Abstract

In this paper, ultra-thin metalenses are proposed to generate converging and non-diffractive vortex beam carrying orbital angular momentum (OAM) in microwave region. Phase changes are introduced to the transmission cross-polarized wave by tailoring spatial orientation of Pancharatnam-Berry phase unit cell. Based on the superposition of phase profile of spiral phase plate and that of a converging lens or an axicon, vortex beam carrying OAM mode generated by the metalens can also exhibit characteristics of a focusing beam or a Bessel beam. Measured field intensities and phase distributions at microwave frequencies verify the theoretical design procedure. The proposed method provides an efficient approach to control the radius of vortex beam carrying OAM mode in microwave wireless applications for medium-short range distance.

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

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
  46. X. Li, M. Pu, Z. Zhao, X. Ma, J. Jin, Y. Wang, P. Gao, and X. Luo, “Catenary nanostructures as compact Bessel beam generators,” Sci. Rep. 6(1), 20524 (2016).
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2017 (9)

C.-W. Qiu and Y. Yang, “Vortex generation reaches a new plateau,” Science 357(6352), 645 (2017).
[Crossref] [PubMed]

V. Grillo, A. H. Tavabi, F. Venturi, H. Larocque, R. Balboni, G. C. Gazzadi, S. Frabboni, P.-H. Lu, E. Mafakheri, F. Bouchard, R. E. Dunin-Borkowski, R. W. Boyd, M. P. J. Lavery, M. J. Padgett, and E. Karimi, “Measuring the orbital angular momentum spectrum of an electron beam,” Nat. Commun. 8, 15536 (2017).
[Crossref] [PubMed]

C. Deng, K. Zhang, and Z. Feng, “Generating and Measuring Tunable Orbital Angular Momentum Radio Beams With Digital Control Method,” IEEE Trans. Antenn. Propag. 65(2), 899–902 (2017).
[Crossref]

Y. Gong, R. Wang, Y. Deng, B. Zhang, N. Wang, N. Li, and P. Wang, “Generation and Transmission of OAM-Carrying Vortex Beams Using Circular Antenna Array,” IEEE Trans. Antenn. Propag. 65(6), 2940–2949 (2017).
[Crossref]

Z. Zhang, S. Xiao, Y. Li, and B. Wang, “A circularly polarized multimode patch antenna for the generation of multiple orbital angular momentum modes,” IEEE Trans. Antenn. Propag. 16, 521–524 (2017).
[Crossref]

W. Zhang, S. Zheng, X. Hui, R. Dong, X. Jin, H. Chi, and X. Zhang, “Mode Division Multiplexing Communication Using Microwave Orbital Angular Momentum: An Experimental Study,” IEEE Trans. Antenn. Propag. 16(2), 1308–1318 (2017).

X. D. Bai, X. L. Liang, Y. T. Sun, P. C. Hu, Y. Yao, K. Wang, J. P. Geng, and R. H. Jin, “Experimental Array for Generating Dual Circularly-Polarized Dual-Mode OAM Radio Beams,” Sci. Rep. 7, 40099 (2017).
[Crossref] [PubMed]

L. Cheng, W. Hong, and Z. Hao, “Design and implementation of planar reflection spiral phase plate for beams with orbital angular momentum,” IET Microw. Antennas Propag. 11(2), 260–264 (2017).
[Crossref]

M. L. N. Chen, L. J. Jiang, and W. E. I. Sha, “Ultrathin Complementary Metasurface for Orbital Angular Momentum Generation at Microwave Frequencies,” IEEE Trans. Antenn. Propag. 65(1), 396–400 (2017).
[Crossref]

2016 (11)

S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurface for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).
[Crossref]

S. Yu, L. Li, G. Shi, C. Zhu, and Y. Shi, “Generating multiple orbital angular momentum vortex beams using a metasurface in radio frequency domain,” Appl. Phys. Lett. 108(24), 241901 (2016).
[Crossref]

W. J. Byun, K. S. Kim, B. S. Kim, Y. S. Lee, M. S. Song, H. D. Choi, and Y. H. Cho, “Multiplexed Cassegrain reflector antenna for simultaneous generation of three orbital angular momentum (OAM) modes,” Sci. Rep. 6(1), 27339 (2016).
[Crossref] [PubMed]

K. Liu, H. Liu, Y. Qin, Y. Cheng, S. Wang, X. Li, and H. Wang, “Generation of OAM beams using phased array in the microwave band,” IEEE Trans. Antenn. Propag. 64(9), 3850–3857 (2016).
[Crossref]

C. Xu, S. Zheng, W. Zhang, Y. Chen, H. Chi, X. Jin, and X. Zhang, “Free-space radio communication employing OAM multiplexing based on Rotman lens,” IEEE Trans. Antenn. Propag. 26(9), 738–740 (2016).

