Abstract

In this letter, a quadratic phase plate (QPP) whose thickness increases quadratically with azimuthal angle φ is proposed. When a beam with initial topological charge m (m could be an arbitrary integer) is passed through the plate, quadratic phase modulation can be expected to expand the initial single orbital angular momentum (OAM) mode to a superimposed OAM state. The obtained multi-OAM state exhibits a comb-like OAM spectrum, which shows a flat region. The power variation of the OAM modes within the flat region is less than 3 dB, while the power for the OAM modes with charge numbers out of the flat region decays rapidly. Moreover, the number of OAM modes within the flat region can reach dozens. This may have potential applications in the field of communication, quantum information and optical manipulation, etc.

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

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2017 (1)

F. Yue, D. Wen, C. Zhang, B. D. Gerardot, W. Wang, S. Zhang, and X. Chen, “Multichannel Polarization-Controllable Superpositions of Orbital Angular Momentum States,” Adv. Mater. 29(15), 1603838 (2017).
[Crossref] [PubMed]

2016 (2)

S. Chen, Y. Cai, G. Li, S. Zhang, and K. W. Cheah, “Geometric metasurface fork gratings for vortex-beam generation and manipulation,” Laser Photonics Rev. 10(2), 322–326 (2016).
[Crossref]

Q. Xiao, C. Klitis, S. Li, Y. Chen, X. Cai, M. Sorel, and S. Yu, “Generation of photonic orbital angular momentum superposition states using vortex beam emitters with superimposed gratings,” Opt. Express 24(4), 3168–3176 (2016).
[Crossref] [PubMed]

2015 (4)

H. Li, M. J. Strain, L. Meriggi, L. Chen, J. Zhu, K. Cicek, J. Wang, X. Cai, M. Sorel, M. G. Thompson, and S. Yu, “On-chip electrical modulation of phase shift between OAM beams with opposite topological charge,” Appl. Phys. Lett. 107, 051102 (2015).
[Crossref]

S. Li and J. Wang, “Adaptive power-controllable orbital angular momentum (OAM) multicasting,” Sci. Rep. 5(1), 9677 (2015).
[Crossref] [PubMed]

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

L. Zhu and J. Wang, “Simultaneous generation of multiple orbital angular momentum (OAM) modes using a single phase-only element,” Opt. Express 23(20), 26221–26233 (2015).
[Crossref] [PubMed]

2013 (1)

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(1), 2432 (2013).
[Crossref] [PubMed]

2012 (1)

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

2011 (3)

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (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. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

2010 (3)

2007 (1)

2006 (3)

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref] [PubMed]

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized Rotation of Atoms from Photons with Orbital Angular Momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref] [PubMed]

C. H. Schmitz, K. Uhrig, J. P. Spatz, and J. E. Curtis, “Tuning the orbital angular momentum in optical vortex beams,” Opt. Express 14(15), 6604–6612 (2006).
[Crossref] [PubMed]

2005 (1)

K. T. Kapale and J. P. Dowling, “Vortex Phase Qubit: Generating Arbitrary, Counterrotating, Coherent Superpositions in Bose-Einstein Condensates via Optical Angular Momentum Beams,” Phys. Rev. Lett. 95(17), 173601 (2005).
[Crossref] [PubMed]

2004 (3)

2003 (2)

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
[Crossref] [PubMed]

2001 (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]

1994 (1)

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

1992 (1)

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

’t Hooft, G. W.

Ahmed, N.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Allen, L.

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]

Andersen, M. F.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized Rotation of Atoms from Photons with Orbital Angular Momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[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(1), 2432 (2013).
[Crossref] [PubMed]

Ashrafi, N.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Ashrafi, S.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Bao, C.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Barnett, S.

Beijersbergen, M. W.

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

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]

Bouchal, Z.

Z. Bouchal and R. Celechovský, “Mixed vortex states of light as information carriers,” New J. Phys. 6(1), 131 (2004).
[Crossref]

Bowman, R.

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

Burge, R. E.

Cai, X.

