Open Access
Add to BibSonomy
Abstract
Vortex beams (VBs) carrying orbital angular moment (OAM) modes have been proven to be promising resources for increasing communication capacity. Although considerable attention has been paid on metasurface-based VB generators due to the unprecedented advantages of metasurface, most applications are usually limited at a single band with a fixed OAM mode. In this work, an emerging dual-band reflection-type coding metasurface is proposed to mitigate these issues by newly engineered meta-atoms, which could achieve independent 2-bit phase modulations at two frequency bands. The proposed coding metasurface could efficiently realize and fully control dual-band VBs carrying frequency selective OAM modes under the linearly polarized incidence. As the first illustrative example, a dual-band VB generator with normal beam direction is fabricated and characterized at two widely used communication bands (Ku and Ka bands). Moreover, by encoding proper coding sequences, versatile beams carrying frequency selective OAM modes can be achieved. Therefore, by adding a gradient phase sequence to the first VB generator, the second one is designed to steer the generated beams to a preset direction, which could enable diverse scenarios. The measurement results of both VB generators agree very well with the numerical ones, validating the full control capability of the proposed approach.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterials, composed of artificially engineered periodic metallic/dielectric building blocks, have attracted great interest in the past few decades and yielded ground-breaking electromagnetic and photonic phenomena [1–4]. Metasurfaces are the two-dimensional (2D) counterparts of metamaterials, enabling complete modulations of the local phase, amplitude, and/or helicity of the electromagnetic wave at a thin interface [5–8]. Due to planar structuring, metasurfaces feature low cost fabrication and easy integration with other devices compared to bulky conventional photonics devices or 3D metamaterials. Therefore, many fascinating phenomena based on metasurfaces have been demonstrated, such as anomalous refraction/reflection [9,10], light focusing [11–13], spin hall effects [14–17], cloaking [18,19], polarization manipulations [20–25], and holograms [26–29]. However, the wavelength-dependent behavior of the metasurface caused by its dispersion nature is one of the critical limitations in the reported meta-devices, which greatly hinders the design freedom at different wavelengths. As a result, most of the previously reported metasurfaces usually function at one single band. In order to meet the growing requirement of multi-functional integration and/or multi-spectral analysis, the multi-wavelength/multi-functional metasurfaces are highly desirable and have been paid a lot of attention recently [30–41]. Among these multi-band metasurface designs, shared-aperture and spatial multiplexing methods are straightforward, but could lead to interleaving-induced efficiency reduction because only partial aperture is contributed to a particular wavelength.
Moreover, as an attractive degree of freedom for fundamental studies in many areas, vortex beams (VBs) could carry theoretically unbounded orthogonal orbital angular momentum (OAM) modes and possess unique characteristics of intensity and phase, playing significant roles in both optical and microwave fields including optical communication, spin-orbit interaction and imaging [42–44]. The conventional method for realizing VBs requires bulky components or un-even surfaces [45,46], which usually increases the system complexity and limits the integration capability. Since the emergence of metasurfaces, a large number of metasurface-based OAM beam generators have been reported [47–51]. However, most of them mainly work at one single band. Moreover, many broadband generators are demonstrated because the required phase distributions for generating the same OAM mode are identical at different frequencies. Recently, a few dual-band OAM beam generators mainly under the circularly polarized incidences are theoretically and experimentally demonstrated [32,35,36]. In addition to the circularly polarized incidences, linear polarization is also of great importance to use OAM in many applications, e.g., telecommunication and astronomy [44,52]. Therefore, the full controls of the dual-band metasurface-based VB generators carrying different OAM modes at two bands could be of particular interest under the linearly polarized incidence.
In this work, we propose a novel method for generating high-efficiency dual-band OAM beams based on the 2-bit reflective metasurface for the linearly polarized wave. The reflection-type or metal/insulator/metal structure is chosen due to the fabrication and assembly simplicities and high-efficiency. The building block (unit cell) of this metasurface consists of a top patterned metallic layer and a ground plane separated by a spacer. The top metallic layer is perforated with an annular slot and a circular hole in the center of the unit cell. Two C-shaped split-ring resonators (CSRRs) with the proper sizes are located in the annular slot and the hole for working at two frequencies independently. As proof of concept demonstrations, two dual-band OAM beam generators carrying two different modes are numerically investigated and experimentally verified at Ku and Ka bands. The first VB generator uses the traditional OAM coding sequences to generate the OAM beam with normal propagation direction carrying different modes at two different operation bands independently. Besides, by encoding proper extra coding sequences, versatile beams carrying frequency selective OAM modes can be achieved. Therefore, for the simplicity, by adding a gradient phase coding sequence to the first OAM generator, the OAM beams in the second one could be steered to the desired propagation direction(s) at two frequency bands, which could overcome the feed blockage issue and enable diverse scenarios. The experiment results are in good consistency with the full-wave simulation results and design goals, validating the proposed method. The proposed scheme could offer an alternative platform for designing dual-band high-performance meta-devices with independent linear polarization wavefront manipulations, which may enhance the information capacity of metasurface-based systems and enable versatile function integrations for advanced compact systems.
