Abstract

We propose an approach for creating optical vortex array (OVA) arranged along arbitrary curvilinear path, based on the coaxial interference of two width-controllable component curves calculated by modified holographic beam shaping technique. The two component curve beams have different radial dimensions as well as phase gradients along each beam such that the number of phase singularity in the curvilinear arranged optical vortex array (CA-OVA) is freely tunable on demand. Hybrid CA-OVA that comprises of multiple OVA structures along different respective curves is also discussed and demonstrated. Furthermore, we study the conversion of CA-OVA into vector mode that comprises of polarization vortex array with varied polarization state distribution. Both simulation and experimental results prove the performance of the proposed method of generating a complex structured vortex array, which is of significance for potential applications including multiple trapping of micro-sized particles.

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

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References

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2017 (6)

2016 (6)

2015 (6)

2014 (1)

2013 (7)

2012 (1)

2011 (7)

I. A. Litvin, A. Dudley, and A. Forbes, “Poynting vector and orbital angular momentum density of superpositions of Bessel beams,” Opt. Express 19(18), 16760–16771 (2011).
[Crossref] [PubMed]

Y. C. Lin, T. H. Lu, K. F. Huang, and Y. F. Chen, “Generation of optical vortex array with transformation of standing-wave Laguerre-Gaussian mode,” Opt. Express 19(11), 10293–10303 (2011).
[Crossref] [PubMed]

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

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011).
[Crossref]

Z. Wang, N. Zhang, and X.-C. Yuan, “High-volume optical vortex multiplexing and de-multiplexing for free-space optical communication,” Opt. Express 19(2), 482–492 (2011).
[Crossref] [PubMed]

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation in light beams,” J. Opt. 13(5), 053001 (2011).
[Crossref]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-Order Poincaré Sphere, Stokes Parameters, and the Angular Momentum of Light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref] [PubMed]

2010 (2)

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
[Crossref] [PubMed]

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[Crossref] [PubMed]

2009 (1)

2007 (3)

2005 (1)

2003 (1)

2001 (2)

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]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

1993 (1)

I. Basistiy, V. Y. Bazhenov, M. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103(5–6), 422–428 (1993).
[Crossref]

1990 (1)

1983 (1)

Aadhi, A.

Abramochkin, E.

Aleksanyan, A.

A. Aleksanyan, N. Kravets, and E. Brasselet, “Multiple-Star System Adaptive Vortex Coronagraphy Using a Liquid Crystal Light Valve,” Phys. Rev. Lett. 118(20), 203902 (2017).
[Crossref] [PubMed]

Alfano, R. R.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-Order Poincaré Sphere, Stokes Parameters, and the Angular Momentum of Light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref] [PubMed]

Alieva, T.

Arlt, J.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Arnold, A. S.

Arrizón, V.

Barnett, S. M.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[Crossref] [PubMed]

Basistiy, I.

I. Basistiy, V. Y. Bazhenov, M. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103(5–6), 422–428 (1993).
[Crossref]

Bazhenov, V. Y.

I. Basistiy, V. Y. Bazhenov, M. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103(5–6), 422–428 (1993).
[Crossref]

Bekshaev, A.

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation in light beams,” J. Opt. 13(5), 053001 (2011).
[Crossref]

Bezryadina, A.

Bliokh, K.

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation in light beams,” J. Opt. 13(5), 053001 (2011).
[Crossref]

Bowman, R.

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

Boyd, R. W.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[Crossref] [PubMed]

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]

Brasselet, E.

A. Aleksanyan, N. Kravets, and E. Brasselet, “Multiple-Star System Adaptive Vortex Coronagraphy Using a Liquid Crystal Light Valve,” Phys. Rev. Lett. 118(20), 203902 (2017).
[Crossref] [PubMed]

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Cao, W.

Castro, I.

Chan, C. T.

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
[Crossref] [PubMed]

Chang, C.

Chen, J. C.

Chen, Y.

Chen, Y. F.

Chen, Z.

