Abstract

Vortex electromagnetic (EM) waves hold promise for their ability to significantly increase the transmission capacity of wireless communication systems via the torsion resistance defined by different topological charges associated with the orbital angular momentum (OAM). However, the application of vortex waves in remote distance transmission is limited by its characteristic of divergence. In this paper, a lens based on a phase-modulation metasurface (MS) is proposed that enables vortex EM waves to converge, thereby improving their propagation performance at microwave frequencies. A phase-shift distribution on the plane of the MS is obtained based on the concept of the optical converging axicon, which can convert a Laguerre-Gaussian (LG) beam to a Bessel beam based on changing the propagation direction. Simulation results verify the ability of the MS lens to achieve OAM beam focusing, which is advantageous for enhancing the propagation directivity and increasing the gain in the main lobes of vortex waves. This is of particular importance in microwave wireless communication applications.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Vortex waves carrying orbital angular momentum (OAM) have received a considerable amount of attention both in the optical and radio frequency domains due to their potential for increasing the spectral efficiency and channel capacity of wireless communications [1]. In 2007, the first attempt was made to demonstrate OAM in the microwave frequency regime, which proved that antenna arrays can be used to generate vortex EM waves with similar characteristics to Laguerre-Gauss vortex beams in the near-axis direction [2]. In 2011, Professor Bo Thidé of the Swedish Institute of Space Physics and his team of Italian colleagues conducted a seminal experiment in the lagoon of Venice [3]. The experiment used a Yagi and a spiral parabolic antenna to send uniform plane waves and vortex EM waves, respectively, realizing that the two signals were transmitted simultaneously in the same frequency band [4, 5]. By exploiting the orthogonality between different OAM modes, vortex EM waves can transfer more information than general electromagnetic waves without transmission bandwidth. Consequently, OAM vortex waves have become an important research focus in wireless communications [6, 7]. However, OAM based EM waves are hollow and divergent. In addition, the degree of the divergence increases as the order of the OAM-mode and the propagation distance increases. This shows that OAM based EM waves are not well-suited for long distance communication. Therefore, it is an important topic of research is to investigate effective methods of creating converging vortex EM waves.

In optics, non-diffractive Bessel beams have become the subject of intense research due to their unique properties including small center spots, unchanged intensity distribution during transmission, highly focused light intensity and self-reconstruction [8]. Because of their advantages of structural simplicity, high conversion efficiency, and high light damage threshold, axicon devices are widely used to experimentally generate Bessel beams. Furthermore, a new method for transformation of a Laguerre-Gaussian beam to a vortex, non-divergent Bessel beam by a helical axicon was proposed in [9,10]. Recently, a lens with a gradient-index was proposed to focus microwave radiation [11–13], which has a subwavelength thickness and a high focusing strength. In addition, the results in [14] showed that a flat MS with a parabolic reflection-phase distribution can focus an impinging plane EM wave to a point image in the reflection geometry. However, the limitation of this lens is that it is only capable of focusing an incident plane wave to a point image relatively close to the lens rather than at a long distance away from it.

A metasurface is a type of composite material composed of artificial subwavelength structures that are typically periodic, which can realize nearly arbitrary control of EM waves (e.g., phase, polarization, propagation) according to its unit cell structure [15]. In optics, a high efficiency all-silicon MS is proposed in [16], which presents good transmission coefficient over a wide bandwidth. An all-metallic MS with high reflection coefficient has also been proposed to control optical beams over a wide bandwidth in [17]. In recent years, MSs have been widely used in conjunction with antennas to increase their performance. In 2011, a V-type antenna structure was proposed to achieve phase control for realizing anomalous transmission and reflection of EM waves [18]. Based on the electromagnetic resonance mechanism, artificial EM materials can, in principle, acquire almost any equivalent permittivity and permeability, which far exceeds the range of parameters available in natural materials. Therefore, MSs are utilized to achieve unprecedented control of EM waves (both radiation intensity and phase distributions). Currently, MSs have important potential applications in stealth technology, antenna technology, microwave and terahertz devices, optoelectronic devices and many other fields [19,20].

In this paper, inspired by the phase-modulation of incident waves on an optical axicon lens [8], we propose a MS lens which is able to converge vortex EM waves. On the basis of the EM wave vector direction, the transmissive-type MS corresponds to the mirrored axicon, modulating the phase across a specific plane instead of a circular conical surface. The formula for determining the required phase-compensation is derived and then applied to design the MS. Ultimately, the numerical simulation results show that the MS converging lens is effective for minimizing the angle of the main lobe while improving the gain of the vortex beams without changing the original spiral phase wavefront.

2. Metasurface lens design

The transformation of a divergent LG beam to a convergent Bessel beam via a mirrored axicon lens is schematically shown in Fig. 1(a). The transformation function of the axicon lens is given in [9], which can be described by Eq. (1):

T(γ)=exp(iαγ)
where the axicon parameter α = k(n − 1)θ is related to the refractive index n for the incident beam of wavelength λ and its internal angle (the angle measured from the axicon base) θ, and the wave number k. By appropriately adjusting the phase distribution on mirrored axicon, the direction of the incident wave has been changed to parallel to the z-axis.

 figure: Fig. 1

Fig. 1 (a) Theoretical transformation of LG beam into Bessel beam by axicon. (b) Schematic view of the vortex EM wave convergence system.

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To achieve the desired convergence property of vortex EM waves, a flat phase-modulated MS lens, which is equivalent to a mirrored axicon lens, is proposed here for use in the microwave domain as shown in Fig. 1(b). By propagating through the MS lens, the vortex wave emitted from a patch antenna array source experiences a non-uniform (inhomogeneous) phase-shift that locally transforms the propagation direction of the incident wave to realize the desired convergent effect.

Suppose we consider the transmission MS lens, which is formed from an M×N array of elements. The transmission function of the MS, which provides the required inhomogeneous phase delay, is given by:

T(m,n)=F(γomn)exp(ilφ+ik|γmnγo|sinθ).
where F is the antenna source pattern function, γomn is the distance between the antenna and mnth element, l is the OAM mode number, k is the wave number, and γmn, γo are the position of the mnth element and the center point of the MS lens, respectively. The angle θ is measured between the electric field transmitting direction of the vortex EM wave and the propagation axis. The numerical value of the desired compensative phase value on the mnth element can be obtained from
ϕmnd=2π|γmn|sinθλ

Theoretically, the distribution of compensative phase shown in Fig. 2(a) can be calculated by using the non-relativity approximation equation for the wave number. The effect of mutual coupling between elements can be ignored in the application of the superposition principle for electromagnetic fields during the evaluation procedure. The desired phase-shift on the MS lens can be calculated in terms of a quasi-continuous phase change based on the sub-wavelength element design. The discrete phase distribution on a MS lens consisting of 16×16 elements is displayed in Fig. 2(b).

 figure: Fig. 2

Fig. 2 Calculated phase distribution required on the MS for compensation.

