Open Access
Add to BibSonomy
Abstract
In the 1990s, it was recognized that light beams carrying orbital angular momentum (OAM) have benefited applications ranging from optical manipulation to quantum information processing. In recent years, attention has been directed towards the opportunities for communication systems due to the inspiring application potential in both the optical and microwave fields. In this paper, a polarization-independent quadri-channel vortex beam generator based on transmissive metasurface is proposed that can achieve selectivity of polarization, 2-bit OAM modes and spatial distribution in the quadri-channel simultaneously. The transmissive metasurface consists of four metallic layers and three dielectric layers and is designed, fabricated, and experimentally demonstrated to generate multi-mode and dual-polarization OAM vortex beams at 10.0 GHz. Orthogonal polarization and 2-bit information are carried by OAM modes +1, −1 + 2 and −2 and a different phase gradient is superimposed at each channel to realize beam steering, ensuring the accuracy and integrity of the information. The simulation and experimental results verify that the vortex beams with different OAM modes in dual polarizations can be flexibly generated by using transmissive metasurfaces. The proposed method and metasurface pave a way to add extra channels to create an additional set of data carriers for space-division multiplexing (SDM).
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metasurfaces, a 2D structure array composed of subwavelength unit cells, because of the usage of flexible artificial elements can provide independent control of both phases and amplitudes to the transmitted or the reflected electromagnetic (EM) waves. Because of these superior properties, metasurfaces have attracted tremendous attention and are under rapid development in recent years. Many metasurface structures have demonstrated wide applications, such as polarization conversion [1], abrupt phase shift [2], and modulations of phase and amplitude [3]. On the other hand, the concepts of digital coding and programmable metasurfaces have rapidly evolved since they were proposed for the first time in 2014 [4]. These metasurface structures created a new connection between the physical metasurface particles and digital codes through the binary codes “0” and “1” that can be realized by the reflection phases 0° and 180° in a coding unit cell. Different types of coding unit cells have been designed to create metasurfaces with various applications [5–10], such as self-adaptively reprogrammable functions [11], active amplifier [12,13], control of harmonic [14] and multichannel direct transmissions [15,16].
With the rapid growth of communication system and in the number of devices that are in use, more flexible hardware architectures, huge capacity of information channels and space-division multiplexing (SDM) in the theories of information and communication are urgently needed for satisfying the substantial demands of communication technology. In view of this, OAM generators based on metasurfaces [17–19] are considered to possess capacity to increase the communication channels in radio frequencies.
OAM can be described by a phase cross section of exp(ilθ), where topological charge l as any unbounded integers, which was first discovered in the 1990s [20–23]. OAM carries extra degree of freedom of angular momentum and unlimited information on the phase distributions of electric field, and the unusual attributes give rise to various applications, such as in optical communication [24,25]. Imaging [26], detection of rotating objects [27] and quantum information processing [28]. After the proposal in 2007 that OAM can be applied in lower frequencies [29], simulations and experiments of the OAM based on metasurface have been verified [30,31], demonstrating applications of OAM in radio frequencies. Some traditional antennas like slot antenna [32,33] and patch antenna [34,35] have been proposed to generate multiple OAM modes, however, feeding system or a complicated exciting circumstance were prohibited their practical applications. Some works about circular polarized vortex beams were generated based on Pancharatnam-Berry phase elements [36–38]. A wide operation bandwidth as the main feature, but there are some defects in the isolation of circular polarizations and transmission efficiency. Most metasurfaces composed of multi-layer structures are designed for linear polarizations recently, one or two modes are arranged on the metasurface for verification [39–41], therefore the mode number and communication ability of OAM is limited. Recently, a series of works on multiple vortex beam generation have been reported applying metasurfaces such as anisotropic [42] and single-layer [43] metasurface. These metasurfaces are reflectarrays, and in order to avoid the shelter of the feed, the vortex beam is designed with a deflection angle. The classic leaky-wave theory and a microwave holography method are also introduced to construct the surface waves carrying different OAM modes excited by a monopole antenna [44]. Broadband high-efficiency multiple vortex beams [45] with independent topological modes and inclination angles are generated, using an interleaved geometric-phase multifunctional metasurface. However, there is little work analyzing the multiple modes of OAM generated with transmissive metasurfaces, and the capacity of information they may carry. Multimode OAM generation with transmissive programmable metasurface [46–50] can be controlled flexibly. The state of elements itself lacks the degree of freedom, which makes it difficult to arrange the phases continuously. Besides, some physical properties about OAM are essential for modern optics [51,52], such as achromatic generation [53] and spin-decoupled metasurface [54].
