Abstract

We proposed an approach for creating three-dimensional (3D) multifocal perfect vortices arrays by using a high numerical aperture objective. The position, orbital angular momentum states, number and diameter of the perfect vortices can be freely modulated by a special designed hybrid phase plate (HPP). HPP could be calculated by 3D phase shifting expression which is derived from Fourier transform theory of the Debye diffraction integral. Furthermore, we developed a novel pixel checkerboard method for adding phase information into the HPP. The segmentation of HPP is related to vortex quality and intensity uniformity. This method could fully use each pixel to modulate the light, since the spatial light modulator has to be used. Small size lattices could generate high quality and uniform intensity vortex arrays in tight focusing region, which may have potential applications in coupling, optical coding and decoding.

© 2016 Optical Society of America

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References

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2017 (1)

D. Deng, Y. Li, Y. Han, J. Ye, Z. Guo, and S. Qu, “Multifocal array with controllable orbital angular momentum modes by tight focusing,” Opt. Commun. 382, 559–564 (2017).
[Crossref]

2016 (9)

T. Mu, Z. Chen, S. Pacheco, R. Wu, C. Zhang, and R. Liang, “Generation of a controllable multifocal array from a modulated azimuthally polarized beam,” Opt. Lett. 41(2), 261–264 (2016).
[Crossref] [PubMed]

J. Ye, Y. Li, Y. Han, D. Deng, Z. Guo, J. Gao, Q. Sun, Y. Liu, and S. Qu, “Excitation and separation of vortex modes in twisted air-core fiber,” Opt. Express 24(8), 8310–8316 (2016).
[Crossref] [PubMed]

C. Zhang, C. Min, L. Du, and X. Yuan, “Perfect optical vortex enhanced surface plasmon excitation for plasmonic structured illumination microscopy imaging,” Appl. Phys. Lett. 108(20), 201601 (2016).
[Crossref]

M. V. Jabir, N. Apurv Chaitanya, A. Aadhi, and G. K. Samanta, “Generation of “perfect” vortex of variable size and its effect in angular spectrum of the down-converted photons,” Sci. Rep. 6, 21877 (2016).
[Crossref] [PubMed]

A. Ryabtsev, S. Pouya, A. Safaripour, M. Koochesfahani, and M. Dantus, “Fluid flow vorticity measurement using laser beams with orbital angular momentum,” Opt. Express 24(11), 11762–11767 (2016).
[Crossref] [PubMed]

J. Baghdady, K. Miller, K. Morgan, M. Byrd, S. Osler, R. Ragusa, W. Li, B. M. Cochenour, and E. G. Johnson, “Multi-gigabit/s underwater optical communication link using orbital angular momentum multiplexing,” Opt. Express 24(9), 9794–9805 (2016).
[Crossref] [PubMed]

Y. S. Rumala, “Sensitivity in frequency dependent angular rotation of optical vortices,” Appl. Opt. 55(8), 2024–2033 (2016).
[Crossref] [PubMed]

J. Liu and J. Wang, “Polarization-insensitive PAM-4-carrying free-space orbital angular momentum (OAM) communications,” Opt. Express 24(4), 4258–4269 (2016).
[Crossref] [PubMed]

M. Zhao, X. Gao, M. Xie, W. Zhai, W. Xu, S. Huang, and W. Gu, “Measurement of the rotational Doppler frequency shift of a spinning object using a radio frequency orbital angular momentum beam,” Opt. Lett. 41(11), 2549–2552 (2016).
[Crossref] [PubMed]

2015 (10)

J. Du and J. Wang, “High-dimensional structured light coding/decoding for free-space optical communications free of obstructions,” Opt. Lett. 40(21), 4827–4830 (2015).
[Crossref] [PubMed]

M. J. Padgett, F. M. Miatto, M. P. Lavery, A. Zeilinger, and R. W. Boyd, “Divergence of an orbital-angular-momentum-carrying beam upon propagation,” New J. Phys. 17(2), 023011 (2015).
[Crossref]

A. Wang, L. Zhu, J. Liu, C. Du, Q. Mo, and J. Wang, “Demonstration of hybrid orbital angular momentum multiplexing and time-division multiplexing passive optical network,” Opt. Express 23(23), 29457–29466 (2015).
[Crossref] [PubMed]

