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Abstract
The generation of multi-mode vortex beams at the same aperture is currently emerging as a research hotspot. In this paper, a method based on a linearly polarized-circularly polarized translational transmission metasurface (TM) is proposed to enable a dual-circularly polarized dual-mode vortex beam generation. Through the judicious implementation of an additional rotational phase and the combination of the initial transmission phase, the phases of the left-hand circularly polarized (LHCP) and right-hand circularly polarized (RHCP) waves can be manipulated arbitrarily and independently. Meanwhile, the design of the array phase is utilized for the dual-mode dual-circularly polarized beam generation. Simulation and sample measurements provide validation data for the feasibility of this method, in which the measurement results are in excellent consistency with the simulation ones. This proposed method paves the way toward the enhancement of the channel capacity of mobile communication.
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1. Introduction
The current spectrum resources are exposed to the challenge of being overloaded on account of the boomingly developing wireless communication technology. The tendency of the communication rate approaching the limit of Shannon's formula is definite, and similarly, the improvement of the transmission capacity is held back by the predicament that multiplexing technology can hardly satisfy the demand of wireless communication. To figure out the solution to the issues, the Orbital Angular Momentum (OAM) [1–3] carried by vortex waves is engineered to provide support with the resources. OAM gaining great attention due to its excellent performance has found widespread applications in both optics and communications [4–8]. Moreover, it has been shown that the use of OAM can be extended to the field of radio frequency (RF). Since then, various types of research have been conducted on the realization of the efficient use of the OAM in the realm of wireless communication. The metasurface possesses distinct superiority in its properties of being ultra-thin, lightweight, and easy to manufacture, in comparison with traditional methods to obtain the beam with OAM in RF band, such as spiral phase plate (SPP) [9,10], spiral parabolic antenna and circular antenna array [11,12].
Metasurfaces, as a two-dimensional planar form of metamaterial, receive wide-ranging favor and concern from international and domestic researchers in virtue of their unique electromagnetic properties and planar structure [13–17]. Subsequent to the introduction of subwavelength components, metasurfaces have accomplished multiple functions that are scarcely possible to perform with conventional materials, such as a range of special effects, including negative refraction through manipulating reflected and refracted waves [18–22]. The results show that the flow of photons contains the nature of regulation and enables to bring about strange beam-bending phenomena to be observed experimentally. The manipulation of OAM beam is fulfilled by the utilization of phase mutation in metasurface, whose techniques, reflective, transmissive, digitally encoded and holographic metasurfaces included currently, with strong points in simple structure and low cost, exhibit the versatility of phase modulation that guarantees the equivalent effect of the focal lens, axial prism and paraboloidal control by phase compensation. A double-layer reflection structure proposed by Shen [23] of Southeast University in 2018 enables to tune OAM beam by means of converting the spherical incident wave into the phase distribution function of a plane wave, which reaches the divergence angle reduction but with the weakness of large size. In 2020, Lee [24] first adopted a single-layer perforated structure to converge OAM beams of modes 1 and 2 on the grounds of the variation in distribution obtained by the characteristics of the focal lens, achieving the result that the reflectance is below 1% in all parts due to its transmission performance which holds superiority over that of multilayer transmissive hypersurfaces. Bai [25] in the same year put forward a digital transmissive hypersurface with a center frequency of 7.5 GHz applying diodes and a controlled bias circuit for flexibly encoding the entire metasurface with 1 b on the basis of the vortex phase wavefront and focal lens phase compensation for a specific mode, realizing a convergent vortex electromagnetic wave with five modes of 0, ± 1, and ±2. This method overcomes the shortcomings of reflective digital hypersurface feeder obscuration and unsatisfactory phase difference stability and meanwhile raises the radiation efficiency and improves OAM purity.