In this paper, we propose a new method to represent a polarization-independent quadri-channel vortex beam generator based on transmissive metasurface. We present a vector beam modulator to carry the multichannel information in OAM modes based on orthogonal information coding method. The coding pattern in the orthogonal polarizations and OAM modes can be transmitted to the receivers with space-division multiplexing to satisfy huge capacity of communication channels. For this purpose, the information generator which has four metallic layers and three dielectric layers is proposed. A cross-dipole element is designed to transmit both x- and y-polarized EM waves, while controlling the transmissive phases independently, carrying orthogonal information and polarization coding bit simultaneously. Four different schemes are designed to obtain four information channels with different OAM modes, high transmission efficiency and complete phase control. The encoded OAM modes +1, −1 + 2 and −2 are carried to generate 2-bit information. In addition, different phase gradient is superimposed at each channel to realize the coding information in the spatial domain and the beam has a certain angle in space, so that the OAM information does not interfere with each other, ensuring the accuracy and integrity of the information. The designed scheme is fabricated, and the results in numerical simulations and experiments show excellent agreements, which verify the good performance of the proposed method. To sum up, coding information generator based on transmissive metasurface provides great potentials in considering to possess capacity to multiplex communication channels and digital communication systems.
2. Design rule: element design and working mechanism of the metasurface
As shown in Fig. 1, we design a transmissive coding metasurface illuminated by dual linear polarization incident waves, and the x-polarized incidences are depicted in the figure as an example. Four x-polarized waves are incident from the center of each channel. Then transmitted waves in x polarization are generated, carrying +1, −1, +2 and −2 modes of OAM, respectively. For y-polarized EM waves, the incident wave is carried out in the same way, and the corresponding transmitted y-polarized waves also carry four modes of OAM. Also, orthogonal property of the coding elements is investigated to construct a multilayer structure, for which two linear polarizations can be tuned independently with high isolation and efficiency. In view of the above, the proposed element is composed of three substrate layers with four cross-dipole metal layers printed on them, so as to satisfy the high-efficiency transmission and to complete the phase coverage.
Fig. 1. Conceptual illustration of the OAM generation based on metasurfaces. After four x-polarized waves illuminate to each center of the four channels, transmitted waves carrying four modes of OAM, with a deflecting angle with respect to z direction, are created. x-polarized waves are depicted for example, and the same consequence happens for y-polarized waves.
To realize the dual polarization and phase control, a kind of cross-dipole element is applied to construct the coding metasurface, as shown in Fig. 2. Each element is composed of three F4B (ɛr = 2.65) substrate layers with four cross-dipole metal layers on it. The geometrical parameters of the element are given in Fig. 2(a), in which w1 is 2.6 mm, w2 is 0.2 mm, p is 10 mm and the thickness of substrate and copper are 1.0 mm and 0.018mm, respectively.
Fig. 2. The geometry of coding elements and the relationships between the amplitude and phase. (a) Vertical view and (b) perspective view of the designed coding elements. (c) The phase and amplitude responses of the coding elements with respect to the length l in the dual-polarization. (d) Phase pattern of different length of lx and ly for x polarization. lx and ly represent different lengths of the elements in the x and y directions.