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Next, the unit cell structure of the MS shown in Fig. 3(b) is designed in order to provide the desired phase distribution. Each element, consisting of four layers of uniform square metallic patches with a cross slotted central metallic patch, is simulated at 10 GHz using the HFSS software. The periodicity P = 0.3λ = 9 mm, and the distance between each layer is t = 0.05λ = 1.5 mm. The slot length and width is 6.5 mm and 0.5 mm respectively. The length of square patches varies from 1 to 7 mm. The metallic parts composing the metasurface are printed on a low loss Arlon AD350ATM substrate having dielectric constant, εr = 3.5 and tangential losses, tan δ = 0.003. The HFSS simulation results of the unit cell shown in Fig. 3(d) indicate that the unit cell can realize a full transmission phase range of 406°, while maintaining the transmission coefficient to be better than −3 dB. Based on the square and cross-slot patch elements, the transmission MS lens with 16×16 elements was designed to focus vortex EM waves at 10 GHz. The final lens design is square with dimension of 14.4×14.4 cm2, as shown in Fig. 3(a).

 figure: Fig. 3

Fig. 3 (a) Top view of the MS lens. (b) Top and perspective views of a square elementary cell. The different geometrical dimensions are: t = 1.5 mm, P = 9 mm, g = 0.5 mm, S = 3.5 mm and l = 6.5 mm. (c) Transmission phase and amplitude of the unit cell 10 GHz. (d) Absorptivity at 10 GHz of the unit cell under different incidence angles. (e) Transmissivity at 10 GHz of the unit cell under different incidence angles.

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From Fig. 3(d), it can be observed that the absorption of the material gradually increases as the incident angle increases. When the incidence angle reaches 80°, the curve of absorption rate changes drastically with geometric parameter S. As shown in Fig. 3(e), the transmission performance of the cell structure also deteriorates as the incident angle increases. When comparing absorptivity and transmission performance as incidence angle changes from 0 to 80°, we observe that the losses of unit cell mainly stem from the low diffraction efficiency at high incidence angles.

3. Numerical verification of proposed converging lens system

In order to verify the proposed MS converging lens, we use the HFSS software to simulate its performance by employing the finite element method. The converging lens system is excited by a circular patch antenna array source consisting of 8 patches with the same phase shift between each of the neighboring elements. The proposed converging lens is placed at a distance 2λ above the antenna source.

Theoretically, efficient convergence can be achieved as long as the radiated beams are not diffracted by the lens. As shown in the Fig. 4, side-lobes level appears for D = 30 mm, 45 mm, 60 mm, and little diffraction also appears on the edges of the MS lens due to small size. However, according to the angle between main lobe and z axis, we can observe that more efficient convergence is obtained with D = 60 mm above the antenna source. So, we chose D = 60 mm to place the MS lens. The performance of the antenna and the converging lens system are both verified over a frequency band varying from 9.3 GHz to 10.3 GHz.

 figure: Fig. 4

Fig. 4 E-field amplitude distribution in the x–z plane of the lens antenna system at 10 GHz for different distance between source and MS lens. (a) D = 30 mm. (b) D = 45 mm. (c) D = 60 mm.

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The amplitude profiles at three different frequencies in the x–z plane perpendicular to the beam axis for the antenna and MS converging lens are presented in Fig. 5. The ability of the antenna to generate a vortex EM wave with topology charge +1 is simulated and presented in Figs. 5(a)–5(c) at 9.3 GHz, 10 GHz, and 10.3 GHz, respectively, which display the vortex EM field amplitude distribution for ϕ = 0 (ϕ is the azimuthal angle of the spherical coordinate system). By further comparing the electric field amplitude distribution of the converging lens to the antenna only, the divergence angle of the main lobe is obviously minimized as shown in Figs. 5(d)–5(f), which also demonstrates that the MS lens operates over a frequency band ranging from 9.3 GHz to 10.3 GHz. Theoretically, the achieved bandwidth is relatively narrow since resonant materials are employed in the design.

 figure: Fig. 5

Fig. 5 Numerical simulation results of the antenna and MS converging lens. (a)–(c) E-field amplitude distribution of the antenna without lens for ϕ = 0 at 9.3 GHz, 10 GHz, and 10.3 GHz. (d)–(f) E-field amplitude distribution of the MS lens antenna source for ϕ = 0 at 9.3 GHz, 10 GHz, and 10.3 GHz.

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The EM field expression indicates that the intensity distribution in the cross-section of the vortex has a donut shape. In Fig. 6, we present the E-field distribution of the source and converging MS lens antenna in the x–z plane at z = 90 mm, 120 mm, and 150 mm with a fixed 2λ distance between the source and MS lens antenna system. A hollow characteristic of the vortex beam results and the divergence angle increases rapidly as the wave propagates further from the source, which can be observed in Figs. 6(a)–6(c). For the MS converging lens, the donut shape of the E-field magnitude distribution at the three different positions are all similar as shown in Figs. 6(d)–6(f), which demonstrates the superior convergence properties of the lens.

 figure: Fig. 6

Fig. 6 Simulated E-field amplitude distribution for z = 90 mm, 120 mm, and 150 mm in the x–y plane at 10 GHz. (a)- (c) Source alone. (d)-(f) Converging MS lens antenna system. The beam of the vortex wave generated by the source is efficietnly converged after transmitting through the lens.

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The phase distribution of the vortex beam is presented in Fig. 7. As a basis for comparison, the theoretical and simulated phase distributions of the antenna and MS converging lens antenna at z = 70 mm are shown in Figs. 7(a) and 7(b), and Figs. 7(c) and 7(d) respectively. The consistency between simulation and theory strongly indicates that the MS converging lens does not change the vortex characteristics of the electromagnetic waves.

 figure: Fig. 7

Fig. 7 (a), (c) Theoretical phase distributions of the antenna array source and MS converging lens, respectively, for the EM field component in the x–y plane. The cross-section is 70mm away from the feed plane, and the phase changes from − π (blue) to π (red). (b), (d) Simulated phase distributions of the antenna and MS converging lens at 10 GHz, respectively, for the EM field component in the x–y plane.

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The 3D simulations for the source and MS converging lens antenna at 9.3 GHz, 10 GHz, and 10.3 GHz are presented in Fig. 8. By comparing of the radiation patterns obtained for the source and converging lens antenna system, it can be observed that the angle between the main lobe and the propagation axis is significantly reduced from about 50° to 18°, and the gain of the main lobe is also considerably increased from 9 dBi to 15 dBi. This is also confirmed by the 2D gain curves in Figs. 8(c), 8(f) and 8(i).

 figure: Fig. 8

Fig. 8 Numerical simulation results of the antenna array source and converging MS lens lens antenna system at 9.3 GHz, 10 GHz and 10.3 GHz. (a), (d), and (g) 3D far-field gain patterns of the antenna array source. (b), (e), and (h) 3D far-field gain patterns of the MS converging lens antenna. (c), (f), and (i) 2D gain patterns of the antenna array source and MS converging lens antenna.