H. Larocque, F. Bouchard, V. Grillo, A. Sit, S. Frabboni, R. E. Dunin-Borkowski, M. J. Padgett, R. W. Boyd, and E. Karimi, “Nondestructive measurement of orbital angular momentum for an electron beam,” Phys. Rev. Lett. 117(15), 154801 (2016).
[Crossref] [PubMed]

M. Krenn, J. Handsteiner, M. Fink, R. Fickler, R. Ursin, M. Malik, and A. Zeilinger, “Twisted light transmission over 143 km,” Proc. Natl. Acad. Sci. U.S.A. 113(48), 13648–13653 (2016).
[Crossref] [PubMed]

Z. Y. Zhou, Y. Li, D. S. Ding, W. Zhang, S. Shi, B. S. Shi, and G. C. Guo, “Orbital angular momentum photonic quantum interface,” Light Sci. Appl. 5(1), e16019 (2016).
[Crossref]

H. Ren, X. Li, Q. Zhang, and M. Gu, “On-chip noninterference angular momentum multiplexing of broadband light,” Science 352(6287), 805–809 (2016).
[Crossref] [PubMed]

M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C. W. Qiu, “Visible-frequency metasurface for structuring and spatially multiplexing optical vortices,” Adv. Mater. 28(13), 2533–2539 (2016).
[Crossref] [PubMed]

X. Li, M. Pu, Z. Zhao, X. Ma, J. Jin, Y. Wang, P. Gao, and X. Luo, “Catenary nanostructures as compact Bessel beam generators,” Sci. Rep. 6(1), 20524 (2016).
[Crossref] [PubMed]

2015 (3)

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
[Crossref] [PubMed]

X. Hui, S. Zheng, Y. Chen, Y. Hu, X. Jin, H. Chi, and X. Zhang, “Multiplexed millimeter wave communication with dual orbital angular momentum (OAM) mode antennas,” Sci. Rep. 5(1), 10148 (2015).
[Crossref] [PubMed]

V. Grillo, G. C. Gazzadi, E. Mafakheri, S. Frabboni, E. Karimi, and R. W. Boyd, “Holographic generation of highly twisted electron beams,” Phys. Rev. Lett. 114(3), 034801 (2015).
[Crossref] [PubMed]

2014 (6)

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
[Crossref]

D. Hakobyan and E. Brasselet, “Left-handed optical radiation torque,” Nat. Photonics 8(8), 610–614 (2014).
[Crossref]

F. Bouchard, I. D. Leon, S. A. Schulz, J. Upham, E. Karimi, and R. W. Boyd, “Optical spin-to-orbital angular momentum conversion in ultra-thin metasurfaces with arbitrary topological charges,” Appl. Phys. Lett. 105(10), 101905 (2014).
[Crossref]

V. Grillo, E. Karimi, G. C. Gazzadi, M. R. Stefano Frabboni, S. Dennis, and R. W. Boyd, “Generation of nondiffracting electron bessel beams,” Phys. Rev. X 4(1), 011013 (2014).
[Crossref]

K. Zhang, X. Ding, L. Zhang, and Q. Wu, “Anomalous three-dimensional refraction in the microwave region by ultra-thin high efficiency metalens with phase discontinuities in orthogonal directions,” New J. Phys. 16(10), 103020 (2014).
[Crossref]

X. Gao, S. Huang, Y. Song, S. Li, Y. Wei, J. Zhou, X. Zheng, H. Zhang, and W. Gu, “Generating the orbital angular momentum of radio frequency signals using optical-true-time-delay unit based on optical spectrum processor,” Opt. Lett. 39(9), 2652–2655 (2014).
[Crossref] [PubMed]

2013 (2)

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
[Crossref] [PubMed]

D. Zelenchuk and V. Fusco, “Split-ring FSS spiral phase plate,” IEEE Antennas Wirel. Propag. Lett. 12, 284–287 (2013).
[Crossref]

2012 (3)

F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14(3), 033001 (2012).
[Crossref]

J. Wang, J. J. 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]

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R. J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-Division Multiplexing Over 96 km of Few-Mode Fiber Using Coherent 6 × 6 MIMO Processing,” J. Lightwave Technol. 30(4), 521–531 (2012).
[Crossref]

2011 (4)

2010 (2)

