Abstract

A high-efficiency technique for optical vortex (OV) generation is proposed and demonstrated. The technique is based on liquid crystal fork gratings with space-variant azimuthal orientations, which are locally controlled via polarization-sensitive alignment layers. Thanks to the optical rewritability of the alignment agent and the dynamic image generation of the digital micro-mirror device, fork gratings can be instantly and arbitrarily reconfigured. Corresponding optical vortices carrying arbitrary azimuthal and radial indices are demonstrated with a conversion efficiency of 98.5%, exhibiting features of polarization control and electrical switching. The technique may pave a bright road toward OV generation, manipulation, and detection.

© 2015 Chinese Laser Press

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2015 (4)

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, e257 (2015).
[Crossref]

D. S. Ding, W. Zhang, Z. Y. Zhou, S. Shi, G. Y. Xiang, X. S. Wang, Y. K. Jiang, B. S. Shi, and G. C. Guo, “Quantum storage of orbital angular momentum entanglement in an atomic ensemble,” Phys. Rev. Lett. 114, 050502 (2015).
[Crossref]

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom in a single photon,” Nature 518, 516–519 (2015).
[Crossref]

L. Wang, X. W. Lin, W. Hu, G. H. Shao, P. Chen, L. J. Liang, B. B. Jin, P. H. Wu, H. Qian, Y. N. Lu, X. Liang, Z. G. Zheng, and Y. Q. Lu, “Broadband tunable liquid crystal terahertz waveplates driven with porous graphene electrodes,” Light Sci. Appl. 4, e253 (2015).
[Crossref]

2014 (7)

X. T. Gan, P. Zhang, S. Liu, F. J. Xiao, and J. L. Zhao, “Beam steering and topological transformations driven by interactions between a discrete vortex soliton and a discrete fundamental soliton,” Phys. Rev. A 89, 013844 (2014).
[Crossref]

Y. X. Ren, G. D. Xie, H. Huang, N. Ahmed, Y. Yan, L. Li, C. J. Bao, M. P. J. Lavery, M. Tur, M. A. Neifeld, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive-optics-based simultaneous pre-and post-turbulence compensation of multiple orbital-angular-momentum beams in a bidirectional free-space optical link,” Optica 1, 376–382 (2014).
[Crossref]

L. X. Chen, J. J. Lei, and J. Romero, “Quantum digital spiral imaging,” Light Sci. Appl. 3, e153 (2014).
[Crossref]

G. Ruffato, M. Massari, and F. Romanato, “Generation of high-order Laguerre-Gaussian modes by means of spiral phase plates,” Opt. Lett. 39, 5094–5097 (2014).
[Crossref]

S. J. Ge, W. Ji, G. X. Cui, B. Y. Wei, W. Hu, and Y. Q. Lu, “Fast switchable optical vortex generator based on blue phase liquid crystal fork grating,” Opt. Mater. Express 4, 2535–2541 (2014).
[Crossref]

Z. C. Zhang, Z. You, and D. P. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light Sci. Appl. 3, e213 (2014).
[Crossref]

B. Y. Wei, W. Hu, Y. Ming, F. Xu, S. Rubin, J. G. Wang, V. Chigrinov, and Y. Q. Lu, “Generating switchable and reconfigurable optical vortices via photopatterning of liquid crystals,” Adv. Mater. 26, 1590–1595 (2014).
[Crossref]

2012 (6)

H. Wu, W. Hu, H. C. Hu, X. W. Lin, G. Zhu, J. W. Choi, V. Chigrinov, and Y. Q. Lu, “Arbitrary photo-patterning in liquid crystal alignments using DMD based lithography system,” Opt. Express 20, 16684–16689 (2012).
[Crossref]

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961–968 (2012).
[Crossref]

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

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12, 3645–3649 (2012).
[Crossref]

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and C. Spielmann, “Strong-field physics with singular light beams,” Nat. Phys. 8, 743–746 (2012).
[Crossref]

Y. M. Li, J. Kim, and M. J. Escuti, “Orbital angular momentum generation and mode transformation with high efficiency using forked polarization gratings,” Appl. Opt. 51, 8236–8245 (2012).
[Crossref]

2011 (2)

R. Cao, Y. Yang, J. G. Wang, J. Bu, M. W. Wang, and X. C. Yuan, “Microfabricated continuous cubic phase plate induced Airy beams for optical manipulation with high power efficiency,” Appl. Phys. Lett. 99, 261106 (2011).
[Crossref]