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The convergence functionality of the lens is further tested for other topological charges at 10 GHz. In Fig. 9, the E-field distribution of vortex waves with topological charges of +2 and +3 are verified. One can easily observe that, through the lens, the divergence angle of the antenna is significantly minimized and the energy in the main lobe is considerable increased, which verifies the excellent convergence efficiency of the MS lens for multiple mode vortex waves.

 figure: Fig. 9

Fig. 9 E-field magnitude distribution of a vortex wave with topological charge of +2 and +3 at 10 GHz. (a)–(b) Antenna array source. (c)–(d) Lens antenna system.

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The transmission losses between lossless MS lens and lossy MS lens from 9.9 GHz to 10.2 GHz are shown in the Fig. 10(a). The inherent losses of the selected substrate is 0.003, and the transmission loss ranges from 0.36 dB to 0.48 dB, indicating that the losses of the MS lens are acceptable. The transmitted efficiency of the MS lens antenna is calculated as follows:

η=PlensPsource×100%.
where Plens is the power transmitted by the MS lens antenna at z = 70 mm, and Psource is the power emitted by the source and incident on the lens.

 figure: Fig. 10

Fig. 10 (a) Transmission losses (dB) resulting from the use of a low-loss substrate and (b) efficiency (%) of the MS lens from 9.9 GHz to 10.25 GHz.

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The transmission losses resulting from the use of a low-loss substrate from 9.9 GHz to 10.25 GHz are shown in Fig. 10(a). Moreover, the transmitted efficiency of the MS lens has been calculated via Eq. (4) and shown from 9.9 GHz to 10.25 GHz in Fig. 10(b). We observe that the the transmission efficiency of the MS lens is more than 75 %, and it is even 88.14 % at 10 GHz. This is consistent with the simulation results of the transmission efficiency of the unit cell.

The corresponding power distributions of source and MS lens antenna at different OAM modes are analyzed based on the purity calculation of OAM modes [21]. The calculation result is shown in Fig. 11. The mode purity of the +1 OAM order vortex wave generated by the source is 0.874. When the vortex wave passes through the MS lens, the mode purity changes to 0.865. It can be observed that the purity of the convergence lens antenna system for the predominant OAM mode is reduced by only 1 % compared to the source alone. The proposed method of convergence has little effect on the purity of vortex wave.

 figure: Fig. 11

Fig. 11 Power distributions at different OAM modes of source alone and MS lens antenna system at 10 GHz.

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The compared simulations of the axicon lens antenna and MS lens antenna are shown in Fig. 12. From Figs. 12(a) and 12(d), it can be clearly observed that the conventional axicon lens and the MS lens can both converge the vortex wave with excellent effect of divergence angle reduction. Simultaneously, by comparing the radiation patterns obtained for the axicon lens and MS lens shown in Figs. 12(b) and 12(e), it can be observed that the angle between the main lobe and the z axis is significantly reduced to 20° and 18°, respectively. This is also confirmed by the 2D gain curves presented in Fig. 12(c), where the gain of the MS lens antenna is found to be slightly higher than the mirrored axicon lens antenna. In addition, Fig. 12(f) presents the reflection coefficient (S11) of the source antenna, axicon lens antenna and MS lens antenna. We can observe that the matching bandwidth are quite similar for the three configurations. Moreover, the MS antenna presents the advantage of being flat, and can therefore be easily integrated in communication systems.

 figure: Fig. 12

Fig. 12 Performance of axicon lens and MS lens at 10 GHz. (a), (d) E-field distributions. (b), (e) 3D far-field antenna gain patterns. (c) 2D gain patterns. (f) Reflection coefficient (S11).

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4. Conclusion

In summary, a flat MS lens which is capable of converging vortex electromagnetic waves has been proposed. The structure of the MS lens can provide a phase variation from 0 to 2π. As numerically verified, the electric field amplitude distribution has been shown to produce a significant convergence effect. Along the propagation direction, the dark spot associated with the EM field intensity increases much slower when the MS converging lens is applied. Both 2D and 3D radiation patterns demonstrate that the proposed lens enhances the directivity of a circular OAM generating array antenna by converging and increasing the level of the main lobe. A numerical study was performed to prove that the lens is able to operate from 9.3 GHz to 10 GHz. Although the lens design was optimized for OAM waves with topology charge +1, it has also shown promising performance for OAM waves with topology charges of +2 and +3. The high performance and practicality of the lens make it a prime candidate for improving the medium-long range distance performance of microwave communication systems based on vortex electromagnetic waves.

Funding

National Natural Science Foundation of China (NSFC) (No. 61601345); Fundamental Research Funds for the Central Universities (No. XJS16046, JB160109); Natural Science Foundation of Shaanxi Province, China (No. 2017JQ6025); The Pennsylvania State University John L. and Genevieve H. McCain Endowed Chair Professorship.

References and links

1. Y. Yan, G. Xie, M. P. 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, 4876 (2014). [CrossRef]   [PubMed]  

2. A. A. Elsakka, V. S. Asadchy, I. A. Faniayeu, S. N. Tcvetkova, and S. A. Tretyakov, “Multifunctional cascaded metamaterials: Integrated transmitarrays,” Ieee Transactions on Antennas Propag. 64, 4266–4276 (2016). [CrossRef]  

3. B. Thide, H. Then, J. Sjoholm, 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, 087701 (2007). [CrossRef]   [PubMed]  

4. F. Tamburini, B. Thide, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7, 195–197 (2011). [CrossRef]  

5. F. Tamburini, E. Mari, A. Sponselli, B. Thide, A. Bianchini, and F. Romanato, “Encoding many channels in the same frequency through radio vorticity: first experimental test,” New J. Phys.14 (2011).

6. R. Feng, J. Yi, S. N. Burokur, L. Kang, H. Zhang, and D. H. Werner, “Orbital angular momentum generation method based on transformation electromagnetics,” Opt Express 26, 11708–11717 (2018). [CrossRef]   [PubMed]  

7. 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, 1351–1360 (2018). [CrossRef]   [PubMed]  

8. B. Zdenek and M. Olivik, “Non-diffractive vector bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995). [CrossRef]  

9. F. Wu, Y. Chen, and D. Guo, “Nanosecond pulsed bessel–gauss beam generated directly from a nd:yag axicon-based resonator,” Appl Opt 46, 4943–4947 (2007). [CrossRef]   [PubMed]  

10. J. Durnin, “Exact solutions for nondiffracting beams. i. the scalar theory,” JOSA A 4, 651–654 (1987). [CrossRef]  

11. F. Wu, “Experiments and theory of facular lattice generated by diffractive axicon,” Acta Opt. Sinica 28, 2250–2254 (2008). [CrossRef]  

12. S. Topuzoski and L. Janicijevic, “Conversion of high-order laguerre-gaussian beams into bessel beams of increased, reduced or zeroth order by use of a helical axicon,” Opt. Commun. 282, 3426–3432 (2009). [CrossRef]  

13. R. Liu, T. Feng, J. Yi, S. N. Burokur, C. Mao, H. Zhang, and D. H. Werner, “All-dielectric transformation medium mimicking a broadband converging lens,” Opt. Express 26, 20331–20341 (2018). [CrossRef]  

14. R. P. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94, 4148 (2009).

15. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat Mater 9, 129–132 (2010). [CrossRef]  

16. L. Q. Liu, X. H. Zhang, Z. Y. Zhao, M. B. Pu, P. Gao, Y. F. Luo, J. J. Jin, C. T. Wang, and X. G. Luo, “Batch fabrication of metasurface holograms enabled by plasmonic cavity lithography,” Adv. Opt. Mater.5 (2017).