S. M. Mohammadi, L. K. S. Daldorff, J. E. S. Bergman, R. L. Karlsson, B. Thidé, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio—a system study,” IEEE Trans. Antenn. Propag. 58(2), 565–572 (2010).
[Crossref]

R. J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
[Crossref]

2007 (1)

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
[Crossref] [PubMed]

2006 (1)

M. V. Berry, M. R. Jeffrey, and J. G. Lunney, “Conical Diffraction: Observations and Theory,” Proc. R. Soc. A 462(2070), 1629–1642 (2006).
[Crossref]

2003 (1)

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82(3), 328–330 (2003).
[Crossref]

2002 (1)

1999 (1)

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “Parametric downconversion for light beams possessing orbital angular momentum,” Phys. Rev. A 59(5), 3950–3952 (1999).
[Crossref]

1998 (1)

1994 (1)

M. W. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5-6), 321–327 (1994).
[Crossref]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

1936 (1)

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50(2), 115–125 (1936).
[Crossref]

Ahmed, N.

J. Wang, J. J. 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]

Aieta, F.

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L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
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F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
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J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “Parametric downconversion for light beams possessing orbital angular momentum,” Phys. Rev. A 59(5), 3950–3952 (1999).
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X. D. Bai, X. L. Liang, Y. T. Sun, P. C. Hu, Y. Yao, K. Wang, J. P. Geng, and R. H. Jin, “Experimental Array for Generating Dual Circularly-Polarized Dual-Mode OAM Radio Beams,” Sci. Rep. 7, 40099 (2017).
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M. W. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5-6), 321–327 (1994).
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E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82(3), 328–330 (2003).
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Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings,” Opt. Lett. 27(13), 1141–1143 (2002).
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Bolle, C.

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Borel, P. I.

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V. Grillo, A. H. Tavabi, F. Venturi, H. Larocque, R. Balboni, G. C. Gazzadi, S. Frabboni, P.-H. Lu, E. Mafakheri, F. Bouchard, R. E. Dunin-Borkowski, R. W. Boyd, M. P. J. Lavery, M. J. Padgett, and E. Karimi, “Measuring the orbital angular momentum spectrum of an electron beam,” Nat. Commun. 8, 15536 (2017).
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H. Larocque, F. Bouchard, V. Grillo, A. Sit, S. Frabboni, R. E. Dunin-Borkowski, M. J. Padgett, R. W. Boyd, and E. Karimi, “Nondestructive measurement of orbital angular momentum for an electron beam,” Phys. Rev. Lett. 117(15), 154801 (2016).
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F. Bouchard, I. D. Leon, S. A. Schulz, J. Upham, E. Karimi, and R. W. Boyd, “Optical spin-to-orbital angular momentum conversion in ultra-thin metasurfaces with arbitrary topological charges,” Appl. Phys. Lett. 105(10), 101905 (2014).
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V. Grillo, A. H. Tavabi, F. Venturi, H. Larocque, R. Balboni, G. C. Gazzadi, S. Frabboni, P.-H. Lu, E. Mafakheri, F. Bouchard, R. E. Dunin-Borkowski, R. W. Boyd, M. P. J. Lavery, M. J. Padgett, and E. Karimi, “Measuring the orbital angular momentum spectrum of an electron beam,” Nat. Commun. 8, 15536 (2017).
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H. Larocque, F. Bouchard, V. Grillo, A. Sit, S. Frabboni, R. E. Dunin-Borkowski, M. J. Padgett, R. W. Boyd, and E. Karimi, “Nondestructive measurement of orbital angular momentum for an electron beam,” Phys. Rev. Lett. 117(15), 154801 (2016).
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V. Grillo, G. C. Gazzadi, E. Mafakheri, S. Frabboni, E. Karimi, and R. W. Boyd, “Holographic generation of highly twisted electron beams,” Phys. Rev. Lett. 114(3), 034801 (2015).
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F. Bouchard, I. D. Leon, S. A. Schulz, J. Upham, E. Karimi, and R. W. Boyd, “Optical spin-to-orbital angular momentum conversion in ultra-thin metasurfaces with arbitrary topological charges,” Appl. Phys. Lett. 105(10), 101905 (2014).
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E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
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V. Grillo, E. Karimi, G. C. Gazzadi, M. R. Stefano Frabboni, S. Dennis, and R. W. Boyd, “Generation of nondiffracting electron bessel beams,” Phys. Rev. X 4(1), 011013 (2014).
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D. Hakobyan and E. Brasselet, “Left-handed optical radiation torque,” Nat. Photonics 8(8), 610–614 (2014).
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Byun, W. J.