2. Design of metasurface unit cells
Figure 1 shows the schematic illustration of the two dual-band metasurface-based OAM generators that can operation at two arbitrary frequencies independently for the linearly cross-polarized reflective wave. Figure 1(a) demonstrates a dual-band metasurface-based OAM generator with normal reflected beams, which could lead to a feed blockage problem. While in Fig. 1(b), by encoding an extra gradient phase sequence, the reflected beams could be steered to the preset directions, which could enable different scenarios and overcome the feed blockage issue. Moreover, multi-beams carrying OAM modes could also be achieved [53] by encoding suitable phase sequences. The proposed dual-band OAM generators are composed of an array of the proposed unit cells depicted in Fig. 2(a). As can be seen from Fig. 2(a) that the unit cell consists of a top patterned metallic layer and a ground plane separated by a spacer of F4B (εr=2.2 and tanδ=0.002) with a thickness of 1.5 mm. The top view of the modified unit cell is depicted in Fig. 2(b) with the detailed parameters. The top metallic layer is perforated with an annual loop and a circular hole, and an outer (inner) CSRR is placed at the center of the loop (hole) to achieve the phase modulation at the lower (higher) frequency band. The outer radius, width and opening angle of CSRR in the hole (loop) are denoted as r1(r2), w1(w2) and α1(α2), respectively. The orientation of the inner (outer) CSRR with respect to the x-axis in the hole (loop) is β1(β2). The phase responses of the unit cell at two distinctive frequencies could be modulated by varying the geometric parameters (α1, α2, r1, r2, w1, w2). Moreover, an additional π phase shift can be achieved by changing the sign of the orientation of the CSRR or flipping the CSRR over x-axis [54,55]. In the designed metasurfaces, the two arbitrary operation frequencies are chosen as f1=18 GHz and f2=28 GHz. In order to verify the novel design and simplify the design process, some of the structure parameters are fixed as follows: w1= w2=0.2, r3=2.45, w3=0.5 and rc=1.7 (unit: mm). The periodicity of the unit cell p and the thickness of the metallic layer t2 are set to be 5 mm and 0.035 mm, respectively.
Fig. 1. Schematic illustration of the reflective metasurface-based OAM generator with (a) normal beam directions and (b) tilted beam directions.
Fig. 2. The (a) 3D view and (b) top view of the proposed building block; the simulated phase distributions at (c) 18 GHz and (d) 28 GHz for all 16 unit cells (the 2-bit phases before and after the slash are for 18 GHz and 28 GHz, respectively); the simulated amplitude distributions at (e) 18 GHz and (f) 28 GHz for all 16 unit cells.
In this dual-band design, the outer (inner) CSRR is adopted to operate at 18 GHz (28 GHz). To obtain 2-bit or four-level phase modulation with 90° phase interval at two frequencies, the geometric parameters of the unit cell are optimized by CST Microwave Studio, where the unit-cell is illuminated by a x-polarized wave and the reflected y-polarized wave is recorded. Besides, in the simulations, the orientation angles of the two CSRRs are set to be β1=β2=45° in order to achieve high reflection amplitude. The opening angles and radiuses for CSRR in the hole (loop) are optimized as α1 = [4°, 63°] and r1 = [2.3, 2.3] (α2 = [23°, 28°] and r2 = [1.5, 1.4]). Moreover, additional π phase shifts for the rest of unit cells can be obtained by simply changing the signs of β1 and β2. Then, the phase and amplitude responses for the 4×4 = 16 unit cells at 18 GHz (28 GHz) are plotted in Fig. 2(c) and Fig. 2(e) (Fig. 2(d) and Fig. 2(f)), respectively. It can be seen from Fig. 2(c) (Fig. 2(d)) that the four-level phase responses could be achieved at 18 GHz (28 GHz). Furthermore, Fig. 2(e) (Fig. 2(f)) demonstrates that the high cross-polarized reflection (larger than 78% at 18 GHz (75% at 28 GHz) in average) can be realized. Thus, it can be concluded from Fig. 2 that the independent 2-bit phase controls can be achieved at two frequencies with high efficiencies.