Chen, Z. G.

Chmyrov, A.

A. Chmyrov, J. Keller, T. Grotjohann, M. Ratz, E. d’Este, S. Jakobs, C. Eggeling, and S. W. Hell, “Nanoscopy with more than 100,000 ‘doughnuts’,” Nat. Methods 10(8), 737–740 (2013).
[Crossref] [PubMed]

Chu, S. C.

Cižmár, T.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011).
[Crossref]

d’Este, E.

A. Chmyrov, J. Keller, T. Grotjohann, M. Ratz, E. d’Este, S. Jakobs, C. Eggeling, and S. W. Hell, “Nanoscopy with more than 100,000 ‘doughnuts’,” Nat. Methods 10(8), 737–740 (2013).
[Crossref] [PubMed]

Deng, D.

Dholakia, K.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011).
[Crossref]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Ding, J.

Du, L.

Dudley, A.

Eggeling, C.

A. Chmyrov, J. Keller, T. Grotjohann, M. Ratz, E. d’Este, S. Jakobs, C. Eggeling, and S. W. Hell, “Nanoscopy with more than 100,000 ‘doughnuts’,” Nat. Methods 10(8), 737–740 (2013).
[Crossref] [PubMed]

Ellinas, D.

Fang, Z. X.

Forbes, A.

Franke-Arnold, S.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[Crossref] [PubMed]

S. Franke-Arnold, J. Leach, M. J. Padgett, V. E. Lembessis, D. Ellinas, A. J. Wright, J. M. Girkin, P. Ohberg, and A. S. Arnold, “Optical ferris wheel for ultracold atoms,” Opt. Express 15(14), 8619–8625 (2007).
[Crossref] [PubMed]

Fu, S.

Gao, C.

Gao, J.

Gao, Y.

García-García, J.

Girkin, J. M.

Gong, L.

Grotjohann, T.

A. Chmyrov, J. Keller, T. Grotjohann, M. Ratz, E. d’Este, S. Jakobs, C. Eggeling, and S. W. Hell, “Nanoscopy with more than 100,000 ‘doughnuts’,” Nat. Methods 10(8), 737–740 (2013).
[Crossref] [PubMed]

Han, Y.

He, C.

S. J. Huang, Z. Miao, C. He, F. F. Pang, Y. C. Li, and T. Y. Wang, “Composite vortex beams by coaxial superposition of Laguerre–Gaussian beams,” Opt. Lasers Eng. 78, 132–139 (2016).
[Crossref]

Hell, S. W.

A. Chmyrov, J. Keller, T. Grotjohann, M. Ratz, E. d’Este, S. Jakobs, C. Eggeling, and S. W. Hell, “Nanoscopy with more than 100,000 ‘doughnuts’,” Nat. Methods 10(8), 737–740 (2013).
[Crossref] [PubMed]

Hu, A.

Huang, H.

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]

Huang, K. F.

Huang, S. J.

S. J. Huang, Z. Miao, C. He, F. F. Pang, Y. C. Li, and T. Y. Wang, “Composite vortex beams by coaxial superposition of Laguerre–Gaussian beams,” Opt. Lasers Eng. 78, 132–139 (2016).
[Crossref]

Ireland, D. G.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[Crossref] [PubMed]

Izdebskaya, Ya.

Jack, B.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[Crossref] [PubMed]

Jakobs, S.

A. Chmyrov, J. Keller, T. Grotjohann, M. Ratz, E. d’Este, S. Jakobs, C. Eggeling, and S. W. Hell, “Nanoscopy with more than 100,000 ‘doughnuts’,” Nat. Methods 10(8), 737–740 (2013).
[Crossref] [PubMed]

Jha, A. K.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[Crossref] [PubMed]

Jia, P.

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]

Jia, W.

Karahroudi, M. K.

Keller, J.

A. Chmyrov, J. Keller, T. Grotjohann, M. Ratz, E. d’Este, S. Jakobs, C. Eggeling, and S. W. Hell, “Nanoscopy with more than 100,000 ‘doughnuts’,” Nat. Methods 10(8), 737–740 (2013).
[Crossref] [PubMed]

Khilo, N.