W. J. Byun, K. S. Kim, B. S. Kim, Y. S. Lee, M. S. Song, H. D. Choi, and Y. H. Cho, “Multiplexed Cassegrain reflector antenna for simultaneous generation of three orbital angular momentum (OAM) modes,” Sci. Rep. 6(1), 27339 (2016).
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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).
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S. M. Mohammadi, L. K. S. Daldorff, J. E. S. Bergman, R. L. Karlsson, B. Thidé, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio—a system study,” IEEE Trans. Antenn. Propag. 58(2), 565–572 (2010).
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B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).
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Chen, M. L. N.

M. L. N. Chen, L. J. Jiang, and W. E. I. Sha, “Ultrathin Complementary Metasurface for Orbital Angular Momentum Generation at Microwave Frequencies,” IEEE Trans. Antenn. Propag. 65(1), 396–400 (2017).
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C. Xu, S. Zheng, W. Zhang, Y. Chen, H. Chi, X. Jin, and X. Zhang, “Free-space radio communication employing OAM multiplexing based on Rotman lens,” IEEE Trans. Antenn. Propag. 26(9), 738–740 (2016).

X. Hui, S. Zheng, Y. Chen, Y. Hu, X. Jin, H. Chi, and X. Zhang, “Multiplexed millimeter wave communication with dual orbital angular momentum (OAM) mode antennas,” Sci. Rep. 5(1), 10148 (2015).
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Cheng, L.

L. Cheng, W. Hong, and Z. Hao, “Design and implementation of planar reflection spiral phase plate for beams with orbital angular momentum,” IET Microw. Antennas Propag. 11(2), 260–264 (2017).
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K. Liu, H. Liu, Y. Qin, Y. Cheng, S. Wang, X. Li, and H. Wang, “Generation of OAM beams using phased array in the microwave band,” IEEE Trans. Antenn. Propag. 64(9), 3850–3857 (2016).
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W. Zhang, S. Zheng, X. Hui, R. Dong, X. Jin, H. Chi, and X. Zhang, “Mode Division Multiplexing Communication Using Microwave Orbital Angular Momentum: An Experimental Study,” IEEE Trans. Antenn. Propag. 16(2), 1308–1318 (2017).

C. Xu, S. Zheng, W. Zhang, Y. Chen, H. Chi, X. Jin, and X. Zhang, “Free-space radio communication employing OAM multiplexing based on Rotman lens,” IEEE Trans. Antenn. Propag. 26(9), 738–740 (2016).

X. Hui, S. Zheng, Y. Chen, Y. Hu, X. Jin, H. Chi, and X. Zhang, “Multiplexed millimeter wave communication with dual orbital angular momentum (OAM) mode antennas,” Sci. Rep. 5(1), 10148 (2015).
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W. J. Byun, K. S. Kim, B. S. Kim, Y. S. Lee, M. S. Song, H. D. Choi, and Y. H. Cho, “Multiplexed Cassegrain reflector antenna for simultaneous generation of three orbital angular momentum (OAM) modes,” Sci. Rep. 6(1), 27339 (2016).
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Choi, H. D.

W. J. Byun, K. S. Kim, B. S. Kim, Y. S. Lee, M. S. Song, H. D. Choi, and Y. H. Cho, “Multiplexed Cassegrain reflector antenna for simultaneous generation of three orbital angular momentum (OAM) modes,” Sci. Rep. 6(1), 27339 (2016).
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Coerwinkel, R.

M. W. Beijersbergen, R. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5-6), 321–327 (1994).
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S. M. Mohammadi, L. K. S. Daldorff, J. E. S. Bergman, R. L. Karlsson, B. Thidé, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio—a system study,” IEEE Trans. Antenn. Propag. 58(2), 565–572 (2010).
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E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
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C. Deng, K. Zhang, and Z. Feng, “Generating and Measuring Tunable Orbital Angular Momentum Radio Beams With Digital Control Method,” IEEE Trans. Antenn. Propag. 65(2), 899–902 (2017).
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Y. Gong, R. Wang, Y. Deng, B. Zhang, N. Wang, N. Li, and P. Wang, “Generation and Transmission of OAM-Carrying Vortex Beams Using Circular Antenna Array,” IEEE Trans. Antenn. Propag. 65(6), 2940–2949 (2017).
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V. Grillo, E. Karimi, G. C. Gazzadi, M. R. Stefano Frabboni, S. Dennis, and R. W. Boyd, “Generation of nondiffracting electron bessel beams,” Phys. Rev. X 4(1), 011013 (2014).
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J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “Parametric downconversion for light beams possessing orbital angular momentum,” Phys. Rev. A 59(5), 3950–3952 (1999).
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Z. Y. Zhou, Y. Li, D. S. Ding, W. Zhang, S. Shi, B. S. Shi, and G. C. Guo, “Orbital angular momentum photonic quantum interface,” Light Sci. Appl. 5(1), e16019 (2016).
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K. Zhang, X. Ding, L. Zhang, and Q. Wu, “Anomalous three-dimensional refraction in the microwave region by ultra-thin high efficiency metalens with phase discontinuities in orthogonal directions,” New J. Phys. 16(10), 103020 (2014).
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Dong, R.

