAM beams, (b)y-polarized OAM beams.
For the purpose of demonstrating the stability of the OAM beams, the electric field phase and magnitude at the plane at z=500mm (25$\lambda_0$) perpendicular to the predesigned directions are simulated at 13GHz, 14GHz, 15GHz and 15.5GHz, which are shown in Fig. 11. The zero-intensity area is caused by the phase singularity of the OAM beam, which clearly exists in the center of the plane, and the helical phase pattern proves the phase change of the OAM beams with mode $l$=±1 within 13–15.5GHz. The anticlockwise (clockwise) 2π phase change in a circle is observed for x- (y-) polarization, proving the preset mode ${l_{x(y )}}$=−1(1).
Fig. 11. The simulated 2D E-field results of dual-beam. The first row is the x-polarized component with ${l_x}$=−1 at the direction of ${\theta _x}$=30°, ${\varphi _x}$=0°, and the second row is the y-polarized component with ${l_y}$=1 at the direction of ${\theta _y}$=30°, ${\varphi _y}$=180°. (a) and (e) at 13 GHz, (b) and (f) at 14 GHz, (c) and (g) at 15 GHz, (d) and (h) at 15.5 GHz.
3. Fabrication and analysis of the reflectarray
In order to validate the design, a prototype of example (1) is fabricated. That is, two OAM beams: (${l_x}$=−1, ${\theta _x}$=30°, ${\varphi _x}$=0°) and (${l_y}$=$1$, ${\theta _y}$=30°, ${\varphi _y}$=180°). The prototype and measurement setup are in Fig. 12(a, b), respectively. The farfield radiation performance are measured by Satimo Starlab under the microwave anechoic chamber. It’s difficult to control the placement rotation of horn, so we adopt the approach to rotate the metasurface. The measured and simulated normalized 2D radiation patterns are shown in Fig. 13 at 13GHz, 14GHz, 15GHz and 15.5GHz. The measured singularities appear at two directions (${\theta _x}$ = 30°, ${\varphi _x}$ = 0°) and (${\theta _y}$ = 30°, ${\varphi _y}$ = 180°), which are consistent with the predesigned dual-beam directions. There is a little deviation between simulated and measured results at 13GHz, which results from the fabrication error and the phase error of metasurface placement. The measured maximum gains and divergence angles for the OAM beam are 19 dBi and 6°, respectively.
Fig. 12. Photograph of the proposed prototype (a) Top view of prototype. (b) reflectarray under test.
Fig. 13. Simulated and measured 2D radiation pattern in the $\varphi$=0° plane at different frequency. (a) at 13GHz, (b) at 14GHz, (c) at 15GHz, (d) at 15.5GHz.
A comparison between the proposed design and previously published OAM metasurfaces has been made in Table 3. Compared to other references, the proposed reflectarray has wider bandwidth except that in Ref. [2]. However, the proposed reflectarray uses only one substrate layer, which saves more costs than that in Ref. [2]. Among the all reference, the proposed reflectarray achieves the most number OAM beams. In addition, the obtained aperture efficiency of the proposed reflectarray is relatively well. By contrast with the holographic metasurface [16], the proposed reflectarray has the wider bandwidth, higher gains and higher aperture efficiency. In all, the advantages of our proposed reflectarrays can be summarized as follows: (1) Multifunction, that is, single-layer, multi-mode, multi-beam, multi-polarization and and wideband. (2) The most OAM beam numbers. (3) Over360° phase range for the dual-polarized unit, (4) High gain and aperture efficiency. (5) Low divergence angle 6°.
Table 3. The Comparison of Our Work and Other Recently Published Work.
4. Conclusion
This paper presents a single-layer wideband dual-polarized reflectarray. The proposed reflectarray can realize multifunctional vortex waves with required OAM mode, beam number, beam direction, and dual polarization in the frequency range of 13–15.5GHz. The developed metasurface has the advantages of multifunction, the most beam number eight beams, high gain 19dBi, low divergence angle 6° and high aperture efficiency 11.54%. The designed multifunctional reflectarray can be applied in multi-region communication coverage with no interference because of the different polarizations and orthogonal OAM modes between adjacent beams.
Funding
Natural Science Foundation of Guangdong Province (2018B030311013); National Natural Science Foundation of China (61071056).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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