Khonina, S. N.

Kotlyar, V. V.

Kovalev, A. A.

Kravets, N.

A. Aleksanyan, N. Kravets, and E. Brasselet, “Multiple-Star System Adaptive Vortex Coronagraphy Using a Liquid Crystal Light Valve,” Phys. Rev. Lett. 118(20), 203902 (2017).
[Crossref] [PubMed]

Kristensen, P.

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]

Kuo, C. F.

Lamstein, J.

Leach, J.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[Crossref] [PubMed]

S. Franke-Arnold, J. Leach, M. J. Padgett, V. E. Lembessis, D. Ellinas, A. J. Wright, J. M. Girkin, P. Ohberg, and A. S. Arnold, “Optical ferris wheel for ultracold atoms,” Opt. Express 15(14), 8619–8625 (2007).
[Crossref] [PubMed]

Leanhardt, A. E.

Lei, T.

J. Liu, C. Min, T. Lei, L. Du, Y. Yuan, S. Wei, Y. Wang, and X. C. Yuan, “Generation and detection of broadband multi-channel orbital angular momentum by micrometer-scale meta-reflectarray,” Opt. Express 24(1), 212–218 (2016).
[Crossref] [PubMed]

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]

Lembessis, V. E.

Li, H.

H. Ma, X. Li, Y. Tai, H. Li, J. Wang, M. Tang, J. Tang, Y. Wang, and Z. Nie, “Generation of Circular Optical Vortex Array,” Annalen. Der. Physik. 529(12), 1700285 (2017).
[Crossref]

Li, X.

H. Ma, X. Li, Y. Tai, H. Li, J. Wang, M. Tang, J. Tang, Y. Wang, and Z. Nie, “Generation of Circular Optical Vortex Array,” Annalen. Der. Physik. 529(12), 1700285 (2017).
[Crossref]

Li, Y.

Li, Y. C.

S. J. Huang, Z. Miao, C. He, F. F. Pang, Y. C. Li, and T. Y. Wang, “Composite vortex beams by coaxial superposition of Laguerre–Gaussian beams,” Opt. Lasers Eng. 78, 132–139 (2016).
[Crossref]

Li, Y. R.

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]

Li, Z. H.

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]

Lin, J.

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]

Lin, Y. C.

Lin, Z.

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
[Crossref] [PubMed]

Litvin, I. A.

Liu, G. N.

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]

Liu, J.

Lu, R. D.

Lu, T. H.

Lu, Y.

Ma, H.

H. Ma, X. Li, Y. Tai, H. Li, J. Wang, M. Tang, J. Tang, Y. Wang, and Z. Nie, “Generation of Circular Optical Vortex Array,” Annalen. Der. Physik. 529(12), 1700285 (2017).
[Crossref]

MacDonald, M. P.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Mair, 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).
[Crossref] [PubMed]

Maleev, I. D.

Miao, Z.

S. J. Huang, Z. Miao, C. He, F. F. Pang, Y. C. Li, and T. Y. Wang, “Composite vortex beams by coaxial superposition of Laguerre–Gaussian beams,” Opt. Lasers Eng. 78, 132–139 (2016).
[Crossref]

Milione, G.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-Order Poincaré Sphere, Stokes Parameters, and the Angular Momentum of Light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref] [PubMed]

Min, C.

Min, C. J.

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]

Mobashery, A.

Moiseev, O. Yu.

Ng, J.

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
[Crossref] [PubMed]

Nie, S.

Nie, Z.

H. Ma, X. Li, Y. Tai, H. Li, J. Wang, M. Tang, J. Tang, Y. Wang, and Z. Nie, “Generation of Circular Optical Vortex Array,” Annalen. Der. Physik. 529(12), 1700285 (2017).
[Crossref]

Niu, H. B.