The performance of the proposed dual-band unit cell will be verified through the proof of concept demonstrations including two dual-band OAM beam generators with normal and tilted beams, which will be discussed in detail in the following sections.
3. Fabrication and measurement
First, a dual-band VB generator with normal beam direction is investigated by adopting the proposed unit cell, which can realize different/same OAM modes or topological charges at 18 and 28 GHz. A VB carrying OAM has a phase distribution of exp(jlФ) at the transverse plane [42], where l and Φ are the mode number and azimuthal angle, respectively. In order to realize an OAM beam with a mode of l, the required phase distribution at mnth element (x = mp, y = np) should satisfy the relationship with the azimuthal angle around the center as
where lj denotes the OAM mode number at frequency fj. Usually, the VB would diverge during the propagation. In order to obtain a compact beam radius along the propagation and increase the propagation length, the focusing factor is added into the VB generator, which could be of great benefit for the receiving system. The focusing phase factor can be expressed as where ${k_j} = {{2\pi } \mathord{\left/ {\vphantom {{2\pi } {{\lambda_j}}}} \right.} {{\lambda _j}}}$ is the propagation constant, F is an arbitrarily chosen focal length, which is set as 200 mm in this design.Therefore, the final phase distribution for a focusing OAM wave can be written as
Accordingly, the required digitized phase distributions for the focusing OAM VB with l1=−1 at 18 GHz and l2=+2 at 28 GHz are illustrated in Fig. 3(a), in which the phases will increase l1×2π and l2×2π along the black dashed line depicted in Fig. 3(a). The metasurface is composed of 41×41 unit cells with an overall dimension of 105×105 mm2. In addition, the designed dual-band VB generator is verified through both full-wave simulations via CST Microwave Studio and experiment. In the full-wave simulations, the open boundary conditions with vacuum space are applied at x-, y- and z-directions, and an x-polarized plane wave is used to illuminate the metasurface from + z-direction. The observation plane is set to be 200 mm above the metasurface with a size of 120×120 mm2. Figure 3(b) depicts the set-up for the measurement, where a feed antenna and a probe are used as the transmitter and receiver, respectively. The lens between the feed antenna and the metasurface converts the emitted spherical wave to a plane wave. Figure 3(c) (Fig. 3(d)) plots the simulated and measured near-field phase and intensity of the electric field (Ey) at 18 GHz (28 GHz). It can be seen from Fig. 3(c) that the two sets of results agree very well with each other and the features of spiral phase and amplitude null caused by the phase singularity can be clearly observed for l1=−1 at 18 GHz. As the rotation direction and number of the spiral arms are determined by the topological charge (i.e., sign and value), the OAM mode of l1 = −1 at 18 GHz can be identified by the diverse direction of rotation in the phase distribution from Fig. 3(c). Similar conclusions can be obtained from Fig. 3(d) for l2=+2 at 28 GHz.Fig. 3. (a) The required phase distributions for the metasurface-based vortex beam generator for l1=−1 at 18 GH and l2=+2 at 28 GHz; (b) the near-field measurement setup for charactering the metasurface-based vortex beam generator; the simulated and measured phase and intensity of the Ey field for (c) l1=−1 at 18 GHz and (d) l2=+2 at 28 GHz at the observation plane. (scale bar: 30 mm)
Moreover, to characterize the efficiency of the VB generator, we calculate the mode purity of the generated OAM beams based on the simulated phase profiles in Figs. 3(c) and 3(d), which could be obtained by decomposing the complex field on a complete basis set of Laguerre-Gaussian modes ($E_{l,p}^{LG}$) [56]. The calculated mode purities of the generated VB are plotted in Fig. 4(a) and Fig. 4(b) for 18 GHz and 28 GHz, respectively. It can be observed from Fig. 4(a) (Fig. 4(b)) that the dominated mode at 18 GHz (28 GHz) is −1 (+2) with a mode purity of 75% (80%). Some phase noise at other modes might be due to the quantization loss and fabrication tolerance.