L. Zhu and J. Wang, “Demonstration of obstruction-free data-carrying N-fold Bessel modes multicasting from a single Gaussian mode,” Opt. Lett. 40(23), 5463–5466 (2015).
[Crossref] [PubMed]

P. Gregg, P. Kristensen, and S. Ramachandran, “Conservation of orbital angular momentum in air core optical fibers,” Optica 2(3), 2334–2536 (2015).
[Crossref]

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

Y. Chen, Z. X. Fang, Y. X. Ren, L. Gong, and R. D. Lu, “Generation and characterization of a perfect vortex beam with a large topological charge through a digital micromirror device,” Appl. Opt. 54(27), 8030–8035 (2015).
[Crossref] [PubMed]

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]

J. Zhang, “Three-dimensional array diffraction-limited foci from Greek ladders to generalized Fibonacci sequences,” Opt. Express 23(23), 30308–30317 (2015).
[Crossref] [PubMed]

L. Zhu, M. Sun, D. Zhang, J. Yu, J. Wen, and J. Chen, “Multifocal array with controllable polarization in each focal spot,” Opt. Express 23(19), 24688–24698 (2015).
[Crossref] [PubMed]

2014 (4)

2013 (8)

S. Ramachandran and P. Kristensen, “Optical vortices in fiber,” Nanophotonics 2(5–6), 455–474 (2013).

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, “Dynamics of microparticles trapped in a perfect vortex beam,” Opt. Lett. 38(22), 4919–4922 (2013).
[Crossref] [PubMed]

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4(6), 2061 (2013).
[PubMed]

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
[Crossref] [PubMed]

Y. S. Rumala and A. E. Leanhardt, “Multiple-beam interference in a spiral phase plate,” J. Opt. Soc. Am. B 30(3), 615–621 (2013).
[Crossref]

S. 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]

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]

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]

2012 (2)

2006 (1)

2004 (1)

Aadhi, A.

M. V. Jabir, N. Apurv Chaitanya, A. Aadhi, and G. K. Samanta, “Generation of “perfect” vortex of variable size and its effect in angular spectrum of the down-converted photons,” Sci. Rep. 6, 21877 (2016).
[Crossref] [PubMed]

Aolita, L.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
[Crossref] [PubMed]

Apurv Chaitanya, N.

M. V. Jabir, N. Apurv Chaitanya, A. Aadhi, and G. K. Samanta, “Generation of “perfect” vortex of variable size and its effect in angular spectrum of the down-converted photons,” Sci. Rep. 6, 21877 (2016).
[Crossref] [PubMed]

Arita, Y.

Arrizón, V.

Baghdady, J.

Barnett, S.

Boyd, R. W.

M. J. Padgett, F. M. Miatto, M. P. Lavery, A. Zeilinger, and R. W. Boyd, “Divergence of an orbital-angular-momentum-carrying beam upon propagation,” New J. Phys. 17(2), 023011 (2015).
[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]

N. Bozinovic, S. Golowich, P. Kristensen, and S. Ramachandran, “Control of orbital angular momentum of light with optical fibers,” Opt. Lett. 37(13), 2451–2453 (2012).
[Crossref] [PubMed]

Brunet, C.

Byrd, M.

Cao, Y.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4(6), 2061 (2013).
[PubMed]

Chen, J.

Chen, M.

Chen, Y.

Chen, Z.

Cochenour, B. M.

Courtial, J.

D’Ambrosio, V.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
[Crossref] [PubMed]

Dantus, M.

Del Re, L.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
[Crossref] [PubMed]

Deng, D.

D. Deng, Y. Li, Y. Han, J. Ye, Z. Guo, and S. Qu, “Multifocal array with controllable orbital angular momentum modes by tight focusing,” Opt. Commun. 382, 559–564 (2017).
[Crossref]

J. Ye, Y. Li, Y. Han, D. Deng, Z. Guo, J. Gao, Q. Sun, Y. Liu, and S. Qu, “Excitation and separation of vortex modes in twisted air-core fiber,” Opt. Express 24(8), 8310–8316 (2016).
[Crossref] [PubMed]

Dholakia, K.

Du, C.

Du, J.

Du, L.

C. Zhang, C. Min, L. Du, and X. Yuan, “Perfect optical vortex enhanced surface plasmon excitation for plasmonic structured illumination microscopy imaging,” Appl. Phys. Lett. 108(20), 201601 (2016).
[Crossref]

Duan, K.