17. X. Xie, X. Li, M. B. Pu, X. L. Ma, K. P. Liu, Y. H. Guo, and X. G. Luo, “Plasmonic metasurfaces for simultaneous thermal infrared invisibility and holographic illusion,” Adv. Funct. Mater. 28, 1706673 (2018). [CrossRef]  

18. N. F. 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, 333–337 (2011). [CrossRef]   [PubMed]  

19. H. T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: physics and applications,” Rep Prog Phys 79, 076401 (2016). [CrossRef]   [PubMed]  

20. F. Ding, A. Pors, and S. I. Bozhevolnyi, “Gradient metasurfaces: a review of fundamentals and applications,” Rep Prog Phys 81, 026401 (2018). [CrossRef]  

21. L. Torner, J. P. Torres, and S. Carrasco, “Digital spiral imaging,” Opt. Express 13, 873–881 (2005). [CrossRef]   [PubMed]  

References

  • View by:

  1. Y. Yan, G. Xie, M. P. 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, 4876 (2014).
    [Crossref] [PubMed]
  2. A. A. Elsakka, V. S. Asadchy, I. A. Faniayeu, S. N. Tcvetkova, and S. A. Tretyakov, “Multifunctional cascaded metamaterials: Integrated transmitarrays,” Ieee Transactions on Antennas Propag. 64, 4266–4276 (2016).
    [Crossref]
  3. B. Thide, H. Then, J. Sjoholm, 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, 087701 (2007).
    [Crossref] [PubMed]
  4. F. Tamburini, B. Thide, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7, 195–197 (2011).
    [Crossref]
  5. F. Tamburini, E. Mari, A. Sponselli, B. Thide, A. Bianchini, and F. Romanato, “Encoding many channels in the same frequency through radio vorticity: first experimental test,” New J. Phys.14 (2011).
  6. R. Feng, J. Yi, S. N. Burokur, L. Kang, H. Zhang, and D. H. Werner, “Orbital angular momentum generation method based on transformation electromagnetics,” Opt Express 26, 11708–11717 (2018).
    [Crossref] [PubMed]
  7. 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, 1351–1360 (2018).
    [Crossref] [PubMed]
  8. B. Zdenek and M. Olivik, “Non-diffractive vector bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
    [Crossref]
  9. F. Wu, Y. Chen, and D. Guo, “Nanosecond pulsed bessel–gauss beam generated directly from a nd:yag axicon-based resonator,” Appl Opt 46, 4943–4947 (2007).
    [Crossref] [PubMed]
  10. J. Durnin, “Exact solutions for nondiffracting beams. i. the scalar theory,” JOSA A 4, 651–654 (1987).
    [Crossref]
  11. F. Wu, “Experiments and theory of facular lattice generated by diffractive axicon,” Acta Opt. Sinica 28, 2250–2254 (2008).
    [Crossref]
  12. S. Topuzoski and L. Janicijevic, “Conversion of high-order laguerre-gaussian beams into bessel beams of increased, reduced or zeroth order by use of a helical axicon,” Opt. Commun. 282, 3426–3432 (2009).
    [Crossref]
  13. R. Liu, T. Feng, J. Yi, S. N. Burokur, C. Mao, H. Zhang, and D. H. Werner, “All-dielectric transformation medium mimicking a broadband converging lens,” Opt. Express 26, 20331–20341 (2018).
    [Crossref]
  14. R. P. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94, 4148 (2009).
  15. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat Mater 9, 129–132 (2010).
    [Crossref]
  16. L. Q. Liu, X. H. Zhang, Z. Y. Zhao, M. B. Pu, P. Gao, Y. F. Luo, J. J. Jin, C. T. Wang, and X. G. Luo, “Batch fabrication of metasurface holograms enabled by plasmonic cavity lithography,” Adv. Opt. Mater.5 (2017).
  17. X. Xie, X. Li, M. B. Pu, X. L. Ma, K. P. Liu, Y. H. Guo, and X. G. Luo, “Plasmonic metasurfaces for simultaneous thermal infrared invisibility and holographic illusion,” Adv. Funct. Mater. 28, 1706673 (2018).
    [Crossref]
  18. N. F. 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, 333–337 (2011).
    [Crossref] [PubMed]
  19. H. T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: physics and applications,” Rep Prog Phys 79, 076401 (2016).
    [Crossref] [PubMed]
  20. F. Ding, A. Pors, and S. I. Bozhevolnyi, “Gradient metasurfaces: a review of fundamentals and applications,” Rep Prog Phys 81, 026401 (2018).
    [Crossref]
  21. L. Torner, J. P. Torres, and S. Carrasco, “Digital spiral imaging,” Opt. Express 13, 873–881 (2005).
    [Crossref] [PubMed]

2018 (5)

R. Feng, J. Yi, S. N. Burokur, L. Kang, H. Zhang, and D. H. Werner, “Orbital angular momentum generation method based on transformation electromagnetics,” Opt Express 26, 11708–11717 (2018).
[Crossref] [PubMed]

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, 1351–1360 (2018).
[Crossref] [PubMed]

R. Liu, T. Feng, J. Yi, S. N. Burokur, C. Mao, H. Zhang, and D. H. Werner, “All-dielectric transformation medium mimicking a broadband converging lens,” Opt. Express 26, 20331–20341 (2018).
[Crossref]

X. Xie, X. Li, M. B. Pu, X. L. Ma, K. P. Liu, Y. H. Guo, and X. G. Luo, “Plasmonic metasurfaces for simultaneous thermal infrared invisibility and holographic illusion,” Adv. Funct. Mater. 28, 1706673 (2018).
[Crossref]

F. Ding, A. Pors, and S. I. Bozhevolnyi, “Gradient metasurfaces: a review of fundamentals and applications,” Rep Prog Phys 81, 026401 (2018).
[Crossref]

2016 (2)

H. T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: physics and applications,” Rep Prog Phys 79, 076401 (2016).
[Crossref] [PubMed]

A. A. Elsakka, V. S. Asadchy, I. A. Faniayeu, S. N. Tcvetkova, and S. A. Tretyakov, “Multifunctional cascaded metamaterials: Integrated transmitarrays,” Ieee Transactions on Antennas Propag. 64, 4266–4276 (2016).
[Crossref]

2014 (1)

Y. Yan, G. Xie, M. P. 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, 4876 (2014).
[Crossref] [PubMed]

2011 (2)

F. Tamburini, B. Thide, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7, 195–197 (2011).
[Crossref]

N. F. 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, 333–337 (2011).
[Crossref] [PubMed]

2010 (1)

