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Abstract
Pancharatnam-Berry (PB) phase, usually utilized for phase manipulation of circularly polarized (CP) waves, has inherent symmetrical response on left-handed polarized (LCP) and right-handed polarized (RCP) for orbital angular momentum (OAM), which severely hinders its application. By modulating both propagation and PB phase allows independent control of LCP and RCP of OAM, but increases the design difficulty. Here, we propose a phase compensation scheme to independent control the CP states of OAM only utilizing PB phase, where arbitrary topological charges and deflection directions of LCP and RCP beams can be realized. Two wideband metasurfaces are designed to independent control the mode, circular polarization and beam directions of OAM at the frequency range of 10-20 GHz. This work significantly motivates the development of polarization division multiplexing in wireless communication system.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Since the photon of orbital angular momentum (OAM) was first introduced from the optics regime to the radio frequency regime by Thide in 2007 [1], OAM carried by vortex beam has attracted considerable interest in microwave frequency bands. OAM vortex beams, characterized by helical phase wavefront of exp(ilφ), in which l is the topological charge or mode, and φ is the azimuthal angle around the propagation axis, can theoretically increase the channel capacity and spectral efficiency due to its infinite orthogonal modes [2,3], which can meet the explosive demands of wireless communications. Up to now, many methods have been presented to generate OAM vortex beams, such as spiral phase plate [4–6] and spiral reflectors [7–9]. By designing specifically spiral structure, the desired helical phase wavefront can be obtained. However, both of these methods suffer from bulky structures and difficult fabrication. The antenna array is another way to generate OAM, but it usually needs a complex feeding network, which increases the design complexity and production cost [10–13]. Most recently, metasurfaces have emerged as a competitive candidate for OAM vortex beams generation due to their significant advantages of low profile, small mass, easy fabrication and deployment, high efficiency and low cost [14–17].
Metasurfaces, composed of subwavelength meta-atoms, can flexibly manipulate the amplitude, phase and polarization of electromagnetic (EM) waves [18–22]. Thus, it is possible to obtain the helical wavefront of OAM vortex beams with metasurfaces. Generally, there are two main ways to modulate phase. One is the propagation phase modulation, which can manipulate the phase by changing the structural parameters of the meta-atoms [23–26]. However, this method usually suffers from narrow bandwidth and mainly focus on linear polarization. The other one is Pancharatnam-Berry (PB) phase modulation, which can effectively manipulate circularly polarized (CP) waves only by varying the orientation of the meta-atoms [27–32], these metasurfaces based on PB phase can successfully generate OAM vortex beams with CP waves illlumination, but only one circular polarization state (LCP or RCP) can be realized. However, multi-polarization can further expand the channel capacity, numerous researches have been reported. Up to now, most of the existing researches focus on multi-polarization OAM vortex beams are the generation and performance regulation of dual linear polarized (LP) OAM vortex beams, with severe limitations for practical applications [33–39]. Aiming at this problem, OAM vortex beams with two CP states have been realized by PB phase metasurface under LP wave illumination [40,41]. However, due to the inherent symmetrical response of PB phase that provide conjugate phase for the two orthogonal CP states, the topological charges and the deflection directions of two CP OAM beams are totally opposite. For instance, if the topological charge and deflection direction of LCP components are l = + 1 and θ = 20° towards the + x direction, and those of RCP components will be l = −1 and θ = −20° towards the –x direction, here, θ is the deflection angle. The two CP vortex beams can be manipulated independently by modulating both the propagation and PB phases [42–45], but it requires multi-layer structure and a large number of optimization parameters, which increases the processing costs and design difficulty. Besides, the working bandwidth is narrow, which restricts its application in broadband wireless communication. Thus, it is of great significance to develop multifunctional OAM metasurfaces with the properties of wideband and independent control of multimode, multibeam and multi-polarization in an easily design and low-cost way.