To simultaneously radiate more OAM modes that allow these beams to be flexibly in the same or diverse directions under the same aperture becomes a requisite for figuring out an effective multiplexing approach. The generation of different patterns and the implementation of principles similar to those already employed in the design of bifocal reflector arrays can be reached by the superposition of aperture fields. The realization of two vortex beams with l = 2 and l = 4 and managing radiation angle optionally based on a single-layer reflection array via the phase superposition method is illustrated in Ref. [26]. Although the design of the dual-focus reflector array essentially allows the pointing direction to be changed within the pointing direction for the array design, it leads to a dilemma in the case of OAM: no other mode is available if the phase is provided only as a linear combination of the phases serving for producing the two specific modes. The idea of irradiating different regions of the array with diverse feeders for generating different OAM patterns in the composite structure, including the emitting array expounded in Ref. [27,28], remains more complex to implement and requires more hardware.
Circular polarized (CP) antennas which enable suppress multipath reflection and Faraday rotation, are widely used in satellite communications and radar. CP TM can be divided into two types: CP feed and linear polarization (LP) feed. The utilization of a CP feed proves to be the most basic and common approach, but the design of the CP feed itself is a complex matter. By applying LP feed that does not need the circular polarizer, the structure is simplified and the manufacturing cost is reduced. In [29], dual-band dual-circle polarized wave generation was achieved by placing u-patch cells with different parameters alternately. However, there is only one type of polarization for each band, LHCP/RHCP. In [30], double circularly polarized wave generation was realized through improving the structure of the Jerusalem cross, but the simultaneous generation of two arbitrarily directed beams could not be attained. The above research works only apply to the case where there is one RHCP wave or one LHCP wave in a band, and it is not yet possible to realize the case where both LHCP and RHCP waves are present.
This paper presents an approach to implement multi-mode OAM waves based on a line polarization-dual circular polarization converter. To achieve independent modulation of the phases of the LHCP and RHCP waves, a line polarization feed source is applied to serve as an incident wave to irradiate the metasurface, where its initial and rotational phases are jointly and separately controlled, and then the LHCP and RHCP waves are transmitted after a series of transmissions. When the phases of the LHCP and RHCP waves are respectively controlled to the OAM spiral phase of the desired mode, the generation of multi-mode vortex beams in the same aperture can be realized. Both simulation and measurement results in good consistency firmly demonstrate the feasibility of the designed method and reveal the excellent performance of the proposed TM. In the simulation, three sets of experiments are set up in simulation to verify the performance of the proposed TM for generating arbitrary beams, whose results indicate that the production of excellent vortex waves can be proceeded under arbitrary combinations of different modes and varying beam orientations. In the measurements, the proposed TM at 7.3 GHz enables generate LHCP vortex waves with l = 1 and RHCP vortex waves with l = −1 under the incidence of line polarized incident wave and the maximum gain can reach 19 dB with the minimum divergence angle of 8 degrees. The research in this paper enables generate two arbitrary beam-pointing CP waves simultaneously in a uniform aperture under the irradiation of LP feed source, which will greatly extend the application range of the device and adapt to the current increasingly complex electromagnetic spectrum environment. What's more, by applying the basis of this method for the generation of vortex beams, this technology can be introduced into short-range wireless communications and holograms, holding a highly promising application prospect.
2. Structure design and simulation
The TM element consisting of two identical layers of a dielectric substrate (F4B, ${\varepsilon _r} = 2.65,{\; }tan\delta = 0.009$) and three layers of metallic structure are depicted in Fig. 1. The upper and lower layers of the unit are set up as the transmitting and receiving layers, respectively, which are composed of double sector-loaded circular metal patches and are connected by metal posts that pass through the metal floor of the middle layer. For the purpose of reducing the influence of the metal ground on the current transmission in the metal posts, a circular ring is excavated in the metal ground of the middle layer and filled with a dielectric. Under the incidence of the incident wave on the receiving layer, it transmits energy through the metal column to the transmitting layer, where the incident wave gets re-radiation. The parameters of the element are listed in Table 1.