Evans, R. A.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4(6), 2061 (2013).
[PubMed]

Fang, Z. X.

Franke-Arnold, S.

Gan, Z.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4(6), 2061 (2013).
[PubMed]

Gao, J.

Gao, X.

García-García, J.

Gibson, G.

Golowich, S.

Gong, L.

Gregg, P.

P. Gregg, P. Kristensen, and S. Ramachandran, “Conservation of orbital angular momentum in air core optical fibers,” Optica 2(3), 2334–2536 (2015).
[Crossref]

Gu, M.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4(6), 2061 (2013).
[PubMed]

Gu, W.

Guo, Z.

D. Deng, Y. Li, Y. Han, J. Ye, Z. Guo, and S. Qu, “Multifocal array with controllable orbital angular momentum modes by tight focusing,” Opt. Commun. 382, 559–564 (2017).
[Crossref]

J. Ye, Y. Li, Y. Han, D. Deng, Z. Guo, J. Gao, Q. Sun, Y. Liu, and S. Qu, “Excitation and separation of vortex modes in twisted air-core fiber,” Opt. Express 24(8), 8310–8316 (2016).
[Crossref] [PubMed]

Han, Y.

D. Deng, Y. Li, Y. Han, J. Ye, Z. Guo, and S. Qu, “Multifocal array with controllable orbital angular momentum modes by tight focusing,” Opt. Commun. 382, 559–564 (2017).
[Crossref]

J. Ye, Y. Li, Y. Han, D. Deng, Z. Guo, J. Gao, Q. Sun, Y. Liu, and S. Qu, “Excitation and separation of vortex modes in twisted air-core fiber,” Opt. Express 24(8), 8310–8316 (2016).
[Crossref] [PubMed]

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, S.

Jabir, M. V.

M. V. Jabir, N. Apurv Chaitanya, A. Aadhi, and G. K. Samanta, “Generation of “perfect” vortex of variable size and its effect in angular spectrum of the down-converted photons,” Sci. Rep. 6, 21877 (2016).
[Crossref] [PubMed]

Jia, W.

Johnson, E. G.

Koochesfahani, M.

Kristensen, P.

P. Gregg, P. Kristensen, and S. Ramachandran, “Conservation of orbital angular momentum in air core optical fibers,” Optica 2(3), 2334–2536 (2015).
[Crossref]

S. Ramachandran and P. Kristensen, “Optical vortices in fiber,” Nanophotonics 2(5–6), 455–474 (2013).

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]

N. Bozinovic, S. Golowich, P. Kristensen, and S. Ramachandran, “Control of orbital angular momentum of light with optical fibers,” Opt. Lett. 37(13), 2451–2453 (2012).
[Crossref] [PubMed]

Kwek, L. C.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
[Crossref] [PubMed]

LaRochelle, S.

Lasser, T.

Lavery, M. P.

M. J. Padgett, F. M. Miatto, M. P. Lavery, A. Zeilinger, and R. W. Boyd, “Divergence of an orbital-angular-momentum-carrying beam upon propagation,” New J. Phys. 17(2), 023011 (2015).
[Crossref]

Leanhardt, A. E.

Leitgeb, R. A.

Leutenegger, M.

Li, S.

S. 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]

Li, W.

Li, Y.

D. Deng, Y. Li, Y. Han, J. Ye, Z. Guo, and S. Qu, “Multifocal array with controllable orbital angular momentum modes by tight focusing,” Opt. Commun. 382, 559–564 (2017).
[Crossref]

J. Ye, Y. Li, Y. Han, D. Deng, Z. Guo, J. Gao, Q. Sun, Y. Liu, and S. Qu, “Excitation and separation of vortex modes in twisted air-core fiber,” Opt. Express 24(8), 8310–8316 (2016).
[Crossref] [PubMed]

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
[Crossref] [PubMed]

Liang, R.

Liu, J.

Liu, Y.

Lu, R. D.

Lu, Y.

Ma, W.

Marrucci, L.

V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
[Crossref] [PubMed]

Mazilu, M.

Messaddeq, Y.

Miatto, F. M.

M. J. Padgett, F. M. Miatto, M. P. Lavery, A. Zeilinger, and R. W. Boyd, “Divergence of an orbital-angular-momentum-carrying beam upon propagation,” New J. Phys. 17(2), 023011 (2015).
[Crossref]

Miller, K.