Tradeoffs between the manufacturing technique, transmissive phase and amplitude are made by adjusting the number of layers and necessary square loop. Here, the element about all cases of different number of layers and square loop is to give expression to the magnitude transmission and phase coverage in Fig. 3. Through data analysis as shown in Fig. 3, the amplitudes of transmissive coefficients of the element with square loop has visible advantage within major variation range of the length l.
Fig. 3. Transmission magnitude and phase versus length of l for cross-dipole elements with and without square loop under x-polarized incidence. The architecture of the element is as follows: (a) one layer element and one layer of medium, (b) two layers elements and two-layer medium, (c) three layers elements and two-layer medium and (d) four layers elements and three-layer medium.
Here, CST Microwave Studio is used to simulate the amplitude and phase of the element. The “unit cell” boundary conditions (BCs) are set in the ± x and ± y directions and the “open add space” condition is set in the ± z direction. The frequency domain solver is used in the sweep of parameters of the element. Furthermore, the condition of phase coverage has obvious distinctions compared with different architectures. Adjusting the architecture of elements, all conditions of range of phase variations in Fig. 3 are summarized in Table 1. One layer of cross-dipole element is hard to satisfy phase coverage, it can be found that the phase variation range has been increased to 87.4° from 48.7° by introducing the square loop in Fig. 3(a). When the architectures are one-layer dielectric cascaded with two layers of cross-dipole metal and two-layer dielectric cascaded with three layers of cross-dipole metal, the phase coverage is 69.2° and 169.4°, respectively. When the square loop is loaded, their phase coverage becomes 146.2° and 284.0°, as shown in Fig. 3(b-c). Finally, the result of four layers of cross-dipole metal cascading three layers of dielectric and loading square loop is 402.4° in comparison with 268.9° without square loop is illustrated in Fig. 3(d). Obviously, the proposed element structure with square loop has a significant increase in phase range, and with the number of layers increasing, transmission phase coverage is fulfilled. Therefore, a square loop has been introduced in four-layer elements, which provides a new freedom to cover a 360° phase-variation range and enhance transmission in Fig. 3.
Table 1. Range of phase coverage (abs value) for different cross-dipole layers with square loop or not. (units: degree)
Due to the orthogonal property of x- and y-polarizations, a high isolation can be achieved to realize multimode OAM waves. But under different length of cross-dipole, the performance of the structure will be affected by the inaccuracy of orthogonal information. This is because when the length of one direction changes (e.g., lx in the x direction or ly in the y direction), the phase information will change slightly from that of the case with lx = ly due to the difference in the length of the orthogonal directions. In the previous design, the structure length in one direction was fixed, and then the phase information was sampled under the change of the other length. Inspired by the method of symmetric sampling of information in our study, we propose a new strategy to control orthogonal information of elements through two orthogonal polarizations. The cross-dipole elements with uniform length l (l = lx = ly) are introduced to design a metasurface to realize OAM vortex beams in dual polarizations. The phase and amplitude responses of the coding elements with respect to the length l in the dual-polarization as shown in Fig. 2(c). Obviously, dual polarizations have phase coverage from 0 to 360°. More remarkably, the element phase responses for x- and y-polarized incident waves are the same, implying that this kind of element with the same length l in the orthogonal directions can work in both linear-polarization channels. Phase pattern of different lengths of lx and ly for x polarization is illustrated in Fig. 2(d). When the metal length of the main polarization is determined, its phase response can be hardly infected by the changing size of the orthogonal direction. This further verifies the good independence of the orthogonal polarization coding bit, which promises the accuracy of the information.