Fig. 1. Schematic diagram of the proposed transmissive metasurface. (a) Visual illustration of the TM consisting of 32 ${\times} $ 32 elements. Dual-mode dual-vortex beam (LHCP with l = 1 and RHCP with l = −1) generated by the line polarization feeder and TM. A diagram of the proposed super-surface multilayer structure is shown on the right. (b) Schematic diagram of the structure of each layer of the TM element.
Table 1. Parameter values of the element
The polarization conversion principle and the phase shift principle are discussed below.
When the TM unit is in the state as shown in Fig. 2(a), the y-polarized incident wave is incident on the receiving layer and the electric field can be expressed as:
The transmitted electric field can be formulated as follows:
The transmission layer is kept unchanged when the emission layer is rotated clockwise by an angle β, as shown in Fig. 2(b). When the new coordinate system is defined as ($x^{\prime},\; y^{\prime}$), the coordinate transformation matrix is:
Then the transmitted wave electric field can be represented as:
Equation (4) describes in detail the amplitude and phase of the LHCP and RHCP components of the transmitted wave, from which the phase information is extracted and expressed as:
Meanwhile, the transmission phase and the rotation phase can be expressed as:
Equation (5) illustrates that the phases of both LHCP and RHCP are comprised of the transmitted phase ${\varphi _i}$ and the additional rotational phase $\beta $, which implies that the separate modulations of LHCP and RHCP are able to be carried out when the transmitting phase ${\varphi _i}$ and the rotational phase $\beta $ are acting simultaneously. This feature is applied to contribute to the ideal target design of LHCP and RHCP and to make the phase information of which correspond to the transmission phase ${\varphi _i}$ and the rotation phase $\beta $ through using Eq. (6).
For both phase implementations, the transmission phase is achieved by means of changing the geometry of the metal patches on the receiving and transmitting layers of the TM unit, while the rotation phase is realized depending on rotating the metal patch of the transmitting layer to a certain angle. Eq. (6) notes that the condition that the phases of LHCP and RHCP cover 360° is indispensable for obtaining arbitrary design of LHCP and RHCP. Furthermore, it is imperative that ${\varphi _i}$ and $\beta $ satisfy the phase offset of 0° −360° and −180° −180°, respectively. How to meet the requirement of 360° phase coverage of the transmitted phase by adjusting the structure size becomes a critical issue on the foundation that the rotational phase offset range enables to be accomplished easily.
The proposed TM element is simulated using CST software, as shown in Fig. 3. Through multivariate analysis of the structural parameters, we conclude that a 360° shift of the transmission phase is achievable by simultaneously adjusting the values of R, α and γ. Figure 3(a) and (b) represent the phase and amplitude response of the TM element at nine states (phase spacing of 45°), with the structural dimensions of each state shown in Table 2. It is important to notice that the discrete points selected here do not affect the continuous tuning of our phase response in subsequent designs. It can be observed from the figures that the transmission amplitude remains at a high level (greater than 0.9) as the phase changes between the range of 7.0GHz-7.6 GHz. Moreover, the figures depict that the TM element exhibits the best amplitude and phase response at 7.3 GHz, and therefore we set the simulation frequency point to 7.3 GHz for the following simulation. Note that in the experiment of Fig. 3(b) we focus only on the circularly polarized wave component in the transmitted wave. Therefore, in comparison with the unitary characteristic of the amplitude changing with the rotation angle in the literature [31], this explains why the transmitted wave information shown in the figure of this paper only undergoes a phase change while the amplitude is close to constant when the beta is changed. In order to show more clearly the variation pattern of phase and amplitude with structural parameters, more parameter scan simulations are performed, as shown in Fig. 3(c) and (d). What the figures illustrate is that the transmission phase satisfies 360° phase shift with the adjustment of the parameters, and the phase and amplitude variations are depicted as well. The preponderance of regulating multiple variables simultaneously lies in the flexibility to optimize the transmission amplitude while allowing to change the phase. It is worth noting that when the annular metal patch of the receiver layer is rotated by 180°, the phase of the transmitted wave undergoes a phase jump of 180°. Consequently, the alteration of the receiving layer patch rotation angle γ is able to bring about a 360° phase shift. According to the research in literature [32], angular stability is one of the important indexes of metasurface performance. Two parameter metasurface elements (Mode 1 and Mode 5 in Table 2) are selected to simulate the angular stability. When theta varies from 0 ° to 30 °, the amplitude is less than 0.5 dB and the phase error is less than 30 °, as depicted in Fig. 3(e) and (f). Here, the error caused by oblique incidence is acceptable for metasurface array design.