Q. Xiao, C. Klitis, S. Li, Y. Chen, X. Cai, M. Sorel, and S. Yu, “Generation of photonic orbital angular momentum superposition states using vortex beam emitters with superimposed gratings,” Opt. Express 24(4), 3168–3176 (2016).
[Crossref] [PubMed]

H. Li, M. J. Strain, L. Meriggi, L. Chen, J. Zhu, K. Cicek, J. Wang, X. Cai, M. Sorel, M. G. Thompson, and S. Yu, “On-chip electrical modulation of phase shift between OAM beams with opposite topological charge,” Appl. Phys. Lett. 107, 051102 (2015).
[Crossref]

Cai, Y.

S. Chen, Y. Cai, G. Li, S. Zhang, and K. W. Cheah, “Geometric metasurface fork gratings for vortex-beam generation and manipulation,” Laser Photonics Rev. 10(2), 322–326 (2016).
[Crossref]

Cao, Y.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Celechovský, R.

Z. Bouchal and R. Celechovský, “Mixed vortex states of light as information carriers,” New J. Phys. 6(1), 131 (2004).
[Crossref]

Cheah, K. W.

S. Chen, Y. Cai, G. Li, S. Zhang, and K. W. Cheah, “Geometric metasurface fork gratings for vortex-beam generation and manipulation,” Laser Photonics Rev. 10(2), 322–326 (2016).
[Crossref]

Chen, L.

H. Li, M. J. Strain, L. Meriggi, L. Chen, J. Zhu, K. Cicek, J. Wang, X. Cai, M. Sorel, M. G. Thompson, and S. Yu, “On-chip electrical modulation of phase shift between OAM beams with opposite topological charge,” Appl. Phys. Lett. 107, 051102 (2015).
[Crossref]

L. Chen and W. She, “Single-photon spin-orbit entanglement violating a Bell-like inequality,” J. Opt. Soc. Am. B 27(6), A7–A10 (2010).
[Crossref]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
[Crossref]

Chen, S.

S. Chen, Y. Cai, G. Li, S. Zhang, and K. W. Cheah, “Geometric metasurface fork gratings for vortex-beam generation and manipulation,” Laser Photonics Rev. 10(2), 322–326 (2016).
[Crossref]

Chen, X.

F. Yue, D. Wen, C. Zhang, B. D. Gerardot, W. Wang, S. Zhang, and X. Chen, “Multichannel Polarization-Controllable Superpositions of Orbital Angular Momentum States,” Adv. Mater. 29(15), 1603838 (2017).
[Crossref] [PubMed]

Chen, Y.

Cicek, K.

H. Li, M. J. Strain, L. Meriggi, L. Chen, J. Zhu, K. Cicek, J. Wang, X. Cai, M. Sorel, M. G. Thompson, and S. Yu, “On-chip electrical modulation of phase shift between OAM beams with opposite topological charge,” Appl. Phys. Lett. 107, 051102 (2015).
[Crossref]

Cladé, P.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized Rotation of Atoms from Photons with Orbital Angular Momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref] [PubMed]

Coerwinkel, R.

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

Courtial, J.

Curtis, J. E.

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(1), 2432 (2013).
[Crossref] [PubMed]

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(1), 2432 (2013).
[Crossref] [PubMed]

Dholakia, K.

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
[Crossref] [PubMed]

Dolinar, S.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Dowling, J. P.

K. T. Kapale and J. P. Dowling, “Vortex Phase Qubit: Generating Arbitrary, Counterrotating, Coherent Superpositions in Bose-Einstein Condensates via Optical Angular Momentum Beams,” Phys. Rev. Lett. 95(17), 173601 (2005).
[Crossref] [PubMed]

Dultz, W.

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
[Crossref] [PubMed]

Eliel, E. R.

Fazal, I. M.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Franke-Arnold, S.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
[Crossref]

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
[Crossref] [PubMed]

Garcés-Chávez, V.

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
[Crossref] [PubMed]

Gerardot, B. D.

F. Yue, D. Wen, C. Zhang, B. D. Gerardot, W. Wang, S. Zhang, and X. Chen, “Multichannel Polarization-Controllable Superpositions of Orbital Angular Momentum States,” Adv. Mater. 29(15), 1603838 (2017).
[Crossref] [PubMed]

Gibson, G.

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

Helmerson, K.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized Rotation of Atoms from Photons with Orbital Angular Momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref] [PubMed]

Huang, H.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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Kapale, K. T.

K. T. Kapale and J. P. Dowling, “Vortex Phase Qubit: Generating Arbitrary, Counterrotating, Coherent Superpositions in Bose-Einstein Condensates via Optical Angular Momentum Beams,” Phys. Rev. Lett. 95(17), 173601 (2005).
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E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
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Klitis, C.