Different from the previously reported coding metamaterials, here we focus on the interaction and operation of informational representation based on the information coding method. In the coding principle of our work, orthogonality of polarization, mode of OAM and spatial information distribution are all embedded on the metasurface. Multiplexed orthogonal information can be independently controlled to exhibit their excellent performance on tailoring the OAM beams. The detailed configuration of four-channel schemes are introduced as illustrated in Fig. 4. The final phase distribution is composed of three parts: the compensation for spherical waves, the phase distributions for different OAM modes, and phase gradient in steps of −30°. Four horns are used as feed, with a focal length of 80 mm. The OAM modes transmitted in four channels (A, B, C and D) are modes +1, −1, +2 and −2, respectively. The coding patterns for OAM modes are given in Fig. 4(b), in which the related radiation patterns in the x and y polarizations are both obtained, synchronously. The phase rotates counterclockwise around the center, decreasing from 360° to 0°. The number of mode can be set to be either positive or negative. When there is only one round in the process of phase rotation around the center, it is defined as mode 1. If there are two rounds, it is mode 2. For example, in channel D, the phase rotates clockwise for two rounds, and it is defined as mode −2.
Fig. 4. (a) Phase comphensation for spherical waves. (b) Coding pattern for OAM modes. (c) Phase gradient. (d) Explanation of the phase gradient generation in B channel.
To generate an OAM beam, an azimuthal phase of ejlφ needs to be introduced to the transmissive wave, where l is the mode number and φ is the azimuthal angle. For the mn-th element of the whole transmissive metasurface, the required compensating phase can be obtained by the following equation as
As shown in Fig. 4, a cross-dipole element is designed to transmit both x- and y-polarized EM waves, while carrying orthogonal information. Four different channels are designed to obtain different OAM modes, high transmission efficiency and complete phase coverage. Furthermore, 2-bit information can be generated by OAM modes +1, −1 + 2 and −2. In addition, different phase gradient is superimposed at each channel to realize the encoding in the spatial domain and the beam has a certain angle in space with low influence to others, and in this way the accuracy and integrity of OAM information can be ensured. In brief, coding principle of polarization-independent quadri-channel vortex beam generator based on transmissive metasurface is demonstrated.
3. Simulation and experimental results
Subsequently, the finite difference time-domain (FDTD) technique is used to simulate the near-field performances of the proposed metasurface. Here, the simulated electric field results extracted in near-field region are performed using the CST Microwave Studio for four channels, as illustrated in Fig. 5. Subsequently, the finite difference time-domain (FDTD) technique is used to simulate the near-field performances of the proposed metasurface. Here, the simulation of electric field distribution in near-field region are performed using the CST Microwave Studio for four channels, as illustrated in Fig. 5. During the simulation of the metasurface, if the feed is placed in the + z direction and the metasurface is in the x-o-y plane, the boundary conditions in x and y directions are set to open. Open add space BC is adopted in the ± z direction. In addition, 300-mm spare space should be added in the direction of the transmitted wave so as to set up the E-field monitor. The near-field sampling plane is set at a distance 195 mm from the metasurface. The phase distributions of near electric field for x-polarization at 10 GHz are depicted in Fig. 5(a-d), and those for y-polarization are given in Fig. 5(e-h). The simulated near fields in Fig. 5 are investigated for the four channels carrying the OAM mode +1, −1 + 2 and −2 whose gradient phase distribution are given in Fig. 6(a-d), respectively. It can be found that a good purity of OAM modes has been demonstrated and the simulation results turn out to be convincing. The spatial phase distributions are illustrated clearly, which demonstrate the stable and reliable of our design.
Fig. 5. Simulated phase distributions of near electric fields of the four channels at the corresponding coding locations. a-d) Under incidence of x-polarized waves at 10 GHz, respectively. e-h) Under incidence of y-polarized waves at 10 GHz, respectively.
Fig. 6. The final gradient phase distribution of four channels. Channels A, B, C and D are designed to generate OAM modes +1, −1, +2 and −2, respectively. (e) The element distributions of the designed coding metasurface.
To verify the feasibility of the proposed work experimentally, the prototype is fabricated and measured at 10 GHz. Different views of the fabricated metasurface sample are shown in Fig. 7, in which acrylic sheet is used to support the metasurface by screws and fixed coaxial to waveguide transducers.
Fig. 7. Different views of the fabricated metasurface sample. a) Perspective view and b) front view of the fabricated metasurface. c) Supporting setup. d) The near-field experimental environment.
