Abstract

As a spatial structured light field, the optical vortex (OV) has attracted extensive attention in recent years. In practice, the OV lattice (OVL) is an optimal candidate for applications of orbital angular momentum (OAM)-based optical communications, microparticle manipulation, and micro/nanofabrication. However, traditional methods for producing OVLs meet a significant challenge: the OVL structures cannot be adjusted freely and form a close-packed arrangement, simultaneously. To overcome these difficulties, we propose an alternative scheme to produce close-packed OVLs (CPOVLs) with controllable structures. By borrowing the concept of the close-packed lattice from solid-state physics, CPOVLs with versatile structures are produced by using logical operations of expanding OV primitive cells combined with the technique of phase mask generation. Then, the existence of OAM states in the CPOVLs is verified. Furthermore, the energy flow and OAM distribution of the CPOVLs are visualized and analyzed. From a light field physics viewpoint, this work increases the adjustment dimensions and extends the fundamental understanding of the OVL, which will introduce novel applications.

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

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References

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2018 (6)

2017 (7)

H. X. Ma, X. Z. Li, Y. P. Tai, H. H. Li, J. G. Wang, M. M. Tang, J. Tang, Y. S. Wang, and Z. G. Nie, “Generation of circular optical vortex array,” Ann. Phys. (Berlin) 529(12), 1700285 (2017).
[Crossref]

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[Crossref]

J. Wang, “Data information transfer using complex optical fields: a review and perspective,” Chin. Opt. Lett. 15(3), 030005 (2017).
[Crossref]

Z. G. Zheng, C. L. Yuan, W. Hu, H. K. Bisoyi, M. J. Tang, Z. Liu, P. Z. Sun, W. Q. Yang, X. Q. Wang, D. Shen, Y. Li, F. Ye, Y. Q. Lu, G. Li, and Q. Li, “Light-patterned crystallographic direction of a self-organized 3D soft photonic crystal,” Adv. Mater. 29(42), 1703165 (2017).
[Crossref] [PubMed]

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. W. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

J. Lamstein, A. Bezryadina, D. Preece, J. C. Chen, and Z. G. Chen, “Optical tug-of-war tweezers: shaping light for dynamic control of bacterial cells,” Chin. Opt. Lett. 15(3), 030010 (2017).
[Crossref]

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[Crossref] [PubMed]

2016 (1)

2015 (5)

S. Li and J. Wang, “A compact trench-assisted multi-orbital-angular-momentum multi-ring fiber for ultrahigh-density space-division multiplexing (19 Rings × 22 Modes),” Sci. Rep. 4(1), 3853 (2015).
[Crossref] [PubMed]

J. A. Rodrigo and T. Alieva, “Freestyle 3D laser traps: tools for studying light-driven particle dynamics and beyond,” Optica 2(9), 812–815 (2015).
[Crossref]

T. Lei, M. Zhang, Y. R. Li, P. Jia, G. N. Liu, X. G. Xu, Z. H. Li, C. J. Min, J. Lin, C. Y. Yu, H. B. Niu, and X. C. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

J. Yu, C. Zhou, Y. Lu, J. Wu, L. Zhu, and W. Jia, “Square lattices of quasi-perfect optical vortices generated by two-dimensional encoding continuous-phase gratings,” Opt. Lett. 40(11), 2513–2516 (2015).
[Crossref] [PubMed]

P. Vaity and L. Rusch, “Perfect vortex beam: Fourier transformation of a Bessel beam,” Opt. Lett. 40(4), 597–600 (2015).
[Crossref] [PubMed]

2014 (1)

2013 (6)

S. H. Li and J. Wang, “Multi-orbital-angular-momentum multi-ring fiber for high-density space-division multiplexing,” IEEE Photonics J. 5(5), 7101007 (2013).
[Crossref]

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, and S. Residori, “Harnessing optical vortex lattices in nematic liquid crystals,” Phys. Rev. Lett. 111(9), 093902 (2013).
[Crossref] [PubMed]