In this work, a phase compensation scheme for independent control of the deflection directions, topological charges and circular polarization of OAM vortex beams is proposed only utilizing PB phase, which greatly reduces the design difficulty. To validate the feasibility of this scheme, two single-layer metasurfaces composed of wideband mata-atoms are designed. The first metasurface M1 can generate LCP and RCP vortex beams with topological charges of l L = −1 and l R = + 1 in the directions of θ L = 20° and θ R = −30° in xoz plane, respectively. And the second metasurface M2 can generate LCP vortex beam (θ L = −20°, l L = −1) and RCP deflected beam (θ R = 45°, l R = 0). Furthermore, the prototype of M1 is fabricated and measured. Both simulated and measured results demonstrate that two OAM vortex beams can be successfully and independently generated with different topological charges, deflection directions and polarization states from 10 to 20 GHz, and the relative bandwidth is 67%.
2. Principle and design
2.1 Phase compensation scheme for independent control of dual CP OAMs
Different from the previous works, this work proposes a phase compensation scheme for simultaneous and independent control of the two CP vortex beams, where arbitrary deflection directions and topological charges of the LCP and RCP components can be realized. As schematically depicted in Fig. 1, the PB phase metasurface is designed to generate two vortex beams with different polarization states, deflection directions and topological charges under the LP normal incidence. Besides, the insets present a 3D radiation pattern and a zoom-in view of the proposed metasurface. Generally, the reflection characteristics of the PB metasurface can be described by the four CP reflection coefficients with linear base as follows [46]:
Fig. 1. Schematic of the metasurface M1 for independent control of mode and circular polarization of OAM vortex beams. Two vortex beams are considered for carrying different topological charges and deflection directions under LP wave normal incidence. The insets present a 3D radiation pattern and a zoom-in view of M1.
To realize the simultaneous and independent control of the two orthogonal CP vortex beams, the metasurface is required to provide independent phase compensation for LCP and RCP components. By independently compensating the desired phase profiles of the two orthogonal CP components and combining them together, the compensation phase of the metasurface and the rotation angle of the meta-atom can be expressed as:
Fig. 2. Schematic of independent manipulation of the two orthogonal CP vortex beams, under the illumination of (a) RCP, (b) LCP and (c) LP wave.
As a LP incident wave normally incident onto the proposed metasurface, it can be decomposed into LCP component and RCP component with equal amplitude. Hence, by controlling the rotation angle of the meta-atoms, one can simultaneously obtain two orthogonal CP vortex beams with independently selected parameters (${\widehat u_\textrm{L}}$, ${\widehat u_\textrm{R}}$, l L, l R).
2.2 Wideband meta-atom design and property analysis
In order to verify the phase compensation scheme, a wideband single-layer meta-atom is designed and schematically shown in Fig. 3(a). The proposed meta-atom is composed of two symmetric U-shaped patches with respect to xoz plane and a metallic ground plane separated by F4B substrate, which thickness is h = 3 mm, relative permittivity is εr = 2.65, and loss tangent is tan δ = 0.001. The other geometrical parameters of the meta-atom are optimized as p = 8 mm, g = 1 mm, l 1 = 5.6 mm, l 2 = 2 mm, and w 1 = w 2 = 0.5 mm. PB phase is introduced by rotating the two U-shaped patches at a rotation angle α to the y-axis, as shown in Fig. 3(b).
Fig. 3. Schematic of the designed wideband meta-atom with (a) original state and (b) rotation angle α.
Generally, the reflective characteristics of a PB meta-atom placed in xoy plane can be described by reflective matrix as $\textrm{R = }\left[ {\begin{array}{*{20}{c}} {{r_{\textrm{xx}}}}&{{r_{\textrm{xy}}}}\\ {{r_{\textrm{yx}}}}&{{r_{\textrm{yy}}}} \end{array}} \right]$. Specially, for the mirror symmetric meta-atom with respect to the xoz or yoz plane, the corresponding r xy and r yx are equal to zero. Therefore, the four CP reflection coefficients in Eq. (1a –d) are only determined by the two LP reflection coefficients r xx and r yy. To obtain a high-efficiency reflection performance within a wide bandwidth, the co-polarized reflection amplitudes |r LL| and |r RR| should be nearly unity, which requires the reflection amplitudes of r xx and r yy to satisfy $|{{r_{\textrm{xx}}}} |= |{{r_{\textrm{yy}}}} |= 1$, and the phase difference between them should be $|{{\varphi_{\textrm{xx}}} - {\varphi_{\textrm{yy}}}} |= \mathrm{\pi }$.