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat Mater 9, 129–132 (2010).
[Crossref]

2009 (2)

R. P. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94, 4148 (2009).

S. Topuzoski and L. Janicijevic, “Conversion of high-order laguerre-gaussian beams into bessel beams of increased, reduced or zeroth order by use of a helical axicon,” Opt. Commun. 282, 3426–3432 (2009).
[Crossref]

2008 (1)

F. Wu, “Experiments and theory of facular lattice generated by diffractive axicon,” Acta Opt. Sinica 28, 2250–2254 (2008).
[Crossref]

2007 (2)

B. Thide, H. Then, J. Sjoholm, 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, 087701 (2007).
[Crossref] [PubMed]

F. Wu, Y. Chen, and D. Guo, “Nanosecond pulsed bessel–gauss beam generated directly from a nd:yag axicon-based resonator,” Appl Opt 46, 4943–4947 (2007).
[Crossref] [PubMed]

2005 (1)

1995 (1)

B. Zdenek and M. Olivik, “Non-diffractive vector bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
[Crossref]

1987 (1)

J. Durnin, “Exact solutions for nondiffracting beams. i. the scalar theory,” JOSA A 4, 651–654 (1987).
[Crossref]

Ahmed, N.

Y. Yan, G. Xie, M. P. 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, 4876 (2014).
[Crossref] [PubMed]

Aieta, F.

N. F. 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, 333–337 (2011).
[Crossref] [PubMed]

Anzolin, G.

F. Tamburini, B. Thide, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7, 195–197 (2011).
[Crossref]

Asadchy, V. S.

A. A. Elsakka, V. S. Asadchy, I. A. Faniayeu, S. N. Tcvetkova, and S. A. Tretyakov, “Multifunctional cascaded metamaterials: Integrated transmitarrays,” Ieee Transactions on Antennas Propag. 64, 4266–4276 (2016).
[Crossref]

Bao, C.

Y. Yan, G. Xie, M. P. 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, 4876 (2014).
[Crossref] [PubMed]

Bergman, J.

B. Thide, H. Then, J. Sjoholm, 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, 087701 (2007).
[Crossref] [PubMed]

Bianchini, A.

F. Tamburini, E. Mari, A. Sponselli, B. Thide, A. Bianchini, and F. Romanato, “Encoding many channels in the same frequency through radio vorticity: first experimental test,” New J. Phys.14 (2011).

Bozhevolnyi, S. I.

F. Ding, A. Pors, and S. I. Bozhevolnyi, “Gradient metasurfaces: a review of fundamentals and applications,” Rep Prog Phys 81, 026401 (2018).
[Crossref]

Burokur, S. N.

R. Feng, J. Yi, S. N. Burokur, L. Kang, H. Zhang, and D. H. Werner, “Orbital angular momentum generation method based on transformation electromagnetics,” Opt Express 26, 11708–11717 (2018).
[Crossref] [PubMed]

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, 1351–1360 (2018).
[Crossref] [PubMed]

R. Liu, T. Feng, J. Yi, S. N. Burokur, C. Mao, H. Zhang, and D. H. Werner, “All-dielectric transformation medium mimicking a broadband converging lens,” Opt. Express 26, 20331–20341 (2018).
[Crossref]

Cao, Y.

Y. Yan, G. Xie, M. P. 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, 4876 (2014).
[Crossref] [PubMed]

Capasso, F.

N. F. 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, 333–337 (2011).
[Crossref] [PubMed]

Carozzi, T. D.

B. Thide, H. Then, J. Sjoholm, 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, 087701 (2007).
[Crossref] [PubMed]

Carrasco, S.

Chen, H. T.

H. T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: physics and applications,” Rep Prog Phys 79, 076401 (2016).
[Crossref] [PubMed]

Chen, Y.

F. Wu, Y. Chen, and D. Guo, “Nanosecond pulsed bessel–gauss beam generated directly from a nd:yag axicon-based resonator,” Appl Opt 46, 4943–4947 (2007).
[Crossref] [PubMed]

Cui, T. J.

R. P. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94, 4148 (2009).

Ding, F.

F. Ding, A. Pors, and S. I. Bozhevolnyi, “Gradient metasurfaces: a review of fundamentals and applications,” Rep Prog Phys 81, 026401 (2018).
[Crossref]

Ding, X.

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, 1351–1360 (2018).
[Crossref] [PubMed]

Durnin, J.

J. Durnin, “Exact solutions for nondiffracting beams. i. the scalar theory,” JOSA A 4, 651–654 (1987).
[Crossref]

Elsakka, A. A.

A. A. Elsakka, V. S. Asadchy, I. A. Faniayeu, S. N. Tcvetkova, and S. A. Tretyakov, “Multifunctional cascaded metamaterials: Integrated transmitarrays,” Ieee Transactions on Antennas Propag. 64, 4266–4276 (2016).
[Crossref]

Faniayeu, I. A.

A. A. Elsakka, V. S. Asadchy, I. A. Faniayeu, S. N. Tcvetkova, and S. A. Tretyakov, “Multifunctional cascaded metamaterials: Integrated transmitarrays,” Ieee Transactions on Antennas Propag. 64, 4266–4276 (2016).
[Crossref]

Feng, R.

R. Feng, J. Yi, S. N. Burokur, L. Kang, H. Zhang, and D. H. Werner, “Orbital angular momentum generation method based on transformation electromagnetics,” Opt Express 26, 11708–11717 (2018).
[Crossref] [PubMed]

Feng, T.

Gaburro, Z.

N. F. 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, 333–337 (2011).
[Crossref] [PubMed]

Gao, P.

L. Q. Liu, X. H. Zhang, Z. Y. Zhao, M. B. Pu, P. Gao, Y. F. Luo, J. J. Jin, C. T. Wang, and X. G. Luo, “Batch fabrication of metasurface holograms enabled by plasmonic cavity lithography,” Adv. Opt. Mater.5 (2017).

Genevet, P.

N. F. 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, 333–337 (2011).
[Crossref] [PubMed]

Gollub, J. G.

R. P. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94, 4148 (2009).

Guo, D.

F. Wu, Y. Chen, and D. Guo, “Nanosecond pulsed bessel–gauss beam generated directly from a nd:yag axicon-based resonator,” Appl Opt 46, 4943–4947 (2007).
[Crossref] [PubMed]

Guo, Y. H.

X. Xie, X. Li, M. B. Pu, X. L. Ma, K. P. Liu, Y. H. Guo, and X. G. Luo, “Plasmonic metasurfaces for simultaneous thermal infrared invisibility and holographic illusion,” Adv. Funct. Mater. 28, 1706673 (2018).
[Crossref]

Huang, H.

Y. Yan, G. Xie, M. P. 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, 4876 (2014).
[Crossref] [PubMed]

Ibragimov, N. H.

B. Thide, H. Then, J. Sjoholm, 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, 087701 (2007).
[Crossref] [PubMed]

Istomin, Y. N.