W. Zhang, S. Zheng, X. Hui, R. Dong, X. Jin, H. Chi, and X. Zhang, “Mode Division Multiplexing Communication Using Microwave Orbital Angular Momentum: An Experimental Study,” IEEE Trans. Antenn. Propag. 16(2), 1308–1318 (2017).

Dunin-Borkowski, R. E.

V. Grillo, A. H. Tavabi, F. Venturi, H. Larocque, R. Balboni, G. C. Gazzadi, S. Frabboni, P.-H. Lu, E. Mafakheri, F. Bouchard, R. E. Dunin-Borkowski, R. W. Boyd, M. P. J. Lavery, M. J. Padgett, and E. Karimi, “Measuring the orbital angular momentum spectrum of an electron beam,” Nat. Commun. 8, 15536 (2017).
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H. Larocque, F. Bouchard, V. Grillo, A. Sit, S. Frabboni, R. E. Dunin-Borkowski, M. J. Padgett, R. W. Boyd, and E. Karimi, “Nondestructive measurement of orbital angular momentum for an electron beam,” Phys. Rev. Lett. 117(15), 154801 (2016).
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Esmaeelpour, M.

Essiambre, R. J.

Estakhri, N. M.

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
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J. Wang, J. J. 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).
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C. Deng, K. Zhang, and Z. Feng, “Generating and Measuring Tunable Orbital Angular Momentum Radio Beams With Digital Control Method,” IEEE Trans. Antenn. Propag. 65(2), 899–902 (2017).
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M. Krenn, J. Handsteiner, M. Fink, R. Fickler, R. Ursin, M. Malik, and A. Zeilinger, “Twisted light transmission over 143 km,” Proc. Natl. Acad. Sci. U.S.A. 113(48), 13648–13653 (2016).
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M. Krenn, J. Handsteiner, M. Fink, R. Fickler, R. Ursin, M. Malik, and A. Zeilinger, “Twisted light transmission over 143 km,” Proc. Natl. Acad. Sci. U.S.A. 113(48), 13648–13653 (2016).
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S. M. Mohammadi, L. K. S. Daldorff, J. E. S. Bergman, R. L. Karlsson, B. Thidé, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio—a system study,” IEEE Trans. Antenn. Propag. 58(2), 565–572 (2010).
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Frabboni, S.

V. Grillo, A. H. Tavabi, F. Venturi, H. Larocque, R. Balboni, G. C. Gazzadi, S. Frabboni, P.-H. Lu, E. Mafakheri, F. Bouchard, R. E. Dunin-Borkowski, R. W. Boyd, M. P. J. Lavery, M. J. Padgett, and E. Karimi, “Measuring the orbital angular momentum spectrum of an electron beam,” Nat. Commun. 8, 15536 (2017).
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H. Larocque, F. Bouchard, V. Grillo, A. Sit, S. Frabboni, R. E. Dunin-Borkowski, M. J. Padgett, R. W. Boyd, and E. Karimi, “Nondestructive measurement of orbital angular momentum for an electron beam,” Phys. Rev. Lett. 117(15), 154801 (2016).
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V. Grillo, G. C. Gazzadi, E. Mafakheri, S. Frabboni, E. Karimi, and R. W. Boyd, “Holographic generation of highly twisted electron beams,” Phys. Rev. Lett. 114(3), 034801 (2015).
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D. Zelenchuk and V. Fusco, “Split-ring FSS spiral phase plate,” IEEE Antennas Wirel. Propag. Lett. 12, 284–287 (2013).
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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).
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Gao, P.

X. Li, M. Pu, Z. Zhao, X. Ma, J. Jin, Y. Wang, P. Gao, and X. Luo, “Catenary nanostructures as compact Bessel beam generators,” Sci. Rep. 6(1), 20524 (2016).
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M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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Gao, X.

Gazzadi, G. C.