M. D. Williams, M. M. Coles, K. Saadi, D. S. Bradshaw, and D. L. Andrews, “Optical vortex generation from molecular chromophore arrays,” Phys. Rev. Lett. 111(15), 153603 (2013).
[Crossref] [PubMed]

C. F. Kuo and S. C. Chu, “Numerical study of the properties of optical vortex array laser tweezers,” Opt. Express 21(22), 26418–26431 (2013).
[Crossref] [PubMed]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

A. S. Ostrovsky, C. Rickenstorff-Parrao, and V. Arrizón, “Generation of the “perfect” optical vortex using a liquid-crystal spatial light modulator,” Opt. Lett. 38(4), 534–536 (2013).
[Crossref] [PubMed]

2012 (5)

E. Brasselet, “Tunable optical vortex arrays from a single nematic topological defect,” Phys. Rev. Lett. 108(8), 087801 (2012).
[Crossref] [PubMed]

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338(6107), 640–643 (2012).
[Crossref] [PubMed]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. 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]

A. E. Willner, J. Wang, and H. Huang, “Applied physics. A different angle on light communications,” Science 337(6095), 655–656 (2012).
[Crossref] [PubMed]

A. Dudley and A. Forbes, “From stationary annular rings to rotating Bessel beams,” J. Opt. Soc. Am. A 29(4), 567–573 (2012).
[Crossref] [PubMed]

2011 (3)

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A 84(1), 013832 (2011).
[Crossref]

J. Becker, P. Rose, M. Boguslawski, and C. Denz, “Systematic approach to complex periodic vortex and helix lattices,” Opt. Express 19(10), 9848–9862 (2011).
[Crossref] [PubMed]

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
[Crossref]

2009 (1)

2007 (1)

2006 (1)

2005 (1)

2004 (1)

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92(1), 013601 (2004).
[Crossref] [PubMed]

2002 (1)

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

2001 (2)

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198(1), 21–27 (2001).
[Crossref]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

1999 (1)

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[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]

Ahmed, N.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. 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]

Alieva, T.

Allen, L.

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[Crossref]

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]

Andrews, D. L.

M. D. Williams, M. M. Coles, K. Saadi, D. S. Bradshaw, and D. L. Andrews, “Optical vortex generation from molecular chromophore arrays,” Phys. Rev. Lett. 111(15), 153603 (2013).
[Crossref] [PubMed]

Arnold, A. S.

Arrizón, V.

Assanto, G.

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, and S. Residori, “Harnessing optical vortex lattices in nematic liquid crystals,” Phys. Rev. Lett. 111(9), 093902 (2013).
[Crossref] [PubMed]

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[Crossref]

Barboza, R.

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, and S. Residori, “Harnessing optical vortex lattices in nematic liquid crystals,” Phys. Rev. Lett. 111(9), 093902 (2013).
[Crossref] [PubMed]

Barnett, S. M.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92(1), 013601 (2004).
[Crossref] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
[Crossref] [PubMed]

Becker, J.

Beijersbergen, M. W.

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]

Bezryadina, A.

Bisoyi, H. K.

Z. G. Zheng, C. L. Yuan, W. Hu, H. K. Bisoyi, M. J. Tang, Z. Liu, P. Z. Sun, W. Q. Yang, X. Q. Wang, D. Shen, Y. Li, F. Ye, Y. Q. Lu, G. Li, and Q. Li, “Light-patterned crystallographic direction of a self-organized 3D soft photonic crystal,” Adv. Mater. 29(42), 1703165 (2017).
[Crossref] [PubMed]

Boguslawski, M.

J. Becker, P. Rose, M. Boguslawski, and C. Denz, “Systematic approach to complex periodic vortex and helix lattices,” Opt. Express 19(10), 9848–9862 (2011).
[Crossref] [PubMed]

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A 84(1), 013832 (2011).
[Crossref]

Bortolozzo, U.