B. Thide, H. Then, J. Sjoholm, 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, 087701 (2007).
[Crossref] [PubMed]

Janicijevic, L.

S. Topuzoski and L. Janicijevic, “Conversion of high-order laguerre-gaussian beams into bessel beams of increased, reduced or zeroth order by use of a helical axicon,” Opt. Commun. 282, 3426–3432 (2009).
[Crossref]

Jin, J. J.

L. Q. Liu, X. H. Zhang, Z. Y. Zhao, M. B. Pu, P. Gao, Y. F. Luo, J. J. Jin, C. T. Wang, and X. G. Luo, “Batch fabrication of metasurface holograms enabled by plasmonic cavity lithography,” Adv. Opt. Mater.5 (2017).

Kang, L.

R. Feng, J. Yi, S. N. Burokur, L. Kang, H. Zhang, and D. H. Werner, “Orbital angular momentum generation method based on transformation electromagnetics,” Opt Express 26, 11708–11717 (2018).
[Crossref] [PubMed]

Kats, M. A.

N. F. 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, 333–337 (2011).
[Crossref] [PubMed]

Khamitova, R.

B. Thide, H. Then, J. Sjoholm, 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, 087701 (2007).
[Crossref] [PubMed]

Kundtz, N.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat Mater 9, 129–132 (2010).
[Crossref]

Lavery, M. P.

Y. Yan, G. Xie, M. P. 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, 4876 (2014).
[Crossref] [PubMed]

Li, L.

Y. Yan, G. Xie, M. P. 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, 4876 (2014).
[Crossref] [PubMed]

Li, X.

X. Xie, X. Li, M. B. Pu, X. L. Ma, K. P. Liu, Y. H. Guo, and X. G. Luo, “Plasmonic metasurfaces for simultaneous thermal infrared invisibility and holographic illusion,” Adv. Funct. Mater. 28, 1706673 (2018).
[Crossref]

Liu, K. P.

X. Xie, X. Li, M. B. Pu, X. L. Ma, K. P. Liu, Y. H. Guo, and X. G. Luo, “Plasmonic metasurfaces for simultaneous thermal infrared invisibility and holographic illusion,” Adv. Funct. Mater. 28, 1706673 (2018).
[Crossref]

Liu, L. Q.

L. Q. Liu, X. H. Zhang, Z. Y. Zhao, M. B. Pu, P. Gao, Y. F. Luo, J. J. Jin, C. T. Wang, and X. G. Luo, “Batch fabrication of metasurface holograms enabled by plasmonic cavity lithography,” Adv. Opt. Mater.5 (2017).

Liu, R.

Liu, R. P.

R. P. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94, 4148 (2009).

Lu, M.

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, 1351–1360 (2018).
[Crossref] [PubMed]

Luo, X. G.

X. Xie, X. Li, M. B. Pu, X. L. Ma, K. P. Liu, Y. H. Guo, and X. G. Luo, “Plasmonic metasurfaces for simultaneous thermal infrared invisibility and holographic illusion,” Adv. Funct. Mater. 28, 1706673 (2018).
[Crossref]

L. Q. Liu, X. H. Zhang, Z. Y. Zhao, M. B. Pu, P. Gao, Y. F. Luo, J. J. Jin, C. T. Wang, and X. G. Luo, “Batch fabrication of metasurface holograms enabled by plasmonic cavity lithography,” Adv. Opt. Mater.5 (2017).

Luo, Y. F.

L. Q. Liu, X. H. Zhang, Z. Y. Zhao, M. B. Pu, P. Gao, Y. F. Luo, J. J. Jin, C. T. Wang, and X. G. Luo, “Batch fabrication of metasurface holograms enabled by plasmonic cavity lithography,” Adv. Opt. Mater.5 (2017).

Ma, X. L.

X. Xie, X. Li, M. B. Pu, X. L. Ma, K. P. Liu, Y. H. Guo, and X. G. Luo, “Plasmonic metasurfaces for simultaneous thermal infrared invisibility and holographic illusion,” Adv. Funct. Mater. 28, 1706673 (2018).
[Crossref]

Mao, C.

Mari, E.

F. Tamburini, E. Mari, A. Sponselli, B. Thide, A. Bianchini, and F. Romanato, “Encoding many channels in the same frequency through radio vorticity: first experimental test,” New J. Phys.14 (2011).

Mock, J. J.

R. P. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94, 4148 (2009).

Molina-Terriza, G.

F. Tamburini, B. Thide, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7, 195–197 (2011).
[Crossref]

Molisch, A. F.

Y. Yan, G. Xie, M. P. 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, 4876 (2014).
[Crossref] [PubMed]

Olivik, M.

B. Zdenek and M. Olivik, “Non-diffractive vector bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
[Crossref]

Padgett, M. J.

Y. Yan, G. Xie, M. P. 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, 4876 (2014).
[Crossref] [PubMed]

Palmer, K.

B. Thide, H. Then, J. Sjoholm, 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, 087701 (2007).
[Crossref] [PubMed]

Pors, A.

F. Ding, A. Pors, and S. I. Bozhevolnyi, “Gradient metasurfaces: a review of fundamentals and applications,” Rep Prog Phys 81, 026401 (2018).
[Crossref]

Pu, M. B.

X. Xie, X. Li, M. B. Pu, X. L. Ma, K. P. Liu, Y. H. Guo, and X. G. Luo, “Plasmonic metasurfaces for simultaneous thermal infrared invisibility and holographic illusion,” Adv. Funct. Mater. 28, 1706673 (2018).
[Crossref]

L. Q. Liu, X. H. Zhang, Z. Y. Zhao, M. B. Pu, P. Gao, Y. F. Luo, J. J. Jin, C. T. Wang, and X. G. Luo, “Batch fabrication of metasurface holograms enabled by plasmonic cavity lithography,” Adv. Opt. Mater.5 (2017).

Ratni, B.

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, 1351–1360 (2018).
[Crossref] [PubMed]

Ren, Y.

Y. Yan, G. Xie, M. P. 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, 4876 (2014).
[Crossref] [PubMed]

Romanato, F.

F. Tamburini, E. Mari, A. Sponselli, B. Thide, A. Bianchini, and F. Romanato, “Encoding many channels in the same frequency through radio vorticity: first experimental test,” New J. Phys.14 (2011).

Sjoholm, J.

B. Thide, H. Then, J. Sjoholm, 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, 087701 (2007).
[Crossref] [PubMed]

Smith, D. R.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat Mater 9, 129–132 (2010).
[Crossref]

R. P. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94, 4148 (2009).

Sponselli, A.

F. Tamburini, E. Mari, A. Sponselli, B. Thide, A. Bianchini, and F. Romanato, “Encoding many channels in the same frequency through radio vorticity: first experimental test,” New J. Phys.14 (2011).

Tamburini, F.

F. Tamburini, B. Thide, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7, 195–197 (2011).
[Crossref]

F. Tamburini, E. Mari, A. Sponselli, B. Thide, A. Bianchini, and F. Romanato, “Encoding many channels in the same frequency through radio vorticity: first experimental test,” New J. Phys.14 (2011).