Distributions of two orthogonal polarized electrical fields are measured by the near-field scanning station. The magnitude and phase of near-field distributions were measured at 150 mm from the metasurface, in which the spatial phase distributions and amplitude nulls could be clearly observed in two polarizations. The feeding frequency ranges from 8 GHz to 12 GHz and the near-field sampling plane has a dimension of 400 mm×400 mm. The number of sampling points is 81×81. The measured magnitudes and phases of x- and y-polarizations are shown in Fig. 8 and 9, corresponding to the simulated phase distributions in Fig. 6(a-d) and (e-h), respectively. We conducted a total of 8 batches of measurement tasks, corresponding to four channels and two polarization modes. Each measurement channel must go through the manual angle adjustment of the metasurface on the support platform.
Fig. 8. Measured phase distributions in near fields of the four channels at the corresponding coding locations. a-d) Under incidence of x-polarized waves at 10 GHz, respectively. e-h) Under incidence of y-polarized waves at 10 GHz, respectively.
Fig. 9. Measured magnitude of E-field distributions at the corresponding coding locations. a-d) Under incidence of x-polarized waves at 10 GHz, respectively. e-h) Under incidence of y-polarized waves at 10 GHz, respectively.
The measured phase and magnitude for the metasurface under x-polarized waves at 10 GHz are depicted in Fig. 8(a-d) and Fig. 9(a-d), and those under y-polarized waves at 10 GHz are depicted in Fig. 8(e-h) and Fig. 9(e-h). The measured results of the proposed four channels carrying the OAM mode +1, −1 + 2 and −2 in both polarizations demonstrate that vortex beams with OAM modes produced by the transmissive metasurface is stable and reliable. In the simulation process, the metasurface is set to tilt so as to obtain the complete electric field distribution. The phase centers of x and y polarization are different, which results in a deviation of the two polarizations in the simulation process. In addition, losses in sample processing and deviations in the experiment will lead to the difference of the electric field distribution under different polarizations.
Figure 10(a) portrays the numerically calculated 3D far-field radiation patterns at 10 GHz, which incarnates OAM mode +1 under y-polarized wave. OAM mode −2 for x polarization as shown in Fig. 10(c). The desirable vortex effect is reinforced by high-directive OAM beam, clear central null field at the origin and very low reflection lobe level. The 2D radiation patterns were measured through the far-field measurement system in the anechoic chamber. From the radiation patterns on x-o-z plane shown in Fig. 10(b), OAM mode +1 is obtained when y-polarized wave incidents at 10 GHz, the measured results are in good agreement with the numerical calculation results, and OAM mode −2 under x-polarized has equally good results in Fig. 10(d). Figure 10 gives the simulated and measured far-field performance of this design. As is shown, for OAM mode +1 under y-polarized wave, the energy is concentrated in main lobe and the gain is 14.3 dB. For OAM mode −2 under x-polarized wave, the gain is 12.6 dB. In the experimental demonstration of the metasurface, we compared the measured gain with that of the standard gain horn. For OAM mode +1 under y-polarized wave and OAM mode −2 under x-polarized wave, the gains are 12.5 dB and 10.2 dB, respectively. The slight difference can be attributed to inevitable fabrication errors.
Fig. 10. The far-field performance of vortex beam generator. Simulated 3D radiation pattern of the metasurface: (a) OAM mode +1 under y-polarized wave and (c) OAM mode −2 under x-polarized wave at 10 GHz. Measured and simulated 2D radiation patterns at xoz plane: (b) OAM mode +1 under y-polarized wave and (d) OAM mode −2 under x-polarized wave at 10 GHz.