When the proposed metasurface is illuminated by LP wave (${\overrightarrow E _{\textrm{in}}}{ = }\frac{{1}}{{\sqrt {2} }}|{\overrightarrow{\rm L} } \rangle { + }\frac{{1}}{{\sqrt {2} }}|{\overrightarrow{\rm R} } \rangle = \frac{{1}}{{\sqrt {2} }}\left[ {\begin{array}{c} {1}\\ j \end{array}} \right] + \frac{{1}}{{\sqrt {2} }}\left[ {\begin{array}{c} {1}\\ {{ - }j} \end{array}} \right]$), the reflective electric fields can be expressed as:
To verify the reflection performance of the designed meta-atom, numerical simulation results can be obtained by using the commercial full-wave solver CST Microwave Studio, and the simulation results of meta-atom are illustrated in Fig. 4(a-d). Figure 4(a) presents the amplitude and phase response of r xx and r yy, together with the phase difference between them. It can be seen that both |r xx| and |r yy| are close to unity and the phase difference between r xx and r yy is almost π within a wide frequency bandwidth from 9 to 21 GHz, the relative bandwidth is 80%. In addition, the working efficiency [27,31] calculated by $\eta = 2{|{({{r_{\textrm{xx}}} - {r_{\textrm{yy}}}} )/2} |^2}/({{{|{{r_{\textrm{xx}}}} |}^2} + {{|{{r_{\textrm{xy}}}} |}^2} + {{|{{r_{\textrm{yx}}}} |}^2} + {{|{{r_{\textrm{yy}}}} |}^2}} )$ is more than 95%, which indicates a good spin-to-orbital conversation performance is realized. Therefore, the co-polarized reflection amplitudes |r LL| and |r RR| are approximately equal to unity, while the cross-polarized reflection amplitudes |r RL| and |r LR| are lower than 0.2 within 9-21 GHz, just as show in Fig. 4(b). More importantly, to ensure wideband property, the reflection phase curves of the meta-atom with different rotation angles should have similar slopes at different frequencies within the working bandwidth. Figure 4(c) and 4(d) present the reflection phase responses of r LL and r RR against the rotation angle α, respectively, it can be seen that both φ LL and φ RR have similar slopes as expected within the working bandwidth for different rotation angles. In addition, the phase variances are precisely twice the rotation angle, as −2α for φ LL and 2α for φ RR.
Fig. 4. (a) Reflection amplitude and phase responses of the meta-atom under x- and y-polarized illuminations. (b) Reflection amplitude responses of the meta-atom under CP illumination. Reflection phase responses of the meta-atom with different rotation angles under (c) LCP and (d) RCP illumination, respectively.
Based on the above theoretical analyses and simulated results, it demonstrates that the phase responses of two orthogonal CP can be manipulated independently while maintaining high amplitude responses and working efficiency in a wide frequency bandwidth by rotating the proposed meta-atom. Due to the relationship between phase response and the rotation angle, once the desired phase profiles of the metasurface are determined, meta-atoms can be rotated with the corresponding rotation angles to achieve the expected functionalities.
2.3 Design of the PB metasurfaces for independent control of dual CP
Based on the aforementioned phase compensation analysis and the wideband meta-atom design, a single-layer metasurface M1 is designed to validate the feasibility for simultaneous and independent regulation of two orthogonal CP vortex beams. This metasurface is composed of 20 × 20 meta-atoms with spatially varying the orientation angles, and the total size of which is 160 mm × 160 mm.