Tang, K.

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, 1351–1360 (2018).
[Crossref] [PubMed]

Taylor, A. J.

H. T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: physics and applications,” Rep Prog Phys 79, 076401 (2016).
[Crossref] [PubMed]

Tcvetkova, S. N.

A. A. Elsakka, V. S. Asadchy, I. A. Faniayeu, S. N. Tcvetkova, and S. A. Tretyakov, “Multifunctional cascaded metamaterials: Integrated transmitarrays,” Ieee Transactions on Antennas Propag. 64, 4266–4276 (2016).
[Crossref]

Tetienne, J. P.

N. F. 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, 333–337 (2011).
[Crossref] [PubMed]

Then, H.

B. Thide, H. Then, J. Sjoholm, 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, 087701 (2007).
[Crossref] [PubMed]

Thide, B.

F. Tamburini, B. Thide, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7, 195–197 (2011).
[Crossref]

B. Thide, H. Then, J. Sjoholm, 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, 087701 (2007).
[Crossref] [PubMed]

F. Tamburini, E. Mari, A. Sponselli, B. Thide, A. Bianchini, and F. Romanato, “Encoding many channels in the same frequency through radio vorticity: first experimental test,” New J. Phys.14 (2011).

Topuzoski, S.

S. Topuzoski and L. Janicijevic, “Conversion of high-order laguerre-gaussian beams into bessel beams of increased, reduced or zeroth order by use of a helical axicon,” Opt. Commun. 282, 3426–3432 (2009).
[Crossref]

Torner, L.

Torres, J. P.

Tretyakov, S. A.

A. A. Elsakka, V. S. Asadchy, I. A. Faniayeu, S. N. Tcvetkova, and S. A. Tretyakov, “Multifunctional cascaded metamaterials: Integrated transmitarrays,” Ieee Transactions on Antennas Propag. 64, 4266–4276 (2016).
[Crossref]

Tur, M.

Y. Yan, G. Xie, M. P. 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, 4876 (2014).
[Crossref] [PubMed]

Wang, C. T.

L. Q. Liu, X. H. Zhang, Z. Y. Zhao, M. B. Pu, P. Gao, Y. F. Luo, J. J. Jin, C. T. Wang, and X. G. Luo, “Batch fabrication of metasurface holograms enabled by plasmonic cavity lithography,” Adv. Opt. Mater.5 (2017).

Werner, D. H.

R. Liu, T. Feng, J. Yi, S. N. Burokur, C. Mao, H. Zhang, and D. H. Werner, “All-dielectric transformation medium mimicking a broadband converging lens,” Opt. Express 26, 20331–20341 (2018).
[Crossref]

R. Feng, J. Yi, S. N. Burokur, L. Kang, H. Zhang, and D. H. Werner, “Orbital angular momentum generation method based on transformation electromagnetics,” Opt Express 26, 11708–11717 (2018).
[Crossref] [PubMed]

Willner, A. E.

Y. Yan, G. Xie, M. P. 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, 4876 (2014).
[Crossref] [PubMed]

Wu, F.

F. Wu, “Experiments and theory of facular lattice generated by diffractive axicon,” Acta Opt. Sinica 28, 2250–2254 (2008).
[Crossref]

F. Wu, Y. Chen, and D. Guo, “Nanosecond pulsed bessel–gauss beam generated directly from a nd:yag axicon-based resonator,” Appl Opt 46, 4943–4947 (2007).
[Crossref] [PubMed]

Wu, Q.

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, 1351–1360 (2018).
[Crossref] [PubMed]

Xie, G.

Y. Yan, G. Xie, M. P. 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, 4876 (2014).
[Crossref] [PubMed]

Xie, X.

X. Xie, X. Li, M. B. Pu, X. L. Ma, K. P. Liu, Y. H. Guo, and X. G. Luo, “Plasmonic metasurfaces for simultaneous thermal infrared invisibility and holographic illusion,” Adv. Funct. Mater. 28, 1706673 (2018).
[Crossref]

Yan, Y.

Y. Yan, G. Xie, M. P. 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, 4876 (2014).
[Crossref] [PubMed]

Yang, X. M.

R. P. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94, 4148 (2009).

Yi, J.

R. Liu, T. Feng, J. Yi, S. N. Burokur, C. Mao, H. Zhang, and D. H. Werner, “All-dielectric transformation medium mimicking a broadband converging lens,” Opt. Express 26, 20331–20341 (2018).
[Crossref]

R. Feng, J. Yi, S. N. Burokur, L. Kang, H. Zhang, and D. H. Werner, “Orbital angular momentum generation method based on transformation electromagnetics,” Opt Express 26, 11708–11717 (2018).
[Crossref] [PubMed]

Yu, N.

H. T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: physics and applications,” Rep Prog Phys 79, 076401 (2016).
[Crossref] [PubMed]

Yu, N. F.

N. F. 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, 333–337 (2011).
[Crossref] [PubMed]

Yuan, Y.

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, 1351–1360 (2018).
[Crossref] [PubMed]

Zdenek, B.

B. Zdenek and M. Olivik, “Non-diffractive vector bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
[Crossref]

Zhang, D.

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, 1351–1360 (2018).
[Crossref] [PubMed]

Zhang, H.

R. Feng, J. Yi, S. N. Burokur, L. Kang, H. Zhang, and D. H. Werner, “Orbital angular momentum generation method based on transformation electromagnetics,” Opt Express 26, 11708–11717 (2018).
[Crossref] [PubMed]

R. Liu, T. Feng, J. Yi, S. N. Burokur, C. Mao, H. Zhang, and D. H. Werner, “All-dielectric transformation medium mimicking a broadband converging lens,” Opt. Express 26, 20331–20341 (2018).
[Crossref]

Zhang, K.

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, 1351–1360 (2018).
[Crossref] [PubMed]

Zhang, X. H.

L. Q. Liu, X. H. Zhang, Z. Y. Zhao, M. B. Pu, P. Gao, Y. F. Luo, J. J. Jin, C. T. Wang, and X. G. Luo, “Batch fabrication of metasurface holograms enabled by plasmonic cavity lithography,” Adv. Opt. Mater.5 (2017).

Zhao, Z.

Y. Yan, G. Xie, M. P. 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, 4876 (2014).
[Crossref] [PubMed]

Zhao, Z. Y.

L. Q. Liu, X. H. Zhang, Z. Y. Zhao, M. B. Pu, P. Gao, Y. F. Luo, J. J. Jin, C. T. Wang, and X. G. Luo, “Batch fabrication of metasurface holograms enabled by plasmonic cavity lithography,” Adv. Opt. Mater.5 (2017).