4. Conclusion
In this paper, a polarization-independent quadri-channel vortex beam generator based on transmissive metasurface has been firstly proposed and demonstrated in both simulation and measurement. Orthogonal polarization, 2-bit information that carried by OAM modes +1, −1 + 2 and −2, and different phase gradient is superimposed at each channel to realize the encoding in the spatial domain. Orthogonal polarization, 2-bit information are carried by OAM modes +1, −1 + 2 and −2 and different phase gradient is superimposed at each channel in the spatial domain, three advantages have been demonstrated with good performance. As expected, the numerical and experimental results show that the proposed transmissive metasurface works stable and reliable. It is noticeable that the presented working mechanism and designing strategy can be adapted to generate dual-polarizations and four modes of vortex beams, which enhances the multiplex-channel capacity further. The proposed polarization-independent quadri-channel vortex beam generator paves a way for possessing enhanced capacity to multiplex communication channels.
Funding
National Key Research and Development Program of China (2017YFA0700201, 2017YFA0700202); National Natural Science Foundation of China (61501112, 61522106, 61571117, 61601507, 61631007, 61701107, 61701108, 61722106, 61731010, 61735010, 61901508, 61971435, 61971437); 111 Project (111-2-05); the Fund for International Cooperation and Exchange of the National Natural Science Foundation of China (61761136007); the Graduate Scientific Research Foundation of Department of Basic Science.
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. L. Cong, W. Cao, X. Zhang, Z. Tian, J. Gu, R. Singh, J. Han, and W. Zhang, “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103(17), 171107 (2013). [CrossRef]
2. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011). [CrossRef]
3. X. Wan, B. G. Cai, Y. B. Li, and T. J. Cui, “Dual-channel near-field control by polarizations using isotropic and inhomogeneous metasurface,” Sci. Rep. 5(1), 15853 (2015). [CrossRef]
4. T. J. Cui, M. Q. Qi, X. Wan, J. Zhao, and Q. Cheng, “Coding metamaterials, digital metamaterials and programmable metamaterials,” Light: Sci. Appl. 3(10), e218 (2014). [CrossRef]
5. Q. Ma and T. J. Cui, “Information metamaterials: bridging the physical world and digital world,” PhotoniX 1(1), 1 (2020). [CrossRef]
6. Q. Ma, Q. R. Hong, X. X. Gao, H. B. Jing, C. Liu, G. D. Bai, Q. Cheng, and T. J. Cui, “Smart sensing metasurface with self-defined functions in dual polarizations,” Nanophotonics 9(10), 3271–3278 (2020). [CrossRef]
7. T. Qiu, X. Shi, J. Wang, Y. Li, S. Qu, Q. Cheng, T. Cui, and S. Sui, “Deep learning: a rapid and efficient route to automatic metasurface design,” Adv. Sci. 6(12), 1900128 (2019). [CrossRef]
8. E. Goi, Q. Zhang, X. Chen, H. Luan, and M. Gu, “Perspective on photonic memristive neuromorphic computing,” PhotoniX 1(1), 3 (2020). [CrossRef]
9. Z. Qiao, Z. Wan, G. Xie, J. Wang, L. Qian, and D. Fan, “Multi-vortex laser enabling spatial and temporal encoding,” PhotoniX 1(1), 13 (2020). [CrossRef]
10. Q. Ma, F. Yang, T. Y. Jin, Z. L. Mei, and T. J. Cui, “Open active cloaking and illusion devices for the Laplace equation,” J. Opt. 18(4), 044004 (2016). [CrossRef]
11. Q. Ma, G. D. Bai, H. B. Jing, C. Yang, L. Li, and T. J. Cui, “Smart metasurface with self-adaptively reprogrammable functions,” Light: Sci. Appl. 8(1), 98 (2019). [CrossRef]