V. Grillo, A. H. Tavabi, F. Venturi, H. Larocque, R. Balboni, G. C. Gazzadi, S. Frabboni, P.-H. Lu, E. Mafakheri, F. Bouchard, R. E. Dunin-Borkowski, R. W. Boyd, M. P. J. Lavery, M. J. Padgett, and E. Karimi, “Measuring the orbital angular momentum spectrum of an electron beam,” Nat. Commun. 8, 15536 (2017).
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V. Grillo, G. C. Gazzadi, E. Mafakheri, S. Frabboni, E. Karimi, and R. W. Boyd, “Holographic generation of highly twisted electron beams,” Phys. Rev. Lett. 114(3), 034801 (2015).
[Crossref] [PubMed]

V. Grillo, E. Karimi, G. C. Gazzadi, M. R. Stefano Frabboni, S. Dennis, and R. W. Boyd, “Generation of nondiffracting electron bessel beams,” Phys. Rev. X 4(1), 011013 (2014).
[Crossref]

Genevet, P.

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).
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X. D. Bai, X. L. Liang, Y. T. Sun, P. C. Hu, Y. Yao, K. Wang, J. P. Geng, and R. H. Jin, “Experimental Array for Generating Dual Circularly-Polarized Dual-Mode OAM Radio Beams,” Sci. Rep. 7, 40099 (2017).
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Goebel, B.

Gong, Y.

Y. Gong, R. Wang, Y. Deng, B. Zhang, N. Wang, N. Li, and P. Wang, “Generation and Transmission of OAM-Carrying Vortex Beams Using Circular Antenna Array,” IEEE Trans. Antenn. Propag. 65(6), 2940–2949 (2017).
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V. Grillo, A. H. Tavabi, F. Venturi, H. Larocque, R. Balboni, G. C. Gazzadi, S. Frabboni, P.-H. Lu, E. Mafakheri, F. Bouchard, R. E. Dunin-Borkowski, R. W. Boyd, M. P. J. Lavery, M. J. Padgett, and E. Karimi, “Measuring the orbital angular momentum spectrum of an electron beam,” Nat. Commun. 8, 15536 (2017).
[Crossref] [PubMed]

H. Larocque, F. Bouchard, V. Grillo, A. Sit, S. Frabboni, R. E. Dunin-Borkowski, M. J. Padgett, R. W. Boyd, and E. Karimi, “Nondestructive measurement of orbital angular momentum for an electron beam,” Phys. Rev. Lett. 117(15), 154801 (2016).
[Crossref] [PubMed]

V. Grillo, G. C. Gazzadi, E. Mafakheri, S. Frabboni, E. Karimi, and R. W. Boyd, “Holographic generation of highly twisted electron beams,” Phys. Rev. Lett. 114(3), 034801 (2015).
[Crossref] [PubMed]

V. Grillo, E. Karimi, G. C. Gazzadi, M. R. Stefano Frabboni, S. Dennis, and R. W. Boyd, “Generation of nondiffracting electron bessel beams,” Phys. Rev. X 4(1), 011013 (2014).
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H. Ren, X. Li, Q. Zhang, and M. Gu, “On-chip noninterference angular momentum multiplexing of broadband light,” Science 352(6287), 805–809 (2016).
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Gu, W.

Guo, G. C.

Z. Y. Zhou, Y. Li, D. S. Ding, W. Zhang, S. Shi, B. S. Shi, and G. C. Guo, “Orbital angular momentum photonic quantum interface,” Light Sci. Appl. 5(1), e16019 (2016).
[Crossref]

Hakobyan, D.

D. Hakobyan and E. Brasselet, “Left-handed optical radiation torque,” Nat. Photonics 8(8), 610–614 (2014).
[Crossref]

Handsteiner, J.

M. Krenn, J. Handsteiner, M. Fink, R. Fickler, R. Ursin, M. Malik, and A. Zeilinger, “Twisted light transmission over 143 km,” Proc. Natl. Acad. Sci. U.S.A. 113(48), 13648–13653 (2016).
[Crossref] [PubMed]

Hao, Z.

L. Cheng, W. Hong, and Z. Hao, “Design and implementation of planar reflection spiral phase plate for beams with orbital angular momentum,” IET Microw. Antennas Propag. 11(2), 260–264 (2017).
[Crossref]

Hasman, E.

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82(3), 328–330 (2003).
[Crossref]

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings,” Opt. Lett. 27(13), 1141–1143 (2002).
[Crossref] [PubMed]

Hong, M.

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1(9), e1500396 (2015).
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Hong, W.