Acta Opt. Sinica (1)

F. Wu, “Experiments and theory of facular lattice generated by diffractive axicon,” Acta Opt. Sinica 28, 2250–2254 (2008).
[Crossref]

Adv. Funct. Mater. (1)

X. Xie, X. Li, M. B. Pu, X. L. Ma, K. P. Liu, Y. H. Guo, and X. G. Luo, “Plasmonic metasurfaces for simultaneous thermal infrared invisibility and holographic illusion,” Adv. Funct. Mater. 28, 1706673 (2018).
[Crossref]

Appl Opt (1)

F. Wu, Y. Chen, and D. Guo, “Nanosecond pulsed bessel–gauss beam generated directly from a nd:yag axicon-based resonator,” Appl Opt 46, 4943–4947 (2007).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

R. P. Liu, X. M. Yang, J. G. Gollub, J. J. Mock, T. J. Cui, and D. R. Smith, “Gradient index circuit by waveguided metamaterials,” Appl. Phys. Lett. 94, 4148 (2009).

Ieee Transactions on Antennas Propag. (1)

A. A. Elsakka, V. S. Asadchy, I. A. Faniayeu, S. N. Tcvetkova, and S. A. Tretyakov, “Multifunctional cascaded metamaterials: Integrated transmitarrays,” Ieee Transactions on Antennas Propag. 64, 4266–4276 (2016).
[Crossref]

J. Mod. Opt. (1)

B. Zdenek and M. Olivik, “Non-diffractive vector bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995).
[Crossref]

JOSA A (1)

J. Durnin, “Exact solutions for nondiffracting beams. i. the scalar theory,” JOSA A 4, 651–654 (1987).
[Crossref]

Nat Commun (1)

Y. Yan, G. Xie, M. P. 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, 4876 (2014).
[Crossref] [PubMed]

Nat Mater (1)

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat Mater 9, 129–132 (2010).
[Crossref]

Nat. Phys. (1)

F. Tamburini, B. Thide, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7, 195–197 (2011).
[Crossref]

Opt Express (2)

R. Feng, J. Yi, S. N. Burokur, L. Kang, H. Zhang, and D. H. Werner, “Orbital angular momentum generation method based on transformation electromagnetics,” Opt Express 26, 11708–11717 (2018).
[Crossref] [PubMed]

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, 1351–1360 (2018).
[Crossref] [PubMed]

Opt. Commun. (1)

S. Topuzoski and L. Janicijevic, “Conversion of high-order laguerre-gaussian beams into bessel beams of increased, reduced or zeroth order by use of a helical axicon,” Opt. Commun. 282, 3426–3432 (2009).
[Crossref]

Opt. Express (2)

Phys Rev Lett (1)

B. Thide, H. Then, J. Sjoholm, 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, 087701 (2007).
[Crossref] [PubMed]

Rep Prog Phys (2)

H. T. Chen, A. J. Taylor, and N. Yu, “A review of metasurfaces: physics and applications,” Rep Prog Phys 79, 076401 (2016).
[Crossref] [PubMed]

F. Ding, A. Pors, and S. I. Bozhevolnyi, “Gradient metasurfaces: a review of fundamentals and applications,” Rep Prog Phys 81, 026401 (2018).
[Crossref]

Science (1)

N. F. 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, 333–337 (2011).
[Crossref] [PubMed]

Other (2)

L. Q. Liu, X. H. Zhang, Z. Y. Zhao, M. B. Pu, P. Gao, Y. F. Luo, J. J. Jin, C. T. Wang, and X. G. Luo, “Batch fabrication of metasurface holograms enabled by plasmonic cavity lithography,” Adv. Opt. Mater.5 (2017).

F. Tamburini, E. Mari, A. Sponselli, B. Thide, A. Bianchini, and F. Romanato, “Encoding many channels in the same frequency through radio vorticity: first experimental test,” New J. Phys.14 (2011).

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Figures (12)

Fig. 1
Fig. 1 (a) Theoretical transformation of LG beam into Bessel beam by axicon. (b) Schematic view of the vortex EM wave convergence system.
Fig. 2
Fig. 2 Calculated phase distribution required on the MS for compensation.
Fig. 3
Fig. 3 (a) Top view of the MS lens. (b) Top and perspective views of a square elementary cell. The different geometrical dimensions are: t = 1.5 mm, P = 9 mm, g = 0.5 mm, S = 3.5 mm and l = 6.5 mm. (c) Transmission phase and amplitude of the unit cell 10 GHz. (d) Absorptivity at 10 GHz of the unit cell under different incidence angles. (e) Transmissivity at 10 GHz of the unit cell under different incidence angles.
Fig. 4
Fig. 4 E-field amplitude distribution in the x–z plane of the lens antenna system at 10 GHz for different distance between source and MS lens. (a) D = 30 mm. (b) D = 45 mm. (c) D = 60 mm.
Fig. 5
Fig. 5 Numerical simulation results of the antenna and MS converging lens. (a)–(c) E-field amplitude distribution of the antenna without lens for ϕ = 0 at 9.3 GHz, 10 GHz, and 10.3 GHz. (d)–(f) E-field amplitude distribution of the MS lens antenna source for ϕ = 0 at 9.3 GHz, 10 GHz, and 10.3 GHz.
Fig. 6
Fig. 6 Simulated E-field amplitude distribution for z = 90 mm, 120 mm, and 150 mm in the x–y plane at 10 GHz. (a)- (c) Source alone. (d)-(f) Converging MS lens antenna system. The beam of the vortex wave generated by the source is efficietnly converged after transmitting through the lens.
Fig. 7
Fig. 7 (a), (c) Theoretical phase distributions of the antenna array source and MS converging lens, respectively, for the EM field component in the x–y plane. The cross-section is 70mm away from the feed plane, and the phase changes from − π (blue) to π (red). (b), (d) Simulated phase distributions of the antenna and MS converging lens at 10 GHz, respectively, for the EM field component in the x–y plane.
Fig. 8
Fig. 8 Numerical simulation results of the antenna array source and converging MS lens lens antenna system at 9.3 GHz, 10 GHz and 10.3 GHz. (a), (d), and (g) 3D far-field gain patterns of the antenna array source. (b), (e), and (h) 3D far-field gain patterns of the MS converging lens antenna. (c), (f), and (i) 2D gain patterns of the antenna array source and MS converging lens antenna.
Fig. 9
Fig. 9 E-field magnitude distribution of a vortex wave with topological charge of +2 and +3 at 10 GHz. (a)–(b) Antenna array source. (c)–(d) Lens antenna system.
Fig. 10
Fig. 10 (a) Transmission losses (dB) resulting from the use of a low-loss substrate and (b) efficiency (%) of the MS lens from 9.9 GHz to 10.25 GHz.
Fig. 11
Fig. 11 Power distributions at different OAM modes of source alone and MS lens antenna system at 10 GHz.
Fig. 12
Fig. 12 Performance of axicon lens and MS lens at 10 GHz. (a), (d) E-field distributions. (b), (e) 3D far-field antenna gain patterns. (c) 2D gain patterns. (f) Reflection coefficient (S11).

Equations (4)

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T ( γ ) = exp ( i α γ )
T ( m , n ) = F ( γ o m n ) exp ( i l φ + i k | γ m n γ o | sin θ ) .
ϕ m n d = 2 π | γ m n | sin θ λ
η = P lens P source × 100 % .

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