12. L. Chen, Q. Ma, H. B. Jing, H. Y. Cui, Y. Liu, and T. J. Cui, “Space-energy digital-coding metasurface based on an active amplifier,” Phys. Rev. Appl. 11(5), 054051 (2019). [CrossRef]
13. Q. Ma, L. Chen, H. B. Jing, Q. R. Hong, H. Y. Cui, Y. Liu, L. Li, and T. J. Cui, “Controllable and programmable nonreciprocity based on detachable digital coding metasurface,” Adv. Opt. Mater. 7(24), 1901285 (2019). [CrossRef]
14. J. Y. Dai, J. Zhao, Q. Cheng, and T. J. Cui, “Independent control of harmonic amplitudes and phases via a time-domain digital coding metasurface,” Light: Sci. Appl. 7(1), 90 (2018). [CrossRef]
15. X. Wan, Q. Zhang, T. Yi Chen, L. Zhang, W. Xu, H. Huang, C. Kun Xiao, Q. Xiao, and T. Jun Cui, “Multichannel direct transmissions of near-field information,” Light: Sci. Appl. 8(1), 60 (2019). [CrossRef]
16. L. Chen, Q. Ma, Q. F. Nie, Q. R. Hong, H. Y. Cui, Y. Ruan, and T. J. Cui, “Dual-polarization programmable metasurface modulator for near-field information encoding and transmission,” Photonics Res. 9(2), 116 (2021). [CrossRef]
17. A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013). [CrossRef]
18. N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014). [CrossRef]
19. E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light: Sci. Appl. 3(5), e167 (2014). [CrossRef]
20. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992). [CrossRef]
21. L. Allen, M. J. Padgett, and M. Babiker, “IV The Orbital Angular Momentum of Light,” in Progress in Optics (Elsevier, 1999), 39, pp. 291–372.
22. G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105(15), 153601 (2010). [CrossRef]
23. A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66 (2015). [CrossRef]
24. 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]
25. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448 (2004). [CrossRef]
26. M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013). [CrossRef]
27. F. Tamburini, G. Anzolin, G. Umbriaco, A. Bianchini, and C. Barbieri, “Overcoming the Rayleigh Criterion Limit with optical vortices,” Phys. Rev. Lett. 97(16), 163903 (2006). [CrossRef]
28. J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329(5992), 662–665 (2010). [CrossRef]
29. M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a Spinning Object Using Light’s Orbital Angular Momentum,” 341, 5 (2013).
30. B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007). [CrossRef]
31. F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14(3), 033001 (2012). [CrossRef]
32. Q. Ma, C. B. Shi, G. D. Bai, T. Y. Chen, A. Noor, and T. J. Cui, “Beam-editing coding metasurfaces based on polarization bit and orbital-angular-momentum-mode bit,” Adv. Opt. Mater. 5(23), 1700548 (2017). [CrossRef]
33. L. Gui, M. R. Akram, D. Liu, C. Zhou, Z. Zhang, and Q. Li, “Circular Slot Antenna Systems for OAM Waves Generation,” Antennas Wirel. Propag. Lett. 16, 1443–1446 (2017). [CrossRef]
34. M. Wang, S. Xu, F. Yang, and M. Li, “Design and measurement of a 1-bit reconfigurable transmitarray with subwavelength H-shaped coupling slot elements,” IEEE Trans. Antennas Propag. 67(5), 3500–3504 (2019). [CrossRef]
35. H. Li, L. Kang, F. Wei, Y.-M. Cai, and Y.-Z. Yin, “A low-profile dual-polarized microstrip antenna array for dual-mode OAM applications,” Antennas Wirel. Propag. Lett. 16, 3022–3025 (2017). [CrossRef]
36. B. Liu, Y. Cui, and R. Li, “A broadband dual-polarized dual-OAM-mode antenna array for OAM communication,” Antennas Wirel. Propag. Lett. 16, 744–747 (2017). [CrossRef]