Fig. 3. Magnitude and phase response of TM elements. (a) Amplitude and phase response of line polarization at the incidence of y-polarized wave. (b) Amplitude and phase response of circular polarization at the incidence of y-polarized wave. When (c)$\gamma = 0^\circ $ and (d) $\gamma = 180^\circ $, phase response of the LHCP transmitted wave at the incidence of y-polarized wave with the variation of α, R. Transmission magnitude and phase for different oblique incidence angles. (e) Mode 1. (f) Mode 5.
Table 2. Parameter values of the element
Independent operation of LHCP and RHCP is accomplishable via ingenious phase design based on using the proposed TM element to design TM array. Combined with the vortex beam generation theory, the generation of dual-mode dual-circularly polarized vortex waves under the same aperture surface can be realized. For vortex phase generation, the phase shift of each point (x, y) in the array is expected to fulfill the relationship with the pericenter azimuth:
where l is the preset number of vortex modes. In light of the principle of generating vortex beams from the metasurface, it is essential to add convergent compensating phases to the vortex phases considering the phase differences caused by the feed source positions. The phase to be provided by each element (i, j) of the metasurface array isRHCP and LHCP can be designed independently and arbitrarily for the beams on the basis of Eq. (5) and the previous discussion. Combining Eq. (8) for a reasonable design of the beam, the required phases of RHCP and LHCP for each element in the array can be obtained separately:
Aiming to verify the OAM beam performance of the proposed element, a $32 \times 32$ elements (384mm ${\times} $ 384 mm) metasurface is designed, and the phases of RHCP and LHCP are individually designed to achieve the results of dual-polarized arbitrary dual-mode. We put forward the assumption that the beam directions of LHCP and RHCP are set to (20°, 90°) and (20°, −90°) separately to illustrate the array phase design principle more vividly. The array phase design process is depicted in Fig. 4 in line with the array design theory described above. The angular values of the transmission phase ${\varphi _i}$ and rotation phase $\beta $ can be calculated by Eq. (6).
Fig. 4. Phase composition of LHCP and RHCP as well as the phase distribution of the generated ${\varphi _i}$ and $\beta $.
Three sets of experiments are set up to test the effectiveness of the TM on arbitrary beams generation, and the data of each set of experiments are shown in Table 3. The full-wave simulation is performed in CST for three groups of experiments at 7.3 GHz, utilizing a standard gain horn antenna serving as the line polarization feed source and excited by the waveguide port method. The boundary in the x and y directions is set to unit cell and the z direction is configured to open add space. The distance from the phase center of the waveguide antenna to the center of the TA aperture is fixed at F = 269 mm and F/D is 0.7. The simulation results are demonstrated in Fig. 4. From the simulated polar direction diagram exhibited in Fig. 5(a), the shape of the vortex beam is more ideal in the simulation results of the three sets of experiments, and the beam direction is highly consistent with the set target value. Moreover, the influence between the generated LHCP and RHCP beams is subtle from the simulation results. Figure 5(b) presents the near-field phase distribution of the two vortex beams in each set of simulations. The number of modes of the generated vortex waves can be read from the phase rotation direction and distribution.
Fig. 5. Simulation results. (a) Polar coordinate direction plot and (b) electric field amplitude and phase plot of Experiment 1. (c) Polar direction and (d) electric field amplitude and phase diagram of experiment 2. (e) Polar direction and (f) electric field amplitude and phase diagram of experiment 3.