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, and S. Residori, “Harnessing optical vortex lattices in nematic liquid crystals,” Phys. Rev. Lett. 111(9), 093902 (2013).
[Crossref] [PubMed]

Bowman, R.

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
[Crossref]

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Bradshaw, D. S.

M. D. Williams, M. M. Coles, K. Saadi, D. S. Bradshaw, and D. L. Andrews, “Optical vortex generation from molecular chromophore arrays,” Phys. Rev. Lett. 111(15), 153603 (2013).
[Crossref] [PubMed]

Brasselet, E.

E. Brasselet, “Tunable optical vortex arrays from a single nematic topological defect,” Phys. Rev. Lett. 108(8), 087801 (2012).
[Crossref] [PubMed]

Chang, C.

Chen, J.

P. Chen, L. L. Ma, W. Duan, J. Chen, S. J. Ge, Z. H. Zhu, M. J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref] [PubMed]

Chen, J. C.

Chen, L. X.

Chen, P.

P. Chen, L. L. Ma, W. Duan, J. Chen, S. J. Ge, Z. H. Zhu, M. J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref] [PubMed]

P. Chen, S. J. Ge, W. Duan, B. Y. Wei, G. X. Cui, W. Hu, and Y. C. Lu, “Digitalized geometric phases for parallel optical spin and orbital angular momentum encoding,” ACS Photonics 4(6), 1333–1338 (2017).
[Crossref]

Chen, Z. G.

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Rickenstorff-Parrao, C.

Rodrigo, J. A.

Rosales-Guzman, C.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. W. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
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J. Becker, P. Rose, M. Boguslawski, and C. Denz, “Systematic approach to complex periodic vortex and helix lattices,” Opt. Express 19(10), 9848–9862 (2011).
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M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A 84(1), 013832 (2011).
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B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. W. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

Rusch, L.

Saadi, K.

M. D. Williams, M. M. Coles, K. Saadi, D. S. Bradshaw, and D. L. Andrews, “Optical vortex generation from molecular chromophore arrays,” Phys. Rev. Lett. 111(15), 153603 (2013).
[Crossref] [PubMed]

Schaeff, C.

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338(6107), 640–643 (2012).
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Z. G. Zheng, C. L. Yuan, W. Hu, H. K. Bisoyi, M. J. Tang, Z. Liu, P. Z. Sun, W. Q. Yang, X. Q. Wang, D. Shen, Y. Li, F. Ye, Y. Q. Lu, G. Li, and Q. Li, “Light-patterned crystallographic direction of a self-organized 3D soft photonic crystal,” Adv. Mater. 29(42), 1703165 (2017).
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Skeldon, K.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92(1), 013601 (2004).
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Spreeuw, R. J. C.

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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L. Stoyanov, G. Maleshkov, M. Zhekova, I. Stefanov, G. G. Paulus, and A. Dreischuh, “Far-field beam reshaping by manipulating the topological charges of hexagonal optical vortex lattices,” J. Opt. 20(9), 095601 (2018).
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L. Stoyanov, G. Maleshkov, M. Zhekova, I. Stefanov, D. N. Neshev, G. G. Paulus, and A. Dreischuh, “Far-field pattern formation by manipulating the topological charges of square-shaped optical vortex lattices,” J. Opt. Soc. Am. B 35(2), 402–409 (2018).
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L. Stoyanov, G. Maleshkov, M. Zhekova, I. Stefanov, D. N. Neshev, G. G. Paulus, and A. Dreischuh, “Far-field pattern formation by manipulating the topological charges of square-shaped optical vortex lattices,” J. Opt. Soc. Am. B 35(2), 402–409 (2018).
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L. Stoyanov, G. Maleshkov, M. Zhekova, I. Stefanov, G. G. Paulus, and A. Dreischuh, “Far-field beam reshaping by manipulating the topological charges of hexagonal optical vortex lattices,” J. Opt. 20(9), 095601 (2018).
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Z. G. Zheng, C. L. Yuan, W. Hu, H. K. Bisoyi, M. J. Tang, Z. Liu, P. Z. Sun, W. Q. Yang, X. Q. Wang, D. Shen, Y. Li, F. Ye, Y. Q. Lu, G. Li, and Q. Li, “Light-patterned crystallographic direction of a self-organized 3D soft photonic crystal,” Adv. Mater. 29(42), 1703165 (2017).
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Tai, Y.