Min, C.

C. Zhang, C. Min, L. Du, and X. Yuan, “Perfect optical vortex enhanced surface plasmon excitation for plasmonic structured illumination microscopy imaging,” Appl. Phys. Lett. 108(20), 201601 (2016).
[Crossref]

Mo, Q.

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J. Ye, Y. Li, Y. Han, D. Deng, Z. Guo, J. Gao, Q. Sun, Y. Liu, and S. Qu, “Excitation and separation of vortex modes in twisted air-core fiber,” Opt. Express 24(8), 8310–8316 (2016).
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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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M. V. Jabir, N. Apurv Chaitanya, A. Aadhi, and G. K. Samanta, “Generation of “perfect” vortex of variable size and its effect in angular spectrum of the down-converted photons,” Sci. Rep. 6, 21877 (2016).
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J. Ye, Y. Li, Y. Han, D. Deng, Z. Guo, J. Gao, Q. Sun, Y. Liu, and S. Qu, “Excitation and separation of vortex modes in twisted air-core fiber,” Opt. Express 24(8), 8310–8316 (2016).
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Zeilinger, A.

M. J. Padgett, F. M. Miatto, M. P. Lavery, A. Zeilinger, and R. W. Boyd, “Divergence of an orbital-angular-momentum-carrying beam upon propagation,” New J. Phys. 17(2), 023011 (2015).
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Appl. Opt. (2)

Appl. Phys. Lett. (1)

C. Zhang, C. Min, L. Du, and X. Yuan, “Perfect optical vortex enhanced surface plasmon excitation for plasmonic structured illumination microscopy imaging,” Appl. Phys. Lett. 108(20), 201601 (2016).
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S. 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. Soc. Am. B (1)

Nanophotonics (1)

S. Ramachandran and P. Kristensen, “Optical vortices in fiber,” Nanophotonics 2(5–6), 455–474 (2013).

Nat. Commun. (2)

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4(6), 2061 (2013).
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V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).
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New J. Phys. (1)

M. J. Padgett, F. M. Miatto, M. P. Lavery, A. Zeilinger, and R. W. Boyd, “Divergence of an orbital-angular-momentum-carrying beam upon propagation,” New J. Phys. 17(2), 023011 (2015).
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Opt. Commun. (1)

D. Deng, Y. Li, Y. Han, J. Ye, Z. Guo, and S. Qu, “Multifocal array with controllable orbital angular momentum modes by tight focusing,” Opt. Commun. 382, 559–564 (2017).
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Opt. Express (13)

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J. Ye, Y. Li, Y. Han, D. Deng, Z. Guo, J. Gao, Q. Sun, Y. Liu, and S. Qu, “Excitation and separation of vortex modes in twisted air-core fiber,” Opt. Express 24(8), 8310–8316 (2016).
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C. Brunet, P. Vaity, Y. Messaddeq, S. LaRochelle, and L. A. Rusch, “Design, fabrication and validation of an OAM fiber supporting 36 states,” Opt. Express 22(21), 26117–26127 (2014).
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L. Zhu, J. Yu, D. Zhang, M. Sun, and J. Chen, “Multifocal spot array generated by fractional Talbot effect phase-only modulation,” Opt. Express 22(8), 9798–9808 (2014).
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L. Zhu, M. Sun, D. Zhang, J. Yu, J. Wen, and J. Chen, “Multifocal array with controllable polarization in each focal spot,” Opt. Express 23(19), 24688–24698 (2015).
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H. Yan, E. Zhang, B. Zhao, and K. Duan, “Free-space propagation of guided optical vortices excited in an annular core fiber,” Opt. Express 20(16), 17904–17915 (2012).
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J. Liu and J. Wang, “Polarization-insensitive PAM-4-carrying free-space orbital angular momentum (OAM) communications,” Opt. Express 24(4), 4258–4269 (2016).
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A. Wang, L. Zhu, J. Liu, C. Du, Q. Mo, and J. Wang, “Demonstration of hybrid orbital angular momentum multiplexing and time-division multiplexing passive optical network,” Opt. Express 23(23), 29457–29466 (2015).
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A. Ryabtsev, S. Pouya, A. Safaripour, M. Koochesfahani, and M. Dantus, “Fluid flow vorticity measurement using laser beams with orbital angular momentum,” Opt. Express 24(11), 11762–11767 (2016).
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Opt. Lett. (10)