Kloosterboer, J. G.

Kristensen, M.

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

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(1), 2432 (2013).
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Lavery, M. P. J.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
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Leach, J.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
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Leaird, D. E.

Li, G.

S. Chen, Y. Cai, G. Li, S. Zhang, and K. W. Cheah, “Geometric metasurface fork gratings for vortex-beam generation and manipulation,” Laser Photonics Rev. 10(2), 322–326 (2016).
[Crossref]

Li, H.

H. Li, M. J. Strain, L. Meriggi, L. Chen, J. Zhu, K. Cicek, J. Wang, X. Cai, M. Sorel, M. G. Thompson, and S. Yu, “On-chip electrical modulation of phase shift between OAM beams with opposite topological charge,” Appl. Phys. Lett. 107, 051102 (2015).
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Li, L.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Li, S.

Li, Y.

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(1), 2432 (2013).
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Long, C. M.

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).
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Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
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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(1), 2432 (2013).
[Crossref] [PubMed]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
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L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
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McGloin, D.

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
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Meriggi, L.

H. Li, M. J. Strain, L. Meriggi, L. Chen, J. Zhu, K. Cicek, J. Wang, X. Cai, M. Sorel, M. G. Thompson, and S. Yu, “On-chip electrical modulation of phase shift between OAM beams with opposite topological charge,” Appl. Phys. Lett. 107, 051102 (2015).
[Crossref]

Molisch, A. F.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
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Natarajan, V.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized Rotation of Atoms from Photons with Orbital Angular Momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
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Oemrawsingh, S. S.

Padgett, M.

Padgett, M. J.

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
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V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
[Crossref] [PubMed]

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref] [PubMed]

Pas’ko, V.

Phillips, W. D.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized Rotation of Atoms from Photons with Orbital Angular Momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
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Piccirillo, B.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
[Crossref]

Ramachandran, S.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Ren, Y.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Ryu, C.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized Rotation of Atoms from Photons with Orbital Angular Momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref] [PubMed]

Santamato, E.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
[Crossref]

Schmitz, C. H.

Schmitzer, H.

V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91(9), 093602 (2003).
[Crossref] [PubMed]

Sciarrino, F.

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(1), 2432 (2013).
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She, W.

L. Chen and W. She, “Single-photon spin-orbit entanglement violating a Bell-like inequality,” J. Opt. Soc. Am. B 27(6), A7–A10 (2010).
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E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
[Crossref]

Slussarenko, S.

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(1), 2432 (2013).
[Crossref] [PubMed]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin–orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82(2), 022115 (2010).
[Crossref]

Sorel, M.

Q. Xiao, C. Klitis, S. Li, Y. Chen, X. Cai, M. Sorel, and S. Yu, “Generation of photonic orbital angular momentum superposition states using vortex beam emitters with superimposed gratings,” Opt. Express 24(4), 3168–3176 (2016).
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H. Li, M. J. Strain, L. Meriggi, L. Chen, J. Zhu, K. Cicek, J. Wang, X. Cai, M. Sorel, M. G. Thompson, and S. Yu, “On-chip electrical modulation of phase shift between OAM beams with opposite topological charge,” Appl. Phys. Lett. 107, 051102 (2015).
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Spagnolo, N.

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(1), 2432 (2013).
[Crossref] [PubMed]

Spatz, J. P.

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).
[Crossref] [PubMed]

Strain, M. J.

H. Li, M. J. Strain, L. Meriggi, L. Chen, J. Zhu, K. Cicek, J. Wang, X. Cai, M. Sorel, M. G. Thompson, and S. Yu, “On-chip electrical modulation of phase shift between OAM beams with opposite topological charge,” Appl. Phys. Lett. 107, 051102 (2015).
[Crossref]

Supradeepa, V. R.

Tao, S. H.

Thompson, M. G.

H. Li, M. J. Strain, L. Meriggi, L. Chen, J. Zhu, K. Cicek, J. Wang, X. Cai, M. Sorel, M. G. Thompson, and S. Yu, “On-chip electrical modulation of phase shift between OAM beams with opposite topological charge,” Appl. Phys. Lett. 107, 051102 (2015).
[Crossref]

Tur, M.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Uhrig, K.

van Houwelingen, J. A.