The topological charges and deflection directions of M1 are set as l L = −1, θ L = 20° for LCP vortex beam and l R = + 1, θ R = −30° for RCP vortex beam, respectively. The corresponding phase profiles of ΦLCP, ΦRCP and Φtotal are calculated from Eq. (2) and depicted in Fig. 5. Firstly, the phase compensation component to compensate the saptial phase delay are calculatd, as shown in the first column of Fig. 5. Next, in order to make the LCP and RCP vortex beams deflect to different directions, a gradient phase profile is introduced. Notably, the deflection direction of LCP and RCP beams can be arbitrarily controlled by introducing certain gradient phase. By substituting θ L = 20° and θ R = −30° into ${k_\textrm{0}}\overrightarrow {{r_{mn}}} \cdot {\widehat u_\textrm{L}}$ and ${k_\textrm{0}}\overrightarrow {{r_{mn}}} \cdot {\widehat u_\textrm{R}}$, respectively, the desired phase gradient is calculated and presented in the second column of Fig. 5. Then, the helical phase profiles for vortex beams carrying different topological charges (l L = −1 for LCP and l R = + 1 for RCP) is shown in the third column of Fig. 5, and the synthesized phase profiles of ΦLCP, ΦRCP are shown in the fourth column of Fig. 5. Finally, according to the phase superposition principle in Eq (2c), the synthesized phase profile of Φtotal of M1 is calculated and presented in the last column of Fig. 5. Therefore, the layout of the meta-atoms can be obtained due to the relationship between the rotation angle and the phase profile ($\alpha = 1/2{\Phi _{\textrm{total}}}$).
In order to verify the wideband performance of M1, the simulated 3D far-field radiation patterns at 10 GHz, 12 GHz, 15 GHz, 18 GHz and 20 GHz are presented in Fig. 6. It can be seen that there are two clearly visible amplitude null (marked with black dashed rings) at each frequency point, which consists with the characteristics of vortex beams. Figure 7 shows the simulated E-field amplitude and phase distributions of LCP and RCP vortex beams at 10-20 GHz. From Fig. 7(a), it can be seen that the amplitude distributions exhibited the typical doughnut-shape (marked with red dashed rings) of vortex beams at the five frequency points, respectively. As for the phase distributions, a clockwise helical phase distribution of l L = −1 for LCP vortex beam and an anticlockwise helical phase distribution for l R = + 1 of RCP vortex beam can be clearly observed at these five frequencies, which can be seen in Fig. 7(b), and it coincides with the characteristics of the OAM as expected.
Fig. 6. Simulated 3D radiation patterns of M1 at 10 GHz, 12 GHz, 15 GHz, 18 GHz and 20 GHz, respectively.
Fig. 7. Simulated E-field results of near-field (a) amplitude and (b) phase distributions of M1 at 10-20 GHz.
The mode purity of LCP and RCP vortex beams generated by M1 is further analyzed and calculated by the following equation:
Fig. 8. Mode purity of (a) LCP and (b) RCP vortex beams at 10 GHz, 12 GHz, 15 GHz, 18 GHz and 20 GHz.
To further demonstrate the capability of the compensation scheme, we designed the second metasurface (M2) that can simultaneously generate LCP vortex beam and RCP deflected beam. M2 contains 20 × 20 meta-atoms with the dimension of 160 mm × 160 mm. Here, the deflection direction and topological charge are set as θ L = −20° and l L = −1 for LCP vortex beam, and the deflection direction of RCP beam is θ R = 45° (mode: l R = 0). Figure 9 displays the simulated 3D far-field patterns of M2 in the frequency band of 10-20 GHz. It can be obviously seen that there is an amplitude null (marked with black dashed rings) and a deflected pencil beam at the chosen frequency points. The simulated amplitude and phase distributions are presented in Fig. 10. From Fig. 10(a), it can be seen that the LCP vortex beams have the typical doughnut-shape amplitude distributions as the frequency covers 10-20 GHz, and the amplitude distribution for RCP beam is as a plane wave with no hollow distribution in the center. As shown in Fig. 10(b), the phase distribution of LCP vortex beam exhibits corresponding helical pattern, and that of RCP beam exhibits as a plane wave.
Fig. 9. (a) Schematic of the multifunctional metasurface M2 at 15 GHz. (b) Simulated 3D far-field radiation patterns at 10-20 GHz.
Fig. 10. Simulated E-field results of near-field (a) amplitude and (b) phase distributions for M2 at 10-20 GHz.