L. Cheng, W. Hong, and Z. Hao, “Design and implementation of planar reflection spiral phase plate for beams with orbital angular momentum,” IET Microw. Antennas Propag. 11(2), 260–264 (2017).
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Z. Y. Zhou, Y. Li, D. S. Ding, W. Zhang, S. Shi, B. S. Shi, and G. C. Guo, “Orbital angular momentum photonic quantum interface,” Light Sci. Appl. 5(1), e16019 (2016).
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S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurface for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).
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S. Yu, L. Li, G. Shi, C. Zhu, and Y. Shi, “Generating multiple orbital angular momentum vortex beams using a metasurface in radio frequency domain,” Appl. Phys. Lett. 108(24), 241901 (2016).
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F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: first experimental test,” New J. Phys. 14(3), 033001 (2012).
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F. Bouchard, I. D. Leon, S. A. Schulz, J. Upham, E. Karimi, and R. W. Boyd, “Optical spin-to-orbital angular momentum conversion in ultra-thin metasurfaces with arbitrary topological charges,” Appl. Phys. Lett. 105(10), 101905 (2014).
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E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
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Wang, Y.

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K. Zhang, X. Ding, L. Zhang, and Q. Wu, “Anomalous three-dimensional refraction in the microwave region by ultra-thin high efficiency metalens with phase discontinuities in orthogonal directions,” New J. Phys. 16(10), 103020 (2014).
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Z. Zhang, S. Xiao, Y. Li, and B. Wang, “A circularly polarized multimode patch antenna for the generation of multiple orbital angular momentum modes,” IEEE Trans. Antenn. Propag. 16, 521–524 (2017).
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C. Xu, S. Zheng, W. Zhang, Y. Chen, H. Chi, X. Jin, and X. Zhang, “Free-space radio communication employing OAM multiplexing based on Rotman lens,” IEEE Trans. Antenn. Propag. 26(9), 738–740 (2016).

Yan, Y.

J. Wang, J. J. 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).
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J. Wang, J. J. 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).
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Yu, N.

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).
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Yu, S.

S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurface for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).
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S. Yu, L. Li, G. Shi, C. Zhu, and Y. Shi, “Generating multiple orbital angular momentum vortex beams using a metasurface in radio frequency domain,” Appl. Phys. Lett. 108(24), 241901 (2016).
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J. Wang, J. J. 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).
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M. Krenn, J. Handsteiner, M. Fink, R. Fickler, R. Ursin, M. Malik, and A. Zeilinger, “Twisted light transmission over 143 km,” Proc. Natl. Acad. Sci. U.S.A. 113(48), 13648–13653 (2016).
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Zhang, K.

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C. Xu, S. Zheng, W. Zhang, Y. Chen, H. Chi, X. Jin, and X. Zhang, “Free-space radio communication employing OAM multiplexing based on Rotman lens,” IEEE Trans. Antenn. Propag. 26(9), 738–740 (2016).

Z. Y. Zhou, Y. Li, D. S. Ding, W. Zhang, S. Shi, B. S. Shi, and G. C. Guo, “Orbital angular momentum photonic quantum interface,” Light Sci. Appl. 5(1), e16019 (2016).
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W. Zhang, S. Zheng, X. Hui, R. Dong, X. Jin, H. Chi, and X. Zhang, “Mode Division Multiplexing Communication Using Microwave Orbital Angular Momentum: An Experimental Study,” IEEE Trans. Antenn. Propag. 16(2), 1308–1318 (2017).

C. Xu, S. Zheng, W. Zhang, Y. Chen, H. Chi, X. Jin, and X. Zhang, “Free-space radio communication employing OAM multiplexing based on Rotman lens,” IEEE Trans. Antenn. Propag. 26(9), 738–740 (2016).

X. Hui, S. Zheng, Y. Chen, Y. Hu, X. Jin, H. Chi, and X. Zhang, “Multiplexed millimeter wave communication with dual orbital angular momentum (OAM) mode antennas,” Sci. Rep. 5(1), 10148 (2015).
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Z. Zhang, S. Xiao, Y. Li, and B. Wang, “A circularly polarized multimode patch antenna for the generation of multiple orbital angular momentum modes,” IEEE Trans. Antenn. Propag. 16, 521–524 (2017).
[Crossref]

Zhao, Z.

X. Li, M. Pu, Z. Zhao, X. Ma, J. Jin, Y. Wang, P. Gao, and X. Luo, “Catenary nanostructures as compact Bessel beam generators,” Sci. Rep. 6(1), 20524 (2016).
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W. Zhang, S. Zheng, X. Hui, R. Dong, X. Jin, H. Chi, and X. Zhang, “Mode Division Multiplexing Communication Using Microwave Orbital Angular Momentum: An Experimental Study,” IEEE Trans. Antenn. Propag. 16(2), 1308–1318 (2017).