Vasnetsov, M.

Vaziri, A.

M. F. Andersen, C. Ryu, P. Cladé, V. Natarajan, A. Vaziri, K. Helmerson, and W. D. Phillips, “Quantized Rotation of Atoms from Photons with Orbital Angular Momentum,” Phys. Rev. Lett. 97(17), 170406 (2006).
[Crossref] [PubMed]

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]

Verstegen, E. J.

Walborn, S. P.

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(1), 2432 (2013).
[Crossref] [PubMed]

Wang, J.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
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S. Li and J. Wang, “Adaptive power-controllable orbital angular momentum (OAM) multicasting,” Sci. Rep. 5(1), 9677 (2015).
[Crossref] [PubMed]

H. Li, M. J. Strain, L. Meriggi, L. Chen, J. Zhu, K. Cicek, J. Wang, X. Cai, M. Sorel, M. G. Thompson, and S. Yu, “On-chip electrical modulation of phase shift between OAM beams with opposite topological charge,” Appl. Phys. Lett. 107, 051102 (2015).
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L. Zhu and J. Wang, “Simultaneous generation of multiple orbital angular momentum (OAM) modes using a single phase-only element,” Opt. Express 23(20), 26221–26233 (2015).
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J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Wang, W.

F. Yue, D. Wen, C. Zhang, B. D. Gerardot, W. Wang, S. Zhang, and X. Chen, “Multichannel Polarization-Controllable Superpositions of Orbital Angular Momentum States,” Adv. Mater. 29(15), 1603838 (2017).
[Crossref] [PubMed]

Wang, Z.

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]

Weiner, A. M.

Wen, D.

F. Yue, D. Wen, C. Zhang, B. D. Gerardot, W. Wang, S. Zhang, and X. Chen, “Multichannel Polarization-Controllable Superpositions of Orbital Angular Momentum States,” Adv. Mater. 29(15), 1603838 (2017).
[Crossref] [PubMed]

Willner, A. E.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Woerdman, J. P.

S. S. Oemrawsingh, J. A. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Production and characterization of spiral phase plates for optical wavelengths,” Appl. Opt. 43(3), 688–694 (2004).
[Crossref] [PubMed]

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

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]

Wu, R.

Xiao, Q.

Xie, G.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Yan, Y.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Yang, J.-Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Yao, A. M.

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Yu, S.

Q. Xiao, C. Klitis, S. Li, Y. Chen, X. Cai, M. Sorel, and S. Yu, “Generation of photonic orbital angular momentum superposition states using vortex beam emitters with superimposed gratings,” Opt. Express 24(4), 3168–3176 (2016).
[Crossref] [PubMed]

H. Li, M. J. Strain, L. Meriggi, L. Chen, J. Zhu, K. Cicek, J. Wang, X. Cai, M. Sorel, M. G. Thompson, and S. Yu, “On-chip electrical modulation of phase shift between OAM beams with opposite topological charge,” Appl. Phys. Lett. 107, 051102 (2015).
[Crossref]

Yuan, X.-C.

Yue, F.

F. Yue, D. Wen, C. Zhang, B. D. Gerardot, W. Wang, S. Zhang, and X. Chen, “Multichannel Polarization-Controllable Superpositions of Orbital Angular Momentum States,” Adv. Mater. 29(15), 1603838 (2017).
[Crossref] [PubMed]

Yue, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

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]

Zhang, C.

F. Yue, D. Wen, C. Zhang, B. D. Gerardot, W. Wang, S. Zhang, and X. Chen, “Multichannel Polarization-Controllable Superpositions of Orbital Angular Momentum States,” Adv. Mater. 29(15), 1603838 (2017).
[Crossref] [PubMed]

Zhang, N.

Zhang, S.

F. Yue, D. Wen, C. Zhang, B. D. Gerardot, W. Wang, S. Zhang, and X. Chen, “Multichannel Polarization-Controllable Superpositions of Orbital Angular Momentum States,” Adv. Mater. 29(15), 1603838 (2017).
[Crossref] [PubMed]

S. Chen, Y. Cai, G. Li, S. Zhang, and K. W. Cheah, “Geometric metasurface fork gratings for vortex-beam generation and manipulation,” Laser Photonics Rev. 10(2), 322–326 (2016).
[Crossref]

Zhao, Z.

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Zhu, J.