37. K. Zhang, Y. Yuan, D. Zhang, X. Ding, B. Ratni, S. N. Burokur, M. Lu, K. Tang, and Q. Wu, “Phase-engineered metalenses to generate converging and non-diffractive vortex beam carrying orbital angular momentum in microwave region,” Opt. Express 26(2), 1351 (2018). [CrossRef]
38. S. Tang, T. Cai, J.-G. Liang, Y. Xiao, C.-W. Zhang, Q. Zhang, Z. Hu, and T. Jiang, “High-efficiency transparent vortex beam generator based on ultrathin Pancharatnam–Berry metasurfaces,” Opt. Express 27(3), 1816 (2019). [CrossRef]
39. M. R. Akram, G. Ding, K. Chen, Y. Feng, and W. Zhu, “Ultrathin single layer metasurfaces with ultra-wideband operation for both transmission and reflection,” Adv. Mater. 32(12), 1907308 (2020). [CrossRef]
40. X. Qi, Z. Zhang, X. Zong, X. Que, Z. Nie, and J. Hu, “Generating dual-mode dual-polarization OAM based on transmissive metasurface,” Sci. Rep. 9(1), 97 (2019). [CrossRef]
41. F. Qin, L. Wan, L. Li, H. Zhang, G. Wei, and S. Gao, “A transmission metasurface for generating OAM beams,” Antennas Wirel. Propag. Lett. 17(10), 1793–1796 (2018). [CrossRef]
42. L. Zhang, J. Guo, and T. Ding, “Ultrathin dual-mode vortex beam generator based on anisotropic coding metasurface,” Sci. Rep. 11(1), 5766 (2021). [CrossRef]
43. 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]
44. D. Zhang, Z. Lin, J. Liu, J. Zhang, Z. Zhang, Z. Hao, and X. Wang, “Broadband high-efficiency multiple vortex beams generated by an interleaved geometric-phase multifunctional metasurface,” Opt. Mater. Express 10(7), 1531–1544 (2020). [CrossRef]
45. X. Meng, J. Wu, Z. Wu, L. Yang, L. Huang, X. Li, T. Qu, and Z. Wu, “Generation of multiple beams carrying different orbital angular momentum modes based on anisotropic holographic metasurfaces in the radio-frequency domain,” Appl. Phys. Lett. 114(9), 093504 (2019). [CrossRef]
46. M. L. N. Chen, L. J. Jiang, and W. E. I. Sha, “Ultrathin complementary metasurface for orbital angular momentum generation at microwave frequencies,” IEEE Trans. Antennas Propag. 65(1), 396–400 (2017). [CrossRef]
47. X. Bai, F. Kong, Y. Sun, G. Wang, J. Qian, X. Li, A. Cao, C. He, X. Liang, R. Jin, and W. Zhu, “High-efficiency transmissive programmable metasurface for multimode OAM generation,” Adv. Opt. Mater. 8(17), 2000570 (2020). [CrossRef]
48. Z. Lin, Z. Ba, and X. Wang, “Broadband high-efficiency Electromagnetic orbital angular momentum beam generation based on a dielectric metasurface,” IEEE Photonics J. 12(3), 1–11 (2020). [CrossRef]
49. F. Bi, Z. Ba, and X. Wang, “Metasurface-based broadband orbital angular momentum generator in millimeter wave region,” Opt. Express 26(20), 25693–25705 (2018). [CrossRef]
50. S. Tang, X. Li, W. Pan, J. Zhou, T. Jiang, and F. Ding, “High-efficiency broadband vortex beam generator based on transmissive metasurface,” Opt. Express 27(4), 4281–4291 (2019). [CrossRef]
51. F. Feng, G. Si, C. Min, X. Yuan, and M. Somekh, “On-chip plasmonic spin-Hall nanograting for simultaneously detecting phase and polarization singularities,” Light: Sci. Appl. 9(1), 95 (2020). [CrossRef]
52. Y. Shen, X. Wang, Z. Xie, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, “Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities,” Light: Sci. Appl. 8(1), 90 (2019). [CrossRef]
53. Y. Guo, S. Zhang, M. Pu, Q. He, J. Jin, M. Xu, Y. Zhang, P. Gao, and X. Luo, “Spin-decoupled metasurface for simultaneous detection of spin and orbital angular momenta via momentum transformation,” Light: Sci. Appl. 10(1), 63 (2021). [CrossRef]
54. 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]