Fig. 4. The calculated mode purity of the vortex beam generator for (a) l1=−1 at 18 GH and (b) l2=+2 at 28 GHz.
Next, we designed a second dual-band OAM beam generator with a tilted beam by adding a deflection factor. By further encoding a linear gradient phase along x-direction to the previous dual-band OAM beam generator, the beam could be steered to a desired direction along the x-direction and the final total phase distribution for the second beam generator can be expressed as [36]:
As illustrated in Fig. 5(a), a final phase mask pattern [M4] for the second VB generator is obtained by adding the deflection gradient phase with a deflection angle of 30° [M3] and focusing phase with a focal length of 200 mm [M1] to the OAM pattern [M2]. Accordingly, the final phase distribution for the vortex metasurface composed of 41×41 unit cells with l1=−1 at 18 GHz (l2=+2 at 28 GHz) is illustrated in Fig. 5(b) (Fig. 5(e)). Figure 5(c) and Fig. 5(d) (Fig. 5(f) and Fig. 5(g)) illustrate the corresponding far-field pattern and phase distribution of the field at 18 GHz (28 GHz) on the uv-plane ($u = \sin \theta \times \cos \varphi, \;v = \sin \theta \times \sin \varphi $) calculated by MATLAB, respectively. In the numerical calculations, each unit cell is modeled as a dipole-like subwavelength scatter with the corresponding discretized phase compensation at the cell center. Figure 5(c) clearly demonstrates that the main lobe appears at θ = 30° and Fig. 5(d) indicates that the OAM beam carries a mode of −1 at 18 GHz as designed. Similar conclusions can be obtained from Fig. 5(f) and Fig. 5(g) for l2=+2 at 28 GHz with a deflection angle of 30°.
Fig. 5. (a) Schematic diagram of the phase addition; (b) the final total phase distribution of the dual-band beam generator for (b) l1=−1 at 18 GHz and (e) l2=+2 at 28 GHz; the calculated (c) far-field scattering pattern and (d) phase distribution for l1=−1 at 18 GHz; the calculated (f) far-field scattering pattern and (g) phase distribution for l2=+2 at 28 GHz.
Full-wave simulations and experimental characterizations are also carried out to verify the second design. Figure 6(a) shows the measurement set-up, where the probe is positioned to receive the reflected wave with an angle (the beam tilting angle) from the metasurface. The amplitudes of the Ey on the XZ plane under the x-polarized normal incidence are plotted in Fig. 6(b). It can be observed from Fig. 6(b) that the reflected beams are deflected to around 30° with respect to the z-axis at both frequencies. In addition, Fig. 6(c) (Fig. 6(d)) displays the normalized simulated and measured near-field intensities and phase distributions of the Ey component on the observation plane (depicted in Fig. 6(b)) perpendicular to the beam direction at 18 GHz (28 GHz). It can be noticed from Fig. 6(c) that the two sets of results are in good agreement with each other and the ring-shaped intensity distribution and the spiral phase distribution demonstrate that the beam is a VB carrying OAM with a mode of l1 = −1 at 18 GHz. Once again, similar conclusions can also be drawn for the results at 28 GHz from Fig. 6(d). Therefore, it can be validated that we can fully control the VB generations by adding different patterns to the OAM metasurfaces.
Fig. 6. (a) The experimental set-up for charactering the OAM beam generator with tilted beam; (b) the near-field amplitude intensities of the beam generator at 18 GHz and 28 GHz on the XZ plane; the simulated and measured phase and amplitude intensity of beam generator for (c) l1=−1 at 18 GHz and (d) l2=+2 at 18 GHz at the observation plane depicted in (b). (scale bar: 30 mm)
4. Conclusion
In summary, we have proposed a novel reflective high-efficiency metasurface with independent 2-bit phase controls at two arbitrary frequencies under linearly polarized incidence. The novel dual-band metasurface unit cell is composed of a perforated top metallic layer printed on a substrate backed by a ground plane. The top patterned layer consists of an outer CSRR and an inner CSRR located at the centers of an annual slot and a circular hole, respectively. The 2-bit phase modulations at two preset frequencies can be achieved by varying the sizes of both CSRRs. Each one of the two CSRRs takes responsibility for generating one OAM mode at one operation band. Based on the proposed metasurface, two dual-band VB generators with normal and tilted beam directions are designed to work at 18 and 28 GHz. The first VB generator could reflect the incident wave back with normal radiation direction carrying OAM modes of −1 and +2 at 18 and 28 GHz, respectively. The designed metasurface-based VB generator is fabricated and characterized, and both the full-wave simulation and experiment results show good performance of the fabricated prototype, validating the proposed method. The second VB generator is achieved by adding an extra gradient phase sequence to steer the beams in order to eliminate the feed blockage effect in the first beam generator, which could further enable different environments. Correspondingly, the beam direction of the second VB generator could be steered to the targeted angle at each frequency. The designed device is also fabricated and characterized. The experiment results agree very well with the numerical investigations and design goals, showing the ability of full controls of the dual-band VB generation method. Since only one metallic layer of the metal/insulator/metal structure is patterned, the proposed metasurfaces could be of great benefit to realize full control of high efficiency and low-profile dual-band meta-devices in a convenient and low-cost way. The proposed concept could open up new possibilities for designing multifunctional meta-devices and be useful in many applications such as spatial mode multiplexing for communications, sensing and astronomy.