3. Fabrication and experimental results
To experimentally validate the phase compensation scheme and the design principle, the prototype of M1 is fabricated using low-cost printed circuit board (PCB) technique and measured in a standard anechoic chamber, as shown in Fig. 11. A photograph of the sample with a zoom-in view is exhibited in Fig. 11(a). The experimental setups of far- and near-field measurements are illustrated in Fig. 11(b) and Fig. 11(c), respectively. As shown in Fig. 11(b), the metasurface and transmitting horn antenna are placed on a turntable plate to provide a 360° rotation in the horizontal plane, and the receiving antenna is placed at a distance of d = 3 m away from the metasurface. The transmitting and receiving antennas are connected to an Agilent N5225A vector network analyzer. The receiving antenna is a wideband horn antenna to measure two orthogonal LP components, and then transform them to obtain the normalized far-field patterns of LCP and RCP vortex beams. As shown in Fig. 11(c), in order to get full view of the amplitude and phase distributions of the deflected LCP and RCP vortex beams, M1 should be rotated to stay parallel to the sampling plane. Here, the rotation angles of the metasurface are set as the deflection angles at 12 GHz, 15 GHz and 18 GHz accordingly as predicted from the far-field measured results. The sampling planes are set at the position of 500 mm (corresponding to 25λ 0 for the center frequency of 15 GHz) away from the center of M1 with an area of 300 mm × 300 mm. A waveguide probe is used as the receiving end whose position is controlled by a motion controller. As the probe is a LP waveguide probe, two rounds of measurements are performed to measure the two orthogonal LP components ${\overrightarrow E _\textrm{x}}$ and ${\overrightarrow E _\textrm{y}}$ of the reflective electric field, and then the LCP and RCP reflective field can be obtained. A small scanning step of 3 mm is selected to acquire amplitude and phase distributions at the scanning planes. With the variation of the position of the field probe via the motion controller, the sampling plane can be covered and the experimental amplitude and phase profiles can be measured.
Fig. 11. (a) Photograph of the fabricated prototype of M1 with a zoom-in view of it. Schematic of experimental setups of (b) far- and (c) near-field measurements.
Due to the limitation of experimental conditions, here, the measured results of the far- and near- field are carried out at 12-18 GHz. The simulated and measured normalized far-field patterns of M1 in xoz plane at frequencies of 12 GHz, 15 GHz, and 18 GHz are displayed in Fig. 12, respectively. It can be obviously seen that the measured results agree well with the simulated ones. The two hollows at different deflection angles suggest that two orthogonal CP vortex beams are successfully generated and deflected into different directions within the working bandwidth. At the center frequency of 15 GHz, the two vortex beams are deflected to θ L = 20° for LCP and θ R = −30° for RCP, respectively, which is consistent with our design. At frequency points of 12 GHz and 18 GHz, the deflection angles of LCP and RCP vortex beams are θ L = 25°, θ R = −39° and θ L = 17°, θ R = −25°, respectively, which are slightly deviated from those of the center frequency due to the frequency dispersion. Figure 13 shows the measured E-field amplitude and phase distributions of LCP and RCP vortex beams at frequencies of 12 GHz, 15 GHz and 18 GHz, respectively. From Fig. 13(a), it can be seen that the amplitude distributions exhibited the typical doughnut-shape (marked with red dashed rings) of vortex beams at the frequencies of 12 GHz, 15 GHz and 18 GHz, respectively. The measured phase distributions in Fig. 13(b) are consistent with the corresponding topological charges for LCP and RCP vortex beams. The measured results agree well with the simulated ones in Fig. 7, which verifies the feasibility for independent manipulation of the two orthogonal CP vortex beams and wideband performance of M1. Furthermore, a performance comparison of M1 with other reported OAM metasurfaces has been exhibited in Table 1. It can be seen that, compared with the previous works, this proposed metasurface M1 has a wider bandwidth. Besides, M1 can simultaneously achieve independent control of topological charges, deflection directions and circular polarization in a broadband frequency range utilizing only a single layer. In addition, M1 can realize polarization independence of DCP only utilizing PB phase, which can greatly reduce the design difficulty compared with the Ref. [45] which combined of the propagation and PB phase to manipulate DCP.
Fig. 12. Simulated and measured normalized far-field patterns of M1 in xoz plane at (a) 12 GHz, (b) 15 GHz and (c) 18 GHz, respectively.