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]

Nolan, D. A.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-Order Poincaré Sphere, Stokes Parameters, and the Angular Momentum of Light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref] [PubMed]

Ohberg, P.

Ostrovsky, A. S.

Padgett, M.

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

Padgett, M. J.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[Crossref] [PubMed]

S. Franke-Arnold, J. Leach, M. J. Padgett, V. E. Lembessis, D. Ellinas, A. J. Wright, J. M. Girkin, P. Ohberg, and A. S. Arnold, “Optical ferris wheel for ultracold atoms,” Opt. Express 15(14), 8619–8625 (2007).
[Crossref] [PubMed]

Pang, F. F.

S. J. Huang, Z. Miao, C. He, F. F. Pang, Y. C. Li, and T. Y. Wang, “Composite vortex beams by coaxial superposition of Laguerre–Gaussian beams,” Opt. Lasers Eng. 78, 132–139 (2016).
[Crossref]

Parmoon, B.

Paterson, L.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Preece, D.

Qasemi, M.

Qi, Y.

Qian, B.

Qu, S.

Ramachandran, S.

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]

Ramos-García, R.

Ratz, M.

A. Chmyrov, J. Keller, T. Grotjohann, M. Ratz, E. d’Este, S. Jakobs, C. Eggeling, and S. W. Hell, “Nanoscopy with more than 100,000 ‘doughnuts’,” Nat. Methods 10(8), 737–740 (2013).
[Crossref] [PubMed]

Ren, Y.

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]

Ren, Y. X.

Rickenstorff-Parrao, C.

Rodrigo, J. A.

Romero, J.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[Crossref] [PubMed]

Rumala, Y. S.

Rusch, L.

Saghafifar, H.

Senthilkumaran, P.

Shvedov, V.

Sibbett, W.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[Crossref] [PubMed]

Singh, R. P.

Skidanov, R. V.

Soifer, V. A.

Soskin, M.

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation in light beams,” J. Opt. 13(5), 053001 (2011).
[Crossref]

I. Basistiy, V. Y. Bazhenov, M. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103(5–6), 422–428 (1993).
[Crossref]

Su, X.

Sun, Q.

Swartzlander, G. A.

Sztul, H. I.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-Order Poincaré Sphere, Stokes Parameters, and the Angular Momentum of Light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref] [PubMed]

Tai, Y.

H. Ma, X. Li, Y. Tai, H. Li, J. Wang, M. Tang, J. Tang, Y. Wang, and Z. Nie, “Generation of Circular Optical Vortex Array,” Annalen. Der. Physik. 529(12), 1700285 (2017).
[Crossref]

Tamm, C.

Tang, J.

H. Ma, X. Li, Y. Tai, H. Li, J. Wang, M. Tang, J. Tang, Y. Wang, and Z. Nie, “Generation of Circular Optical Vortex Array,” Annalen. Der. Physik. 529(12), 1700285 (2017).
[Crossref]

Tang, M.

H. Ma, X. Li, Y. Tai, H. Li, J. Wang, M. Tang, J. Tang, Y. Wang, and Z. Nie, “Generation of Circular Optical Vortex Array,” Annalen. Der. Physik. 529(12), 1700285 (2017).
[Crossref]

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).
[Crossref] [PubMed]

Vaity, P.

Vasilyeu, R.

Vasnetsov, M. V.

I. Basistiy, V. Y. Bazhenov, M. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103(5–6), 422–428 (1993).
[Crossref]

Vaughan, J. M.

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).
[Crossref] [PubMed]

Volyar, A.

Vyas, S.

Wang, J.

H. Ma, X. Li, Y. Tai, H. Li, J. Wang, M. Tang, J. Tang, Y. Wang, and Z. Nie, “Generation of Circular Optical Vortex Array,” Annalen. Der. Physik. 529(12), 1700285 (2017).
[Crossref]

J. Wang, “Advances in communications using optical vortices,” Photon. Res. 4(5), B14–B28 (2016).
[Crossref]

Wang, S.

Wang, T.

Wang, T. Y.