J. Du and J. Wang, “High-dimensional structured light coding/decoding for free-space optical communications free of obstructions,” Opt. Lett. 40(21), 4827–4830 (2015).
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M. Zhao, X. Gao, M. Xie, W. Zhai, W. Xu, S. Huang, and W. Gu, “Measurement of the rotational Doppler frequency shift of a spinning object using a radio frequency orbital angular momentum beam,” Opt. Lett. 41(11), 2549–2552 (2016).
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L. Zhu and J. Wang, “Demonstration of obstruction-free data-carrying N-fold Bessel modes multicasting from a single Gaussian mode,” Opt. Lett. 40(23), 5463–5466 (2015).
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N. Bozinovic, S. Golowich, P. Kristensen, and S. Ramachandran, “Control of orbital angular momentum of light with optical fibers,” Opt. Lett. 37(13), 2451–2453 (2012).
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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).
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J. García-García, C. Rickenstorff-Parrao, R. Ramos-García, V. Arrizón, and A. S. Ostrovsky, “Simple technique for generating the perfect optical vortex,” Opt. Lett. 39(18), 5305–5308 (2014).
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T. Mu, Z. Chen, S. Pacheco, R. Wu, C. Zhang, and R. Liang, “Generation of a controllable multifocal array from a modulated azimuthally polarized beam,” Opt. Lett. 41(2), 261–264 (2016).
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Optica (1)

P. Gregg, P. Kristensen, and S. Ramachandran, “Conservation of orbital angular momentum in air core optical fibers,” Optica 2(3), 2334–2536 (2015).
[Crossref]

Sci. Rep. (1)

M. V. Jabir, N. Apurv Chaitanya, A. Aadhi, and G. K. Samanta, “Generation of “perfect” vortex of variable size and its effect in angular spectrum of the down-converted photons,” Sci. Rep. 6, 21877 (2016).
[Crossref] [PubMed]

Science (1)

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 (6)

Fig. 1
Fig. 1 Geometry schematic diagram of the focusing field.
Fig. 2
Fig. 2 Phase patterns for generating perfect vortices with the topological charges (a) l = 1, (b) l = 10, (c) l = 20. (d), (e) and (f) are the corresponding normalized intensity of the perfect vortices. (g), (h) and (i) are the interference patterns with spherical wave for identifying the topological charges.
Fig. 3
Fig. 3 (a) Cross section intensity distribution of perfect vortices (topological charges l = 1, 5, 10, 15 and 20), (b) relationship between axicon parameter η and topological charges for keeping the diameter of vortices as 7.03μm.
Fig. 4
Fig. 4 Schematic of PCBM with lattices as (a) 8 × 8 pixels, (b) 5 × 5 pixels, and (c) single pixel. (d), (e), (f) and (g), (h), (i) are the corresponding HPP patterns and intensity distribution of perfect vortices arrays in 2D focal plane with topological charges l = 2, 4, 6 and 8.
Fig. 5
Fig. 5 Relationship between lattice size and intensity uniformity. (a) Normalized intensity of perfect vortices with changing of lattices size, (b) the intensity uniformity of arrays.
Fig. 6
Fig. 6 3D multifocal perfect vortices array. (a) HPP calculated by Pixel Checkerboard Method. (b) and (c) are the first and second focal plane. (d) Normalized intensity of these arrays in 3D focusing region. (e) and (f) are the interference patterns with spherical wave, respectively.

Equations (5)

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E ( x , y , z ) = [ U ( θ , ϕ ) E t ( θ , ϕ ) exp ( i k z z ) / cos θ ] exp [ i ( k x x + k y y ) ] d k x d k y = F { U ( θ , ϕ ) E t ( θ , ϕ ) exp ( i k z z ) / cos θ } ,
E t ( θ , ϕ ) = t p ( E i e p ) e r + t s ( E i e s ) e s ,
e x p ( i φ ) = exp [ i ( l ϕ + η r ) ] ,
E ( x Δ x , y Δ y , z Δ z ) = F { exp [ i ( k x Δ x + k y Δ y + k z Δ z ) ] U ( θ , ϕ ) E t ( θ , ϕ ) exp ( i k z z ) / cos θ } ,
e x p ( i φ ) = exp [ i ( l ϕ + η r k x Δ x k y Δ y k z Δ z ) ] ,

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