Fig. 13. Measured E-field results of near-field (a) amplitude and (b) phase distributions of M1 at 10 GHz, 12 GHz, 15 GHz, 18 GHz and 20 GHz.
Table 1. Performance comparison of M1 with other reported worksa
4. Conclusion
In summary, a phase compensation scheme has been proposed to realize independent control of the LCP and RCP vortex beams with the customized deflected directions and topological charges only utilizing PB phase. Compared with the previous works, this method reduces the design difficulty and has low-profile. To demonstrate the feasibility of this scheme, two single-layer wideband metasurfaces consisting of wideband meta-atoms are designed to achieve independent control of two orthogonal CP vortex beams from 10 to 20 GHz under the LP normal incidence. Moreover, this scheme can be further applied to transmission-type metasurfces and other frequency band with proper phase profiles, and has great potential in future wireless communication systems.
Funding
National Natural Science Foundation of China (62201415); Fundamental Research Funds for the Central Universities (20103227473); Shaanxi Fundamental Science Research Project for Mathematics and Physics (22JSQ015); Qin Chuang Yuan Citing High-level Innovation and Entrepreneurship Talent Projects (QCYRCXM-2022-349); National Natural Science Foundation of China for Outstanding Young Scholars (62022064).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly at this time but may be obtained from the authors upon reasonable request.
References
1. B. Thidé, H. Then, J. Sjöholm, et al., “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007). [CrossRef]
2. J. Wang, J. Y. Yang, I. M. Fazal, et al., “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012). [CrossRef]
3. Y. Yan, G. Xie, M. P. J. Lavery, et al., “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5(1), 4876 (2014). [CrossRef]
4. L. Cheng, W. Hong, and Z. C. Hao, “Generation of electromagnetic waves with arbitrary orbital angular momentum modes,” Sci. Rep. 4(1), 4814 (2014). [CrossRef]
5. X. Hui, S. Zheng, Y. Hu, et al., “Ultralow reflectivity spiral phase plate for generation of millimeter-wave OAM beam,” IEEE Antennas Wireless Propag. Lett. 14, 966–969 (2015). [CrossRef]
6. Y. Chen, S. Zheng, Y. Li, et al., “A flat-lensed spiral phase plate based on phase-shifting surface for generation of millimeter-wave OAM beam,” IEEE Antennas Wireless Propag. Lett. 15, 1156–1158 (2016). [CrossRef]
7. F. Tamburini, E. Mari, B. Thidé, et al., “Experimental verification of photon angular momentum and vorticity with radio techniques,” Appl. Phys. Lett. 99(20), 204102 (2011). [CrossRef]
8. F. Tamburini, E. Mari, A. Sponselli, et al., “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14(3), 033001 (2012). [CrossRef]
9. W. Byun, K. Kim, B. Kim, et al., “Multiplexed cassegrain reflector antenna for simultaneous generation of three orbital angular momentum (OAM) modes,” Sci. Rep. 6(1), 27339 (2016). [CrossRef]
10. B. Liu, Y. Cui, and R. Li, “A broadband dual-polarized dual-OAM-mode antenna array for OAM communication,” IEEE Antennas Wireless Propag. Lett. 16, 744–747 (2017). [CrossRef]
11. K. Liu, H. Liu, Y. Qin, et al., “Generation of OAM beams using phased array in the microwave band,” IEEE Trans. Antennas Propag. 64(9), 3850–3857 (2016). [CrossRef]
12. X. D. Bai, X. L. Liang, Y. T. Sun, et al., “Experimental Array for Generating Dual Circularly-Polarized Dual-Mode OAM Radio Beams,” Sci. Rep. 7(1), 40099 (2017). [CrossRef]
13. H. Li, L. Kang, and K. Dong, “Generating tunable orbital angular momentum radio beams with dual-circular-polarization and dual-mode characteristics,” IEEE Access 8, 211248–211254 (2020). [CrossRef]