Table 3. OAM modes and beam direction in the experiments
3. Fabrication and measurement
In the measurements, we chose the proposed parameters of the first set of experiments to design the metasurface array (experimental number 1 in Table 3), and a 32 ${\times} $ 32 (384mm ${\times} $ 384 mm) experimental sample was fabricated and measured in a microwave darkroom using the printed circuit board technique so as to demonstrate the performance of the proposed transmissive metasurface exhibited in experiments. The physical sample, the test scene and the measurement results are presented in Fig. 6, respectively. As can be seen from Fig. 6(c), measured results are in excellent agreement with the simulation results. The highest gain of both vortex beams is 19 dB, where the divergence angle of the LHCP vortex beam with l = 1 is 8 degrees and that of the RHCP vortex beam with l = −1 is 8.2 degrees. From Fig. 6(d), it can be observed that the angular neutral ratio in the beam direction is lower than 3 dB, and the lowest ratio enables to reach 0.48 dB, which indicates that the generated circularly polarized wave effect is ideal and consistent with the simulation results. The near-field measurements of the RHCP and LHCP beams are displayed in Fig. 6(e-h) separately. The near-field amplitude distribution exhibits a circular characteristic with lower central energy, while the near-field phase distribution exhibits a vortex characteristic, in which the phases of RHCP and LHCP appear an opposite trend, which is in conformity with the simulation results.
Fig. 6. Sample production and measurement results. (a) TM samples. (b) Test scenario. (c) Far-field orientation diagram of simulation and measurement. (d) Simulated and measured axial ratios. (e), (g) Measured near-field phase and electric field magnitude of LHCP. (f), (h) Measured near-field phase and magnitude of RHCP.
In addition, we give a comparison of our antenna with that of other representative works in literatures in the aspects of generated polarization, number of beams, and OAM modes, etc, as listed in Table 4. In comparison, the proposed metasurface in this paper possesses the ability to convert a linearly polarized incident wave into dual-circularly polarized wave as well as the advantage of flexible beam manipulation. The transmissive metasurface investigated in this paper holds a wide range of application scenarios in communication transmission. In addition, the proposed metasurface is capable of generating two independently controllable beams at 7.3 GHz simultaneously, and the designed array achieves orbital angular momentum with modes ${\pm} 1$ and ${\pm} 2$.
Table 4. Comparisons with other multi-mode OAM metasurface antennasa
4. Conclusion
In conclusion, this paper presents a method for the generation of independently controllable dual-mode vortex beams. The generation of dual-circularly polarized dual-mode vortex waves is achieved by using the proposed transmission metasurface with a double-layer substrate. It is demonstrated by a theoretical derivation that the introduced additional rotational phase and initial transmission phase can separate and independently control the LHCP and RHCP. Both simulations and measurements verify that the proposed TM is capable of generating a dual-mode vortex beam with mode number ${\pm} 1/{\pm} 2$ and that the beam direction possesses the feature of being designed arbitrarily. Additionally, both simulations and measurements validate the feasibility of the method and demonstrate the fine performance of the proposed TM, which meets the expected results. The proposed and demonstrated TM provides a reference for the generation of multi-mode vortex beams and may trigger potential applications in multiplatform wireless communication systems and multichannel imaging systems.
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.