Funding
Natural Science Foundation of Shanghai (16ZR1445800); Shanghai Pujiang Program (18PJ1403200); Fundamental Research Funds for the Central Universities; National Science Foundation (1661749).
Acknowledgments
Mingbo Xin and Rensheng Xie contributed equally to this work.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
References
1. J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef]
2. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314(5801), 977–980 (2006). [CrossRef]
3. H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006). [CrossRef]
4. S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012). [CrossRef]
5. 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]
6. A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar Photonics with Metasurfaces,” Science 339(6125), 1232009 (2013). [CrossRef]
7. A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015). [CrossRef]
8. J. Li, S. Chen, H. Yang, J. Li, P. Yu, H. Cheng, C. Gu, H.-T. Chen, and J. Tian, “Simultaneous Control of Light Polarization and Phase Distributions Using Plasmonic Metasurfaces,” Adv. Funct. Mater. 25(5), 704–710 (2015). [CrossRef]
9. S. Sun, K.-Y. Yang, C.-M. Wang, T.-K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W.-T. Kung, G.-Y. Guo, L. Zhou, and D. P. Tsai, “High-Efficiency Broadband Anomalous Reflection by Gradient Meta-Surfaces,” Nano Lett. 12(12), 6223–6229 (2012). [CrossRef]
10. S. Liu, A. Noor, L. L. Du, L. Zhang, Q. Xu, K. Luan, T. Q. Wang, Z. Tian, W. X. Tang, J. G. Han, W. L. Zhang, X. Y. Zhou, Q. Cheng, and T. J. Cui, “Anomalous Refraction and Nondiffractive Bessel-Beam Generation of Terahertz Waves through Transmission-Type Coding Metasurfaces,” ACS Photonics 3(10), 1968–1977 (2016). [CrossRef]
11. X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light: Sci. Appl. 2(4), e72 (2013). [CrossRef]
12. R. Fleury, D. L. Sounas, and A. Alù, “Negative Refraction and Planar Focusing Based on Parity-Time Symmetric Metasurfaces,” Phys. Rev. Lett. 113(2), 023903 (2014). [CrossRef]
13. M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016). [CrossRef]
14. X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic Spin Hall Effect at Metasurfaces,” Science 339(6126), 1405–1407 (2013). [CrossRef]
15. A. Shaltout, J. Liu, A. Kildishev, and V. Shalaev, “Photonic spin Hall effect in gap-plasmon metasurfaces for on-chip chiroptical spectroscopy,” Optica 2(10), 860–863 (2015). [CrossRef]
16. Z. Li, W. Liu, H. Cheng, S. Chen, and J. Tian, “Manipulation of the Photonic Spin Hall Effect with High Efficiency in Gold-Nanorod-Based Metasurfaces,” Adv. Opt. Mater. 5(20), 1700413 (2017). [CrossRef]
17. S. Xiao, F. Zhong, H. Liu, S. Zhu, and J. Li, “Flexible coherent control of plasmonic spin-Hall effect,” Nat. Commun. 6(1), 8360 (2015). [CrossRef]
18. X. Ni, Z. J. Wong, M. Mrejen, Y. Wang, and X. Zhang, “An ultrathin invisibility skin cloak for visible light,” Science 349(6254), 1310–1314 (2015). [CrossRef]
19. Y. Yang, L. Jing, B. Zheng, R. Hao, W. Yin, E. Li, C. M. Soukoulis, and H. Chen, “Full-Polarization 3D Metasurface Cloak with Preserved Amplitude and Phase,” Adv. Mater. 28(32), 6866–6871 (2016). [CrossRef]
20. Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric Meta-Reflectarray for Broadband Linear Polarization Conversion and Optical Vortex Generation,” Nano Lett. 14(3), 1394–1399 (2014). [CrossRef]