14. M. Chen, J. J. Li, and W. Sha, “Ultrathin complementary metasurface for orbital angular momentum generation at microwave Frequencies,” IEEE Trans. Antennas Propag. 65(1), 396–400 (2017). [CrossRef]
15. Z. H. Jiang, L. Kang, W. Hong, et al., “Highly efficient broadband multiplexed millimeter-wave vortices from metasurface-enabled transmit-arrays of subwavelength thickness,” Phys. Rev. Appl. 9(6), 064009 (2018). [CrossRef]
16. K. Zhang, Y. Yuan, D. Zhang, et al., “Phase-engineered metalenses to generate converging and non-diffractive vortex beam carrying orbital angular momentum in microwave region,” Opt. Express 26(2), 1351–1360 (2018). [CrossRef]
17. M. Xin, R. Xie, G. Zhai, et al., “Full control of dual-band vortex beams using a high-efficiency single-layer bi-spectral 2-bit coding metasurface,” Opt. Express 28(12), 17374–17383 (2020). [CrossRef]
18. N. Yu, P. Genevet, M. A. Kats, et al., “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011). [CrossRef]
19. X. G. Luo, “Principles of electromagnetic waves in metasurfaces,” Sci. China: Phys., Mech. Astron. 58(9), 594201 (2015). [CrossRef]
20. M. Wang, D. Liao, J. Y. Dai, et al., “Dual-Polarized reconfigurable metasurface for multifunctional control of electromagnetic waves,” IEEE Trans. Antennas Propag. 70(6), 4539–4548 (2022). [CrossRef]
21. S. Liu, T. J. Cui, Q. Xu, et al., “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light: Sci. Appl. 5(5), e16076 (2016). [CrossRef]
22. H. Ahmed, A. A. Rahim, H. Maab, et al., “Polarization insensitive all-dielectric metasurfaces for the ultraviolet domain,” Opt. Mater. Express 10(4), 1083–1091 (2020). [CrossRef]
23. T. J. Cui, M. Q. Qi, X. Wan, et al., “Coding metamaterials, digital metamaterials and programmable metamaterials,” Light: Sci. Appl. 3(10), e218 (2014). [CrossRef]
24. S. Yu, L. Li, G. Shi, et al., “Generating multiple orbital angular momentum vortex beams using a metasurface in radio frequency domain,” Appl. Phys. Lett. 108(24), 662 (2016). [CrossRef]
25. S. Yu, L. Li, and G. Shi, “Dual-polarization and dual-mode orbital angular momentum radio vortex beam generated by using reflective metasurface,” Appl. Phys. Express 9(8), 082202 (2016). [CrossRef]
26. C. Huang, W. Pan, X. Ma, et al., “Multi-spectral metasurface for different functional control of reflection waves,” Sci. Rep. 6(1), 23291 (2016). [CrossRef]
27. H. X. Xu, H. Liu, X. Ling, et al., “Broadband vortex beam generation using multimode Pancharatnam–Berry metasurface,” IEEE Trans. Antennas Propag. 65(12), 7378–7382 (2017). [CrossRef]
28. H. Ma, X. Kong, P. Chen, et al., “Broadband vortex beams generation with narrow divergence angle using polarization insensitive metasurface,” IEEE Access 8, 218062–218068 (2020). [CrossRef]
29. L. Yu, X. Li, Z. Qi, et al., “Wideband circularly polarized dual-mode vortex beams reflectarray design using dual-semi-split-loop elements,” IEEE Antennas Wireless Propag. Lett. 18(12), 2676–2680 (2019). [CrossRef]
30. D. Zhang, Z. Lin, J. Liu, et al., “Broadband high-efficiency multiple vortex beams generated by an interleaved geometric-phase multifunctional metasurface,” Opt. Mater. Express 10(7), 1531–1544 (2020). [CrossRef]
31. L. J. Yang, S. Sun, and W. Sha, “Ultrawideband reflection-type metasurface for generating integer and fractional orbital angular momentum,” IEEE Trans. Antennas Propag. 68(3), 2166–2175 (2020). [CrossRef]
32. K. Chen, Y. Feng, Z. Yang, et al., “Geometric phase coded metasurface: from polarization dependent directive electromagnetic wave scattering to diffusion-like scattering,” Sci. Rep. 6(1), 35968 (2016). [CrossRef]