S. J. Huang, Z. Miao, C. He, F. F. Pang, Y. C. Li, and T. Y. Wang, “Composite vortex beams by coaxial superposition of Laguerre–Gaussian beams,” Opt. Lasers Eng. 78, 132–139 (2016).
[Crossref]

Wang, Y.

H. Ma, X. Li, Y. Tai, H. Li, J. Wang, M. Tang, J. Tang, Y. Wang, and Z. Nie, “Generation of Circular Optical Vortex Array,” Annalen. Der. Physik. 529(12), 1700285 (2017).
[Crossref]

J. Liu, C. Min, T. Lei, L. Du, Y. Yuan, S. Wei, Y. Wang, and X. C. Yuan, “Generation and detection of broadband multi-channel orbital angular momentum by micrometer-scale meta-reflectarray,” Opt. Express 24(1), 212–218 (2016).
[Crossref] [PubMed]

Wang, Z.

Wei, S.

Weihs, G.

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]

Weiss, C. O.

Willetts, D. V.

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).
[Crossref] [PubMed]

Wright, A. J.

Wu, J.

Xia, J.

Xu, X. G.

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]

Yao, A. M.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[Crossref] [PubMed]

Ye, J.

Yu, C. Y.

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]

Yu, J.

Yuan, X. C.

J. Liu, C. Min, T. Lei, L. Du, Y. Yuan, S. Wei, Y. Wang, and X. C. Yuan, “Generation and detection of broadband multi-channel orbital angular momentum by micrometer-scale meta-reflectarray,” Opt. Express 24(1), 212–218 (2016).
[Crossref] [PubMed]

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]

Yuan, X.-C.

Yuan, Y.

Yue, Y.

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]

Zeilinger, 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).
[Crossref] [PubMed]

Zeng, T.

Zhang, M.

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]

Zhang, N.

Zhou, C.

Zhu, L.

Annalen. Der. Physik. (1)

H. Ma, X. Li, Y. Tai, H. Li, J. Wang, M. Tang, J. Tang, Y. Wang, and Z. Nie, “Generation of Circular Optical Vortex Array,” Annalen. Der. Physik. 529(12), 1700285 (2017).
[Crossref]

Appl. Opt. (5)

Chin. Opt. Lett. (1)

J. Opt. (1)

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation in light beams,” J. Opt. 13(5), 053001 (2011).
[Crossref]

J. Opt. Soc. Am. (1)

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

J. Opt. Soc. Am. B (4)

J. Opt. Technol. (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. Methods (1)

A. Chmyrov, J. Keller, T. Grotjohann, M. Ratz, E. d’Este, S. Jakobs, C. Eggeling, and S. W. Hell, “Nanoscopy with more than 100,000 ‘doughnuts’,” Nat. Methods 10(8), 737–740 (2013).
[Crossref] [PubMed]

Nat. Photonics (2)

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

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011).
[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).
[Crossref] [PubMed]

Opt. Commun. (1)

I. Basistiy, V. Y. Bazhenov, M. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103(5–6), 422–428 (1993).
[Crossref]

Opt. Eng. (1)

Y. S. Rumala, “Propagation of structured light beams after multiple reflections in a spiral phase plate,” Opt. Eng. 54(11), 111306 (2015).
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Opt. Express (11)