21. X. Gao, X. Han, W. Cao, H. O. Li, H. F. Ma, and T. J. Cui, “Ultrawideband and High-Efficiency Linear Polarization Converter Based on Double V-Shaped Metasurface,” IEEE Trans. Antennas Propag. 63(8), 3522–3530 (2015). [CrossRef]
22. W. Liu, S. Chen, Z. Li, H. Cheng, P. Yu, J. Li, and J. Tian, “Realization of broadband cross-polarization conversion in transmission mode in the terahertz region using a single-layer metasurface,” Opt. Lett. 40(13), 3185–3188 (2015). [CrossRef]
23. Y. Chen, J. Gao, and X. Yang, “Direction-Controlled Bifunctional Metasurface Polarizers,” Laser Photonics Rev. 12(12), 1800198 (2018). [CrossRef]
24. K. Chen, G. Ding, G. Hu, Z. Jin, J. Zhao, Y. Feng, T. Jiang, A. Alù, and C.-W. Qiu, “Directional Janus Metasurface,” Adv. Mater. 32(2), 1906352 (2020). [CrossRef]
25. S. Xiao, J. Wang, F. Liu, S. Zhang, X. Yin, and J. Li, “Spin-dependent optics with metasurfaces,” Nanophotonics 6(1), 215–234 (2017). [CrossRef]
26. X. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4(1), 2807 (2013). [CrossRef]
27. G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015). [CrossRef]
28. L. Li, T. J. Cui, W. Ji, S. Liu, J. Ding, X. Wan, Y. B. Li, M. Jiang, C.-W. Qiu, and S. Zhang, “Electromagnetic reprogrammable coding-metasurface holograms,” Nat. Commun. 8(1), 197 (2017). [CrossRef]
29. D. Wen, F. Yue, G. Li, G. Zheng, K. Chan, S. Chen, M. Chen, K. F. Li, P. W. H. Wong, K. W. Cheah, E. Y. B. Pun, S. Zhang, and X. Chen, “Helicity multiplexed broadband metasurface holograms,” Nat. Commun. 6(1), 8241 (2015). [CrossRef]
30. F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015). [CrossRef]
31. E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “Multiwavelength polarization-insensitive lenses based on dielectric metasurfaces with meta-molecules,” Optica 3(6), 628–633 (2016). [CrossRef]
32. T. Wang, R. Xie, S. Zhu, J. Gao, M. Xin, S. An, B. Zheng, H. Li, Y. Lin, H. Zhang, G. Zhai, and J. Ding, “Dual-Band High Efficiency Terahertz Meta-Devices Based on Reflective Geometric Metasurfaces,” IEEE Access 7, 58131–58138 (2019). [CrossRef]
33. J. Ding, S. An, B. Zheng, and H. Zhang, “Multiwavelength Metasurfaces Based on Single-Layer Dual-Wavelength Meta-Atoms: Toward Complete Phase and Amplitude Modulations at Two Wavelengths,” Adv. Opt. Mater. 5(10), 1700079 (2017). [CrossRef]
34. R. Xie, G. Zhai, X. Wang, D. Zhang, L. Si, H. Zhang, and J. Ding, “High-Efficiency Ultrathin Dual-Wavelength Pancharatnam–Berry Metasurfaces with Complete Independent Phase Control,” Adv. Opt. Mater. 7(20), 1900594 (2019). [CrossRef]
35. K. Liu, G. Wang, T. Cai, B. Dai, Y. Xiao, H. Li, and W. Guo, “Dual-frequency geometric phase metasurface for dual-mode vortex beam generator,” J. Phys. D: Appl. Phys. 52(25), 255002 (2019). [CrossRef]
36. 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]
37. G. D. Bai, Q. Ma, S. Iqbal, L. Bao, H. B. Jing, L. Zhang, H. T. Wu, R. Y. Wu, H. C. Zhang, C. Yang, and T. J. Cui, “Multitasking Shared Aperture Enabled with Multiband Digital Coding Metasurface,” Adv. Opt. Mater. 6(21), 1800657 (2018). [CrossRef]
38. Z. Shi, M. Khorasaninejad, Y.-W. Huang, C. Roques-Carmes, A. Y. Zhu, W. T. Chen, V. Sanjeev, Z.-W. Ding, M. Tamagnone, K. Chaudhary, R. C. Devlin, C.-W. Qiu, and F. Capasso, “Single-Layer Metasurface with Controllable Multiwavelength Functions,” Nano Lett. 18(4), 2420–2427 (2018). [CrossRef]