33. H. F. Huang and S. N. Li, “Single-layer dual-frequency unit for multifunction OAM reflectarray applications at microwave range,” Opt. Lett. 45(18), 5165–5168 (2020). [CrossRef]
34. Y. Huang, X. Li, X. Guo, et al., “A reflective metasurface for generating dual-mode dual-polarized high-order Bessel vortex beams with equal divergence angle,” IET Microw. Antennas Propag. 16(8), 489–496 (2022). [CrossRef]
35. H. F. Huang and S. H. Xie, “Single-layer substrate wideband reflectarray with dual-polarization for multiple OAM beams,” OSA Continuum 4(8), 2082–2090 (2021). [CrossRef]
36. X. Meng, J. Wu, Z. Wu, et al., “Dual-polarized reflectarray for generating dual beams with two different orbital angular momentum modes based on independent feeds in C- and X-bands,” Opt. Express 26(18), 23185–23195 (2018). [CrossRef]
37. W. Fu, H. Wang, and X. Zhang, “Generating dual-polarized orbital angular momentum radio beams with dual-bowtie cell,” AIP Advances 9(11), 115004 (2019). [CrossRef]
38. P. Gao and R. Yang, “Generating Different Polarized Multiple Vortex Beams at Different Frequencies from Laminated Meta-Surface Lenses,” Micromachines 13(1), 61 (2022). [CrossRef]
39. K. Zhang, Y. Wang, S. N. Burokur, et al., “Generating dual-polarized vortex beam by detour phase: from phase gradient metasurfaces to metagratings,” IEEE Trans. Microw. Theory Techn. 70(1), 200–209 (2022). [CrossRef]
40. K. Liu, G. Wang, T. Cai, et al., “Dual-frequency geometric phase metasurface for dual-mode vortex beam generator,” J. Phys. D: Appl. Phys. 52(25), 255002 (2019). [CrossRef]
41. L. Zhang, S. Liu, L. Li, et al., “Spin-controlled multiple pencil beams and vortex beams with different polarizations generated by Pancharatnam-Berry coding metasurfaces,” ACS Appl. Mater. Interface 9(41), 36447–36455 (2017). [CrossRef]
42. J. S. Li and J. Z. Chen, “Simultaneous and independent regulation of circularly polarized terahertz wave based on metasurface,” Opt. Express 30(12), 20298–20310 (2022). [CrossRef]
43. G. Ding, K. Chen, N. Zhang, et al., “Independent wavefront tailoring in full polarization channels by helicity-decoupled metasurface,” Ann. Phys. 534(4), 2100546 (2022). [CrossRef]
44. H. X. Xu, L. Han, Y. Li, et al., “Completely spin-decoupled dual-phase hybrid metasurfaces for arbitrary wavefront control,” ACS Photonics 6(1), 211–220 (2019). [CrossRef]
45. G. Ding, K. Chen, X. Luo, et al., “Dual-helicity decoupled coding metasurface for independent spin-to-orbital angular momentum conversion,” Phys. Rev. Appl. 11(4), 044043 (2019). [CrossRef]
46. H. X. Xu, G. M. Wang, T. Cai, et al., “Tunable Pancharatnam–Berry metasurface for dynamical and high-efficiency anomalous reflection,” Opt. Express 24(24), 27836–27848 (2016). [CrossRef]
47. P. Nayeri, F. Yang, and A. Z. Elsherbeni, “Design and Experiment of a Single-Feed Quad-Beam Reflectarray Antenna,” IEEE Trans. Antenna Propag. 60(2), 1166–1171 (2012). [CrossRef]
48. C. Xue, H. Zhao, T. Li, et al., “Efficient generation of a dual-polarized vortex wave with an ultrathin Huygens’ metasurface,” Opt. Express 30(21), 39175–39187 (2022). [CrossRef]
49. X. Gao, L. Tang, X. Wu, et al., “Broadband and high-efficiency ultrathin pancharatnam-berry metasurfaces for generating X-band orbital angular momentum beam,” J. Phys. D: Appl. Phys. 54(7), 075104 (2021). [CrossRef]
50. C. Ji, J. Song, C. Huang, et al., “Dual-band vortex beam generation with different OAM modes using single-layer metasurface,” Opt. Express 27(1), 34–44 (2019). [CrossRef]