Tai, Y. P.

H. X. Ma, X. Z. Li, Y. P. Tai, H. H. Li, J. G. Wang, M. M. Tang, J. Tang, Y. S. Wang, and Z. G. Nie, “Generation of circular optical vortex array,” Ann. Phys. (Berlin) 529(12), 1700285 (2017).
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H. X. Ma, X. Z. Li, Y. P. Tai, H. H. Li, J. G. Wang, M. M. Tang, J. Tang, Y. S. Wang, and Z. G. Nie, “Generation of circular optical vortex array,” Ann. Phys. (Berlin) 529(12), 1700285 (2017).
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H. Ma, X. Li, Y. Tai, H. Li, J. Wang, M. Tang, Y. Wang, J. Tang, and Z. Nie, “In situ measurement of the topological charge of a perfect vortex using the phase shift method,” Opt. Lett. 42(1), 135–138 (2017).
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Tang, M. J.

P. Chen, L. L. Ma, W. Duan, J. Chen, S. J. Ge, Z. H. Zhu, M. J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30(10), 1705865 (2018).
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H. X. Ma, X. Z. Li, Y. P. Tai, H. H. Li, J. G. Wang, M. M. Tang, J. Tang, Y. S. Wang, and Z. G. Nie, “Generation of circular optical vortex array,” Ann. Phys. (Berlin) 529(12), 1700285 (2017).
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Tsai, Y. L.

Tur, M.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. 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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Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
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R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, and S. Residori, “Harnessing optical vortex lattices in nematic liquid crystals,” Phys. Rev. Lett. 111(9), 093902 (2013).
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S. Li and J. Wang, “A compact trench-assisted multi-orbital-angular-momentum multi-ring fiber for ultrahigh-density space-division multiplexing (19 Rings × 22 Modes),” Sci. Rep. 4(1), 3853 (2015).
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S. H. Li and J. Wang, “Multi-orbital-angular-momentum multi-ring fiber for high-density space-division multiplexing,” IEEE Photonics J. 5(5), 7101007 (2013).
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A. E. Willner, J. Wang, and H. Huang, “Applied physics. A different angle on light communications,” Science 337(6095), 655–656 (2012).
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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. 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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H. X. Ma, X. Z. Li, Y. P. Tai, H. H. Li, J. G. Wang, M. M. Tang, J. Tang, Y. S. Wang, and Z. G. Nie, “Generation of circular optical vortex array,” Ann. Phys. (Berlin) 529(12), 1700285 (2017).
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Z. G. Zheng, C. L. Yuan, W. Hu, H. K. Bisoyi, M. J. Tang, Z. Liu, P. Z. Sun, W. Q. Yang, X. Q. Wang, D. Shen, Y. Li, F. Ye, Y. Q. Lu, G. Li, and Q. Li, “Light-patterned crystallographic direction of a self-organized 3D soft photonic crystal,” Adv. Mater. 29(42), 1703165 (2017).
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Wang, Y. S.