39. B. Wang, F. Dong, Q.-T. Li, D. Yang, C. Sun, J. Chen, Z. Song, L. Xu, W. Chu, Y.-F. Xiao, Q. Gong, and Y. Li, “Visible-Frequency Dielectric Metasurfaces for Multiwavelength Achromatic and Highly Dispersive Holograms,” Nano Lett. 16(8), 5235–5240 (2016). [CrossRef]
40. R. A. Deshpande, F. Ding, and S. Bozhevolnyi, “Dual-Band Metasurfaces Using Multiple Gap-Surface Plasmon Resonances,” ACS Appl. Mater. Interfaces 12(1), 1250–1256 (2020). [CrossRef]
41. H.-X. Xu, G. Hu, M. Jiang, S. Tang, Y. Wang, C. Wang, Y. Huang, X. Ling, H. Liu, and J. Zhou, “Wavevector and Frequency Multiplexing Performed by a Spin-Decoupled Multichannel Metasurface,” Adv. Mater. Technol. 5(1), 1900710 (2020). [CrossRef]
42. L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96(16), 163905 (2006). [CrossRef]
43. Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-Orbital Angular Momentum Conversion in a Strongly Focused Optical Beam,” Phys. Rev. Lett. 99(7), 073901 (2007). [CrossRef]
44. 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]
45. 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,” Antennas Wirel. Propag. Lett. 14, 966–969 (2015). [CrossRef]
46. B. Allen, T. Pelham, Y. Wu, T. Drysdale, D. Isakov, C. Gamlath, C. J. Stevens, G. Hilton, M. A. Beach, and P. S. Grant, “Experimental evaluation of 3D printed spiral phase plates for enabling an orbital angular momentum multiplexed radio system,” R. Soc. Open Sci. 6(12), 191419 (2019). [CrossRef]
47. R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin-to–orbital angular momentum conversion of light,” Science 358(6365), 896–901 (2017). [CrossRef]
48. 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), 1351–1360 (2018). [CrossRef]
49. S. Jiang, C. Chen, H. Zhang, and W. Chen, “Achromatic electromagnetic metasurface for generating a vortex wave with orbital angular momentum (OAM),” Opt. Express 26(5), 6466–6477 (2018). [CrossRef]
50. G. Ding, K. Chen, T. Jiang, B. Sima, J. Zhao, and Y. Feng, “Full control of conical beam carrying orbital angular momentum by reflective metasurface,” Opt. Express 26(16), 20990 (2018). [CrossRef]
51. Y.-W. Huang, N. A. Rubin, A. Ambrosio, Z. Shi, R. C. Devlin, C.-W. Qiu, and F. Capasso, “Versatile total angular momentum generation using cascaded J-plates,” Opt. Express 27(5), 7469–7484 (2019). [CrossRef]
52. M. Harwit, “Photon Orbital Angular Momentum in Astrophysics,” Astrophys. J. 597(2), 1266–1270 (2003). [CrossRef]
53. S. Iqbal, H. A. Madni, S. Liu, L. Zhang, and T. J. Cui, “Full controls of OAM vortex beam and realization of retro and negative reflections at oblique incidence using dual-band 2-bit coding metasurface,” Mater. Res. Express 6(12), 125804 (2019). [CrossRef]
54. X. Zhang, Z. Tian, W. Yue, J. Gu, S. Zhang, J. Han, and W. Zhang, “Broadband Terahertz Wave Deflection Based on C-shape Complex Metamaterials with Phase Discontinuities,” Adv. Mater. 25(33), 4567–4572 (2013). [CrossRef]
55. J. Ding, N. Xu, H. Ren, Y. Lin, W. Zhang, and H. Zhang, “Dual-Wavelength Terahertz Metasurfaces with Independent Phase and Amplitude Control at Each Wavelength,” Sci. Rep. 6(1), 34020 (2016). [CrossRef]
56. P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012). [CrossRef]