S. Franke-Arnold, J. Leach, M. J. Padgett, V. E. Lembessis, D. Ellinas, A. J. Wright, J. M. Girkin, P. Ohberg, and A. S. Arnold, “Optical ferris wheel for ultracold atoms,” Opt. Express 15(14), 8619–8625 (2007).
[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).
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Z. Wang, N. Zhang, and X.-C. Yuan, “High-volume optical vortex multiplexing and de-multiplexing for free-space optical communication,” Opt. Express 19(2), 482–492 (2011).
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J. Liu, C. Min, T. Lei, L. Du, Y. Yuan, S. Wei, Y. Wang, and X. C. Yuan, “Generation and detection of broadband multi-channel orbital angular momentum by micrometer-scale meta-reflectarray,” Opt. Express 24(1), 212–218 (2016).
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D. Deng, Y. Li, Y. Han, X. Su, J. Ye, J. Gao, Q. Sun, and S. Qu, “Perfect vortex in three-dimensional multifocal array,” Opt. Express 24(25), 28270–28278 (2016).
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I. A. Litvin, A. Dudley, and A. Forbes, “Poynting vector and orbital angular momentum density of superpositions of Bessel beams,” Opt. Express 19(18), 16760–16771 (2011).
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R. Vasilyeu, A. Dudley, N. Khilo, and A. Forbes, “Generating superpositions of higher-order Bessel beams,” Opt. Express 17(26), 23389–23395 (2009).
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Y. Qi, C. Chang, and J. Xia, “Speckleless holographic display by complex modulation based on double-phase method,” Opt. Express 24(26), 30368–30378 (2016).
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Z. Chen, T. Zeng, B. Qian, and J. Ding, “Complete shaping of optical vector beams,” Opt. Express 23(14), 17701–17710 (2015).
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Y. C. Lin, T. H. Lu, K. F. Huang, and Y. F. Chen, “Generation of optical vortex array with transformation of standing-wave Laguerre-Gaussian mode,” Opt. Express 19(11), 10293–10303 (2011).
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J. A. Rodrigo, T. Alieva, E. Abramochkin, and I. Castro, “Shaping of light beams along curves in three dimensions,” Opt. Express 21(18), 20544–20555 (2013).
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Opt. Lasers Eng. (1)

S. J. Huang, Z. Miao, C. He, F. F. Pang, Y. C. Li, and T. Y. Wang, “Composite vortex beams by coaxial superposition of Laguerre–Gaussian beams,” Opt. Lasers Eng. 78, 132–139 (2016).
[Crossref]

Opt. Lett. (6)

Photon. Res. (1)

Phys. Rev. Lett. (3)

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104(10), 103601 (2010).
[Crossref] [PubMed]

A. Aleksanyan, N. Kravets, and E. Brasselet, “Multiple-Star System Adaptive Vortex Coronagraphy Using a Liquid Crystal Light Valve,” Phys. Rev. Lett. 118(20), 203902 (2017).
[Crossref] [PubMed]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-Order Poincaré Sphere, Stokes Parameters, and the Angular Momentum of Light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref] [PubMed]

Science (3)

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329(5992), 662–665 (2010).
[Crossref] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292(5518), 912–914 (2001).
[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]

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Figures (13)