H. X. Ma, X. Z. Li, Y. P. Tai, H. H. Li, J. G. Wang, M. M. Tang, J. Tang, Y. S. Wang, and Z. G. Nie, “Generation of circular optical vortex array,” Ann. Phys. (Berlin) 529(12), 1700285 (2017).
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P. Chen, S. J. Ge, W. Duan, B. Y. Wei, G. X. Cui, W. Hu, and Y. C. Lu, “Digitalized geometric phases for parallel optical spin and orbital angular momentum encoding,” ACS Photonics 4(6), 1333–1338 (2017).
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A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
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M. D. Williams, M. M. Coles, K. Saadi, D. S. Bradshaw, and D. L. Andrews, “Optical vortex generation from molecular chromophore arrays,” Phys. Rev. Lett. 111(15), 153603 (2013).
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Willner, A. E.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. 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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A. E. Willner, J. Wang, and H. Huang, “Applied physics. A different angle on light communications,” Science 337(6095), 655–656 (2012).
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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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Wu, J.

Wu, S. T.

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P. Chen, L. L. Ma, W. Duan, J. Chen, S. J. Ge, Z. H. Zhu, M. J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30(10), 1705865 (2018).
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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. 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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Yang, J. Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. 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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Z. G. Zheng, C. L. Yuan, W. Hu, H. K. Bisoyi, M. J. Tang, Z. Liu, P. Z. Sun, W. Q. Yang, X. Q. Wang, D. Shen, Y. Li, F. Ye, Y. Q. Lu, G. Li, and Q. Li, “Light-patterned crystallographic direction of a self-organized 3D soft photonic crystal,” Adv. Mater. 29(42), 1703165 (2017).
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Z. G. Zheng, C. L. Yuan, W. Hu, H. K. Bisoyi, M. J. Tang, Z. Liu, P. Z. Sun, W. Q. Yang, X. Q. Wang, D. Shen, Y. Li, F. Ye, Y. Q. Lu, G. Li, and Q. Li, “Light-patterned crystallographic direction of a self-organized 3D soft photonic crystal,” Adv. Mater. 29(42), 1703165 (2017).
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Yuan, C.

Yuan, C. L.

Z. G. Zheng, C. L. Yuan, W. Hu, H. K. Bisoyi, M. J. Tang, Z. Liu, P. Z. Sun, W. Q. Yang, X. Q. Wang, D. Shen, Y. Li, F. Ye, Y. Q. Lu, G. Li, and Q. Li, “Light-patterned crystallographic direction of a self-organized 3D soft photonic crystal,” Adv. Mater. 29(42), 1703165 (2017).
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Yuan, X. C.

T. Lei, M. Zhang, Y. R. Li, P. Jia, G. N. Liu, X. G. Xu, Z. H. Li, C. J. Min, J. Lin, C. Y. Yu, H. B. Niu, and X. C. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
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N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. 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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Zeilinger, A.

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338(6107), 640–643 (2012).
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A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
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T. Lei, M. Zhang, Y. R. Li, P. Jia, G. N. Liu, X. G. Xu, Z. H. Li, C. J. Min, J. Lin, C. Y. Yu, H. B. Niu, and X. C. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
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Zhang, W. H.

Zhang, Y. W.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. W. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
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Zhekova, M.

L. Stoyanov, G. Maleshkov, M. Zhekova, I. Stefanov, G. G. Paulus, and A. Dreischuh, “Far-field beam reshaping by manipulating the topological charges of hexagonal optical vortex lattices,” J. Opt. 20(9), 095601 (2018).
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L. Stoyanov, G. Maleshkov, M. Zhekova, I. Stefanov, D. N. Neshev, G. G. Paulus, and A. Dreischuh, “Far-field pattern formation by manipulating the topological charges of square-shaped optical vortex lattices,” J. Opt. Soc. Am. B 35(2), 402–409 (2018).
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Z. G. Zheng, C. L. Yuan, W. Hu, H. K. Bisoyi, M. J. Tang, Z. Liu, P. Z. Sun, W. Q. Yang, X. Q. Wang, D. Shen, Y. Li, F. Ye, Y. Q. Lu, G. Li, and Q. Li, “Light-patterned crystallographic direction of a self-organized 3D soft photonic crystal,” Adv. Mater. 29(42), 1703165 (2017).
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Zhu, L.

Zhu, Z. H.