H. Li, M. J. Strain, L. Meriggi, L. Chen, J. Zhu, K. Cicek, J. Wang, X. Cai, M. Sorel, M. G. Thompson, and S. Yu, “On-chip electrical modulation of phase shift between OAM beams with opposite topological charge,” Appl. Phys. Lett. 107, 051102 (2015).
[Crossref]

Zhu, L.

Adv. Mater. (1)

F. Yue, D. Wen, C. Zhang, B. D. Gerardot, W. Wang, S. Zhang, and X. Chen, “Multichannel Polarization-Controllable Superpositions of Orbital Angular Momentum States,” Adv. Mater. 29(15), 1603838 (2017).
[Crossref] [PubMed]

Adv. Opt. Photonics (2)

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,” Adv. Opt. Photonics 7(1), 66–106 (2015).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

H. Li, M. J. Strain, L. Meriggi, L. Chen, J. Zhu, K. Cicek, J. Wang, X. Cai, M. Sorel, M. G. Thompson, and S. Yu, “On-chip electrical modulation of phase shift between OAM beams with opposite topological charge,” Appl. Phys. Lett. 107, 051102 (2015).
[Crossref]

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

Laser Photonics Rev. (1)

S. Chen, Y. Cai, G. Li, S. Zhang, and K. W. Cheah, “Geometric metasurface fork gratings for vortex-beam generation and manipulation,” Laser Photonics Rev. 10(2), 322–326 (2016).
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Nat. Commun. (1)

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(1), 2432 (2013).
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Nat. Photonics (2)

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
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J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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Nature (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).
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D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
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New J. Phys. (1)

Z. Bouchal and R. Celechovský, “Mixed vortex states of light as information carriers,” New J. Phys. 6(1), 131 (2004).
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Opt. Commun. (1)

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Opt. Express (5)

Opt. Lett. (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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L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
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Sci. Rep. (1)

S. Li and J. Wang, “Adaptive power-controllable orbital angular momentum (OAM) multicasting,” Sci. Rep. 5(1), 9677 (2015).
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Other (1)

S. S. R. Oemrawsingh, “Optical Dislocations and Quantum Entanglement,” Ph.D. dissertation (Leiden University, 2004).

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Figures (5)

Fig. 1
Fig. 1 Schematic diagram of the QPP with T = 2π and α = π.
Fig. 2
Fig. 2 Numerical results of the relative power of each OAM mode of the output beam. (a) for (n0-1)s = 20λ with α = π, (b) for (n0-1)s = 20λ with α = π/2, (c) for (n0-1)s = 30λ with α = π and (d) for (n0-1)s = 30λ with α = π/2.
Fig. 3
Fig. 3 Relationship between the number κ of the OAM modes within the flat region and s under considering N = 1.
Fig. 4
Fig. 4 Dependence of shift D of the central OAM mode of the OAM comb on α for different s under N = 1. The results of (n0-1)s/λ = 10, 20, and 30 are plotted by green dots, orange dots and blue dots, respectively.
Fig. 5
Fig. 5 Relative power of each OAM mode of the output beam. (a) and (b) are the results of N = 2, α = π/2 with (n0-1)s/λ = 20 and 30, respectively; and (c) and (d) are the results of N = 3, α = π/3 with (n0-1)s/λ = 20 and 30, respectively.

Equations (7)

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l( φ )={ l 0 + l s ( φα 2π ) 2 ,0φ 2π N l( φ+qT ),T= 2π N ,
ϕ( φ )={ k 0 l s ( n 0 1 ) [ ( φα )/ 2π ] 2 + k 0 ( n 0 l 0 + l s ) , 0φ 2π N ϕ( φ+qT ), T= 2π N ,
G ^ ( φ )={ e i k 0 ( n 0 l 0 + l s ) e i k 0 l s ( n 0 1 ) [ ( φα )/ 2π ] 2 |mm|,0φ 2π N G ^ ( φ+qT ),T= 2π N .
G ^ = e i k 0 ( n 0 l 0 + l s ) n= F( nN ) | m+nNm|,
F( nN )= N 2π 0 2π/N e i k 0 l s ( n 0 1 ) [ ( φα )/ 2π ] 2 e inNφ dφ,
P( nN )= | m+nN| ψ | 2 = | F( nN ) | 2 ,
| ψ = e i k 0 ( n 0 l 0 + l s ) n F( nN ) | m+nN,

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