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

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    [Crossref]
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    [Crossref] [PubMed]
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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)

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

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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