X. D. Qiu, F. S. Li, W. H. Zhang, Z. H. Zhu, and L. X. Chen, “Spiral phase contrast imaging in nonlinear optics: seeing phase objects using invisible illumination,” Optica 5(2), 208–212 (2018).
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P. Chen, L. L. Ma, W. Duan, J. Chen, S. J. Ge, Z. H. Zhu, M. J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30(10), 1705865 (2018).
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ACS Photonics (1)

P. Chen, S. J. Ge, W. Duan, B. Y. Wei, G. X. Cui, W. Hu, and Y. C. Lu, “Digitalized geometric phases for parallel optical spin and orbital angular momentum encoding,” ACS Photonics 4(6), 1333–1338 (2017).
[Crossref]

Adv. Mater. (2)

Z. G. Zheng, C. L. Yuan, W. Hu, H. K. Bisoyi, M. J. Tang, Z. Liu, P. Z. Sun, W. Q. Yang, X. Q. Wang, D. Shen, Y. Li, F. Ye, Y. Q. Lu, G. Li, and Q. Li, “Light-patterned crystallographic direction of a self-organized 3D soft photonic crystal,” Adv. Mater. 29(42), 1703165 (2017).
[Crossref] [PubMed]

P. Chen, L. L. Ma, W. Duan, J. Chen, S. J. Ge, Z. H. Zhu, M. J. Tang, R. Xu, W. Gao, T. Li, W. Hu, and Y. Q. Lu, “Digitalizing self-assembled chiral superstructures for optical vortex processing,” Adv. Mater. 30(10), 1705865 (2018).
[Crossref] [PubMed]

Ann. Phys. (Berlin) (1)

H. X. Ma, X. Z. Li, Y. P. Tai, H. H. Li, J. G. Wang, M. M. Tang, J. Tang, Y. S. Wang, and Z. G. Nie, “Generation of circular optical vortex array,” Ann. Phys. (Berlin) 529(12), 1700285 (2017).
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Chin. Opt. Lett. (2)

IEEE Photonics J. (1)

S. H. Li and J. Wang, “Multi-orbital-angular-momentum multi-ring fiber for high-density space-division multiplexing,” IEEE Photonics J. 5(5), 7101007 (2013).
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J. Opt. (1)

L. Stoyanov, G. Maleshkov, M. Zhekova, I. Stefanov, G. G. Paulus, and A. Dreischuh, “Far-field beam reshaping by manipulating the topological charges of hexagonal optical vortex lattices,” J. Opt. 20(9), 095601 (2018).
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J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Light Sci. Appl. (1)

T. Lei, M. Zhang, Y. R. Li, P. Jia, G. N. Liu, X. G. Xu, Z. H. Li, C. J. Min, J. Lin, C. Y. Yu, H. B. Niu, and X. C. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4(3), e257 (2015).
[Crossref]

Nat. Photonics (2)

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. 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. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
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Nat. Phys. (1)

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. W. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13(4), 397–402 (2017).
[Crossref]

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
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Opt. Commun. (1)

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198(1), 21–27 (2001).
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Opt. Lett. (6)

Optica (2)

Photon. Res. (1)

Phys. Rev. A (2)

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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M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A 84(1), 013832 (2011).
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Phys. Rev. Lett. (5)

E. Brasselet, “Tunable optical vortex arrays from a single nematic topological defect,” Phys. Rev. Lett. 108(8), 087801 (2012).
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R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, and S. Residori, “Harnessing optical vortex lattices in nematic liquid crystals,” Phys. Rev. Lett. 111(9), 093902 (2013).
[Crossref] [PubMed]

M. D. Williams, M. M. Coles, K. Saadi, D. S. Bradshaw, and D. L. Andrews, “Optical vortex generation from molecular chromophore arrays,” Phys. Rev. Lett. 111(15), 153603 (2013).
[Crossref] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88(25), 257901 (2002).
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J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92(1), 013601 (2004).
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S. Li and J. Wang, “A compact trench-assisted multi-orbital-angular-momentum multi-ring fiber for ultrahigh-density space-division multiplexing (19 Rings × 22 Modes),” Sci. Rep. 4(1), 3853 (2015).
[Crossref] [PubMed]

Science (3)

A. E. Willner, J. Wang, and H. Huang, “Applied physics. A different angle on light communications,” Science 337(6095), 655–656 (2012).
[Crossref] [PubMed]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338(6107), 640–643 (2012).
[Crossref] [PubMed]

Other (2)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999) Ch. 2.