Fig. 1
Fig. 1 The simulated results of the shaped ring curves, which are calculated under the same initial radius but different widths.
Fig. 2
Fig. 2 Reconstructed result of the 2D ring curve in the focal plane by simulation. (a), (b) and (c) are the intensity distribution of the inner (R1 = 0.15mm, l1 = 4), outer (R2 = 0.19mm, l2 = −4) and overlapped ring. (d), (e) and (f) are the phase patterns corresponding to (a), (b) and (c), respectively. The number of dark dots appeared in (c) is consistent with the formula N = |l2-l1| = |-4-4| = 8. The corresponding phase vortex at each dot is marked out by black circles.
Fig. 3
Fig. 3 Simulation results of the generated CA-OVA. The intensity and phase distributions of the inner, outer and overlapped curves are shown. The odd columns indicate the intensity and the even columns reveal the corresponding phase distribution. Top row: CA-OVA along square curve (e1). The parameters of the inner and outer curves are R01 = 0.15mm, l1 = 4 and R02 = 0.19mm, l2 = −4 respectively. Middle row: R01 = 0.15mm, l1 = 4 and R02 = 0.19mm, l2 = −4 are used for the generation of CA-OVA along four-horn star-like curve (e2). Bottom row: CA-OVA along five-horn star-like curve, where R01 = 0.15mm and R02 = 0.19mm. But the topological charges of the inner and outer curves are changed to l1 = 5 and l2 = −5 such that ten optical vortices are appeared and arranged in (e3).
Fig. 4
Fig. 4 Simulation results of the generated CA-OVA with different initial phase shifts of Δφ0 = 0, π/2, π, 3π/2 and 2π. The position variation of the hollows is observed by the reference of blue dotted lines. The number of vortex is N = 8.
Fig. 5
Fig. 5 Maps of the orbital transverse energy flows in the cross section of CA-OVA structures.
Fig. 6
Fig. 6 The theoretical demonstration of the CA-PVA. (a) and (c) are the amplitude and phase distribution of the left and right circularly polarized CA-OVA. (b) is the polarization distribution of the resulted PVA. (e)-(f) are the Stokes parameters of the resulted PVA.
Fig. 7
Fig. 7 Schematic of the optical setup to generate CA-OVA. P: polarizer. BE: beam expander. M: mirror. BS:beam splitter. SLM: spatial light modulator. L: convex lenses (f1 = 400mm, f2 = 300mm f3 = 100mm and f4 = 200mm) . CCD: charge-coupled device.
Fig. 8
Fig. 8 Interference patterns between the CA-OVA and a spherical wave. The number of vortex is N = 8 in (a) and (b) while N = 10 in (c) and (d), respectively.
Fig. 9
Fig. 9 Experimental generation of different CA-OVA beams. The number of vortex in each CA-OVA is N = 8 in (a)-(c) and N = 10 in (d)-(f).
Fig. 10
Fig. 10 Experimental generation of CA-OVA beams with different initial phase shifts where the hollows can rotate around the corresponded beam circumferences.
Fig. 11
Fig. 11 Simulated and experimental results of generating hybrid CA-OVA. The hybrid CA-OVA is consisted of four individual CA-OVA structure aligned along ring, square, four-horn star-like and five-horn star-like curve. (a) and (c) are the simulation results. (b) and (d) are the corresponding experimental results.
Fig. 12
Fig. 12 Schematic of the optical setup to generate CA-PVA. P: polarizer. BE: beam expander. M: mirror. BS:beam splitter. SLM: spatial light modulator. L: convex lenses (f1 = 400mm, f2 = 300mm f3 = 100mm). CCD: charge-coupled device. R: Ronchi Grating. QWP: quarter-wave plate. The fast axis direction of the two quarter-wave plates are orthogonal.
Fig. 13
Fig. 13 The experiment results of generated CA-PVA. For the five-horn star-like pattern, the topological charges of the inner and outer curves are l1 = 5, l2 = −5 in the calculation of Etotal-L(x, y) and l1 = −5, l2 = 5 in the calculation of Etotal-R(x, y). For other patterns, the topological charges are the same as in the calculation of ring pattern (l1 = 4, l2 = −4 for Etotal-L and l1 = −4, l2 = 4 for Etotal-R).

Tables (1)

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Table 1 Parameters of curves

Equations (9)

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H(x,y)= 1 L 0 T φ(x,y,t)| c 2 ' (t) |dt ,
| c 2 ' (t) |= [ x 0 ' (t) ] 2 + [ y 0 ' (t) ] 2 ,L= 0 T | c 2 ' (t) | dt,
φ(x,y,t)=exp( i ω 0 2 [ φ 0 +y x 0 (t)x y 0 (t) ]+ iσ ω 0 2 0 τ [ x 0 (τ) y 0 ' (τ) y 0 (τ) x 0 ' (τ) ] dτ ) ,
E( x,y )= i=1 n A i H R i (x,y) ,
E total ( x,y )= E 1 ( x,y )| φ 01 + E 2 ( x,y )| φ 02 ,
p = S / c 2 = ε 0 2 ω ¯ Im[ E OVA * ×( × E OVA ) ] ,
p s = ε 0 2 ω ¯ Im[ ×( E OVA * × E OVA ) ] ,
p o = ε 0 2 ω ¯ Im[ E OVA * () E OVA ] ,
E hybrid ( x,y )= i=1 n S E i ( x,y )exp[ ik( x u i f + y v i f ) ] ,

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