References
1. P. Zheng, Q. Dai, Z. Li, Z. Ye, J. Xiong, H. Liu, G. Zheng, and S. Zhang, “Metasurface-based key for computational imaging encryption,” Sci. Adv. 7(21), eabg0363 (2021). [CrossRef]
2. X. Fang, H. Ren, and M. Gu, “Orbital angular momentum holography for high-security encryption,” Nat. Photonics 14(2), 102–108 (2020). [CrossRef]
3. H. Sroor, Y. Huang, B. Sephton, D. Naidoo, A. Valles, V. Ginis, C. Qiu, A. Ambrosio, F. Capasso, A. Forbes, F. Capasso, and A. Forbes, “High-purity orbital angular momentum states from a visible metasurface laser,” Nat. Photonics 14(8), 498–503 (2020). [CrossRef]
4. Y. Yan, G. Xie, M. P. J. Lavery, H. Huang, N. Ahmed, C. Bao, Y. Ren, Y. Cao, L. Li, Z. Zhao, A. F. Molisch, M. Tur, M. J. Padgett, and A. E. Willner, “High-capacity millimetre-wave communications with orbital angular momentum multiplexing,” Nat. Commun. 5(1), 4876 (2014). [CrossRef]
5. F. Tamburini, E. Mari, B. Thide, C. Barbieri, and F. Romanato, “Experimental verification of photon angular momentum and vorticity with radio techniques,” Appl. Phys. Lett. 99(20), 204102 (2011). [CrossRef]
6. J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012). [CrossRef]
7. M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015). [CrossRef]
8. X. Luo, “Subwavelength optical engineering with metasurface waves,” Adv. Opt. Mater. 6(7), 1701201 (2018). [CrossRef]
9. X. Hui, S. Zheng, Y. Hu, C. Xu, X. Jin, H. Chi, and X. Zhang, “Ultralow reflectivity spiral phase plate for generation of millimeter-wave OAM beam,” IEEE Antennas Wirel. Propag. Lett. 14, 966–969 (2015). [CrossRef]
10. Y. Chen, S. Zheng, Y. Li, X. Hui, X. Jin, H. Chi, and X. Zhang, “A flat-lensed spiral phase plate based on phase-shifting surface for generation of millimeter-wave OAM beam,” IEEE Antennas Wirel. Propag. Lett. 15, 1156–1158 (2016). [CrossRef]
11. Q. Bai, A. Tennant, and B. Allen, “Experimental circular phased array for generating OAM radio beams,” Electron. Lett. 50(20), 1414–1415 (2014). [CrossRef]
12. X. Hui, S. Zheng, Y. Chen, Y. Hu, X. Jin, H. Chi, and X. Zhang, “Multiplexed millimeter wave communication with dual orbital angular momentum (OAM) mode antennas,” Sci. Rep. 5(1), 10148 (2015). [CrossRef]
13. S. Li, Y. Li, L. Zhang, Z. Luo, B. Han, R. Li, X. Cao, Q. Cheng, and T. Cui, “Programmable controls to scattering properties of a radiation array,” Laser Photonics Rev. 15(2), 2000449 (2021). [CrossRef]
14. S. J. Li, B. W. Han, Z. Y. Li, X. B. Liu, G. S. Huang, R. Q. Li, and X. Y. Cao, “Transmissive coding metasurface with dual-circularly polarized multi-beam,” Opt. Express 30(15), 26362 (2022). [CrossRef]
15. B. Han, S. Li, Z. Li, G. Huang, J. Tian, and X. Cao, “Asymmetric transmission for dual-circularly and linearly polarized waves based on a chiral metasurface,” Opt. Express 29(13), 19643 (2021). [CrossRef]
16. Z. Li, W. Liu, H. Cheng, D. Y. Choi, S. Chen, and J. Tian, “Spin-selective full-dimensional manipulation of optical waves with chiral mirror,” Adv. Mater. 32(26), 1907983 (2020). [CrossRef]
17. Q. Song, S. Khadir, S. Vézian, B. Damilano, P. D. Mierry, S. Chenot, and P. Genevet, “Bandwidth-unlimited polarization-maintaining metasurfaces,” Sci. Adv. 7(5), eabe1112 (2021). [CrossRef]