C. Xu, S. Zheng, W. Zhang, Y. Chen, H. Chi, X. Jin, and X. Zhang, “Free-space radio communication employing OAM multiplexing based on Rotman lens,” IEEE Trans. Antenn. Propag. 26(9), 738–740 (2016).

X. Hui, S. Zheng, Y. Chen, Y. Hu, X. Jin, H. Chi, and X. Zhang, “Multiplexed millimeter wave communication with dual orbital angular momentum (OAM) mode antennas,” Sci. Rep. 5(1), 10148 (2015).
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Zhou, J.

Zhou, X.

S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurface for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).
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Z. Y. Zhou, Y. Li, D. S. Ding, W. Zhang, S. Shi, B. S. Shi, and G. C. Guo, “Orbital angular momentum photonic quantum interface,” Light Sci. Appl. 5(1), e16019 (2016).
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Zhu, B.

Zhu, C.

S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurface for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).
[Crossref]

S. Yu, L. Li, G. Shi, C. Zhu, and Y. Shi, “Generating multiple orbital angular momentum vortex beams using a metasurface in radio frequency domain,” Appl. Phys. Lett. 108(24), 241901 (2016).
[Crossref]

Adv. Mater. (1)

M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C. W. Qiu, “Visible-frequency metasurface for structuring and spatially multiplexing optical vortices,” Adv. Mater. 28(13), 2533–2539 (2016).
[Crossref] [PubMed]

Appl. Phys. Lett. (4)

F. Bouchard, I. D. Leon, S. A. Schulz, J. Upham, E. Karimi, and R. W. Boyd, “Optical spin-to-orbital angular momentum conversion in ultra-thin metasurfaces with arbitrary topological charges,” Appl. Phys. Lett. 105(10), 101905 (2014).
[Crossref]

S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurface for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic principle of the metalens generating focusing vortex beam with OAM mode. The inset shows the unit cell structure where the lattice period a = 11.1 mm, the thickness of substrate with relative permittivity εr = 2.2 is w = 2 mm, and θ is the rotation angle of unit cell. (b) Simulated transmission coefficients of the cross-polarized component. (c) Phase changes of the unit cells with different rotation angles under circularly polarized incidence.
Fig. 2
Fig. 2 Simulation and measurement results of the transmitted cross-polarized wave emitted from the metalens generating pure vortex beam and converging vortex beam with topological charge of 3, and photograph of measurement setup. (a) Simulated distribution of energy in xoz plane and xoy plane for (b) z = 5λ0 and (c) z = 1.67λ0 for pure vortex beam. (d) Simulated distributions of energy at xoz plane and xoy plane for (e) z = 5λ0 and (f) z = 1.67λ0 for converging vortex beam. The insets show the simulated phase distribution in corresponding xoy planes. (g) Measured distributions of energy in xoz plane and xoy plane for (h) z = 5λ0 and (i) z = 1.67λ0 for pure vortex beam. (j) Measured distribution of energy in xoz plane and xoy plane for (k) z = 5λ0 and (l) z = 1.67λ0 for converging vortex beam. The insets show the measured phase distribution in corresponding xoy plane. (m) The top view and (n) front view of the measurement setup, the distance between horn antenna and fabricated metalens d > 10λ0.
Fig. 3
Fig. 3 Simulation and measurement results of the transmitted cross-polarized wave emitted from metalens generating non-diffracting vortex beam with OAM mode having a topological charge of 1. (a) Simulated energy distribution in the xoz plane and xoy plane for (b) z = 10λ0, (c) z = 16.7λ0 and (d) z = 23.3λ0. The insets show simulated phase distribution in the corresponding xoy planes. (e) Measured energy distribution in xoz plane and xoy plane for (f) z = 5λ0, and (g) z = 20λ0. The insets show measured phase distribution in the corresponding xoy planes.
Fig. 4
Fig. 4 Normalized energy intensity of Bessel-like OAM beam and Laguerre-Gaussian beam generated by metalenses with the same diameter in xoy planes for (a) z = 26λ0, (b) z = 50λ0 and (c) z = 100λ0.
Fig. 5
Fig. 5 Efficiency of metalenses generating converging vortex beam and non-diffraction vortex beam.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

| E out = η E | E in +( η R e ±i2θ | R + η L e i2θ | L )
φ l (x,y)=larctan(y/x)
θ OAM+Conv (x,y)= 1 2 [larctan(y/x)+π( f 2 +( x 2 + y 2 ) | f |)/ λ 0 ]
θ OAM+Bessel (x,y)= 1 2 [larctan( y x )+ x 2 + y 2 sinβ]

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