J. W. Goodman, Introduction to Fourier Optics (Viva Books Private Limited, 2007).

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Figures (7)

Fig. 1
Fig. 1 Routes to produce CPOVLs with controllable structures. Route I: a→b→c, to produce a square OVL by expanding a square primitive cell (PC1). Route II: d→e→f, to produce a close-packed hexagonal OVL. Route III: d→g→h, to produce a close-packed triangular OVL. The hexagonal and triangular OVLs are generated by the intersection of two expanding rhombic primitive cells: PC2 and PC3, respectively.
Fig. 2
Fig. 2 Schematics of (a) the generation of the phase mask and (b) the experimental setup.
Fig. 3
Fig. 3 Close-packed arrangement conditions of OVLs with different structures. Each row of a1–a4 indicates that the interval between two adjacent lattice elements in the OVL increases gradually. Each column of b1–b4 indicates that two adjacent lattice elements have the same interval but different structures. Column b3 demonstrates the OVL intensity under the critical condition that satisfies close-packed arrangement and exact distinction conditions, simultaneously. The TC values (OAM) are given as random integers within [-10 10]. The intensity pattern and corresponding phase distribution of a hexagonal OVL are presented in (c) and (d), respectively. To observe explicitly for the printout readers, the brightness of all experimental intensity patterns is increased, similarly hereinafter.
Fig. 4
Fig. 4 Interference patterns between the OVL and its conjugate image. The interferograms in the three columns demonstrate the superposition of 1, 4, and 9 lattice elements, respectively. Superposed areas are represented as Dirac symbols of |l1, l2>. These patterns verify the existence of the optical vortices by the spiral shape of the coherent fringes, and the TCs can be determined by counting the number of spiral fringes. Insets are magnified × 5 and the central peaks are blocked.
Fig. 5
Fig. 5 Expansion of square, hexagonal, and triangular OVLs. During the expansion, inner OVs maintain their OAM states. OVs on outer sides are reassigned random integers within [-10 10] as their OAM states. The intensity profiles at the red and blue dotted-line positions of the OVLs are demonstrated in the third-column panel. The critical condition of two adjacent OVs is determined by double peaks or the full width at half maximum (FWHM) of a single peak.
Fig. 6
Fig. 6 Energy flow (upper panel) and OAM distributions (lower panel) of the close-packed arrangement OVLs (numerical simulation results) corresponding to the first column of Fig. 5. In the energy-flow images, the arrow and its length represent the direction and magnitude of the energy flow at this point, respectively. In the OAM distribution images, ⊙ represents the helical axis, whose direction obeys the right-hand rule.
Fig. 7
Fig. 7 More complex OVLs with controlled structures: (a) fractional hexagonal lattice with multi-gaps, (b) hollow rhombus-shaped lattice, (c) “Olympic rings”-shaped lattice, (d) honeycomb-shaped lattice, and (e) hollow hexagram-shaped lattice.

Equations (3)

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( a b )=d( 1 0 sin( θπ/2 ) cos( θπ/2 ) )( x y )T( x y )
Lattice= n=1 N { exp[ jk( n1 )ρ α n ] exp( j l n φ )exp[ j2π( S n,1 x+ S n,2 y ) ] }
E( u,v ) n=1 N { exp[ j l n arctan( v S n,2 u S n,1 ) ]exp[ ( ( u S n,1 ) 2 + ( v S n,2 ) 2 r n ) 2 ω 2 ] }

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