18. R. Niemiec, C. Brousseau, K. Mahdjoubi, O. Emile, and A. Ménard, “Characterization of an OAM flat-plate antenna in the millimeter frequency band,” IEEE Antennas Wirel. Propag. Lett. 13(1), 1011–1014 (2014). [CrossRef]
19. N. Yu, P. Genevet, and M. A. Kats, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011). [CrossRef]
20. A. Díaz-Rubio, A. Asadchy, Elsakka, A. Tretyakov, and Sergei, “From the generalized reflection law to the realization of perfect anomalous reflectors,” Sci. Adv. 3(8), e1602714 (2017). [CrossRef]
21. F. Aieta, A. Kabiri, and P. Genevet, “Reflection and refraction of light from metasurfaces with phase discontinuities,” J. Nanophotonics 6(1), 063532 (2012). [CrossRef]
22. S. Zhang, H. Zhang, and B. Di, “Intelligent omnisurfaces: Ubiquitous wireless transmission by reflective-refractive metasurfaces,” IEEE Trans. Wirel. Commun. 21(1), 219–233 (2022). [CrossRef]
23. Y. Shen, J. Yang, H. Meng, W. Meng, and S. Hu, “Generating millimeter-wave Bessel beam with orbital angular momentum using reflective-type metasurface inherently integrated with source,” Appl. Phys. Lett. 112(14), 141901.1 (2018). [CrossRef]
24. I. Lee, A. Sawant, and E. Choi, “High-Directivity Orbital Angular Momentum Antenna for Millimeter-Wave Wireless Communications,” IEEE Trans. Antennas Propag. 69(7), 4189–4194 (2021). [CrossRef]
25. X. Bai, F. Kong, Y. Sun, G. Wang, and W. Zhu, “High-Efficiency Transmissive Programmable Metasurface for Multi-mode OAM Generation,” Adv. Opt. Mater. 8(17), 2000570 (2020). [CrossRef]
26. M. Beccaria, G. Dassano, and P. Pirinoli, “Single-Layer, Multimode OAM Reflectarray Antennas,” IEEE Antennas Wirel. Propag. Lett. 22(5), 980–984 (2023). [CrossRef]
27. B. Liu, S. -W. Wong, K. W. Tam, X. Zhang, and Y. Li, “Multifunctional Orbital Angular Momentum Generator with High-Gain Low-Profile Broadband and Programmable Characteristics,” IEEE Trans. Antennas Propag. 70(2), 1068–1076 (2022). [CrossRef]
28. E. Koohkan, S. Jarchi, A. Ghorbani, and M. Bod, “Vortex Beam Generation Based on Plasma Reflect-Array Surface at Microwave Frequencies,” IEEE Trans. Plasma Sci. 49(7), 2086–2092 (2021). [CrossRef]
29. Y. Cai, K. Li, W. Li, S. Gao, Y. Yin, L. Zhao, and W. Hu, “Dual-Band Circularly Polarized Transmitarray With Single Linearly Polarized Feed,” IEEE Trans. Antennas Propag. 68(6), 5015–5020 (2020). [CrossRef]
30. G. Wu, S. Qu, S. Yang, and C. Chan, “Broadband, Single-Layer Dual Circularly Polarized Reflectarrays With Linearly Polarized Feed,” IEEE Trans. Antennas Propag. 64(10), 4235–4241 (2016). [CrossRef]
31. H. Rajabalipanah, A. Abdolali, J. Shabanpour, A. Momeni, and A. Cheldavi, “Asymmetric Spatial Power Dividers Using Phase–Amplitude Metasurfaces Driven by Huygens Principle,” ACS Omega 4(10), 14340–14352 (2019). [CrossRef]
32. J. Shabanpour and C. R. Simovski, “Angular and Polarization Stability of Broadband Reconfigurable Intelligent Surfaces of Binary Type,” IEEE Access 10, 126253–126268 (2022). [CrossRef]
33. S. Li, Z. Li, G. Huang, X. Liu, R. Li, and X. Cao, “Digital coding transmissive metasurface for multi-OAM-beam,” Front. Phys. 17(6), 62501 (2022). [CrossRef]
34. C. Ji, J. Song, C. Huang, X. Wu, and X. Luo, “Dual-band vortex beam generation with different OAM modes using single-layer metasurface,” Opt. Express 27(1), 34–44 (2019). [CrossRef]