S. Slussarenko, A. Murauski, T. Du, V. Chigrinov, L. Marrucci, and E. Santamato, “Tunable liquid crystal q-plates with arbitrary topological charge,” Opt. Express 19, 4085–4090 (2011).
[Crossref]

2010 (2)

M. Granata, C. Buy, R. Ward, and M. Barsuglia, “Higher-order Laguerre-Gauss mode generation and interferometry for gravitational wave detectors,” Phys. Rev. Lett. 105, 231102 (2010).
[Crossref]

X. L. Wang, J. Chen, Y. N. Li, J. P. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105, 253602 (2010).
[Crossref]

2008 (2)

2007 (3)

Y. J. Liu, X. W. Sun, Q. Wang, and D. Luo, “Electrically switchable optical vortex generated by a computer-generated hologram recorded in polymer-dispersed liquid crystals,” Opt. Express 15, 16645–16650 (2007).
[Crossref]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[Crossref]

H. Choi, J. H. Woo, J. W. Wu, D. W. Kim, T. K. Lim, and S. H. Song, “Holographic inscription of helical wavefronts in a liquid crystal polarization grating,” Appl. Phys. Lett. 91, 141112 (2007).
[Crossref]

2006 (3)

C. Provenzano, P. Pagliusi, and G. Cipparrone, “Highly efficient liquid crystal based diffraction grating induced by polarization holograms at the aligning surfaces,” Appl. Phys. Lett. 89, 121105 (2006).
[Crossref]

V. Presnyakov, K. Asatryan, T. Galstian, and V. Chigrinov, “Optical polarization grating induced liquid crystal micro-structure using azo-dye command layer,” Opt. Express 14, 10558–10564 (2006).
[Crossref]

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

2005 (2)

G. Foo, D. M. Palacios, and G. A. Swartzlander, “Optical vortex coronagraph,” Opt. Lett. 30, 3308–3310 (2005).
[Crossref]

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref]

2004 (1)

J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71–78 (2004).
[Crossref]

1998 (2)

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, “High-order Laguerre-Gaussian laser modes for studies of cold atoms,” Opt. Commun. 156, 300–306 (1998).
[Crossref]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[Crossref]

1996 (1)

M. Schadt, H. Seiberle, and A. Schuster, “Optical patterning of multi-domain liquid-crystal,” Nature 381, 212–215 (1996).
[Crossref]

1994 (1)

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

1992 (2)

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[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, 8185–8189 (1992).
[Crossref]

1990 (1)

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 429–431 (1990).

1987 (1)

M. V. Berry, “The adiabatic phase and Pancharatnam’s phase for polarized light,” J. Mod. Opt. 34, 1401–1407 (1987).
[Crossref]

1986 (1)

S. T. Wu, “Birefringence dispersions of liquid crystals,” Phys. Rev. A 33, 1270–1274 (1986).
[Crossref]

1966 (1)

1956 (1)

S. Pancharatnam, “Generalized theory of interference and its applications. Part I. Coherent pencils,” Proc. Indian Acad. Sci. A 44, 247–262 (1956).

’t Hooft, G. W.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref]

Ahmed, N.

Y. X. Ren, G. D. Xie, H. Huang, N. Ahmed, Y. Yan, L. Li, C. J. Bao, M. P. J. Lavery, M. Tur, M. A. Neifeld, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive-optics-based simultaneous pre-and post-turbulence compensation of multiple orbital-angular-momentum beams in a bidirectional free-space optical link,” Optica 1, 376–382 (2014).
[Crossref]

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

Aiello, A.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref]

Allen, L.

S. Franke-Arnold, L. Allen, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–313 (2008).
[Crossref]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[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, 8185–8189 (1992).
[Crossref]

Ando, T.

Aoki, N.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12, 3645–3649 (2012).
[Crossref]

Aolita, L.

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961–968 (2012).
[Crossref]

Arlt, J.

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, “High-order Laguerre-Gaussian laser modes for studies of cold atoms,” Opt. Commun. 156, 300–306 (1998).
[Crossref]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[Crossref]

Asatryan, K.

Bao, C. J.

Barsuglia, M.

M. Granata, C. Buy, R. Ward, and M. Barsuglia, “Higher-order Laguerre-Gauss mode generation and interferometry for gravitational wave detectors,” Phys. Rev. Lett. 105, 231102 (2010).
[Crossref]

Bazhenov, V. Y.

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 429–431 (1990).

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 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, 8185–8189 (1992).
[Crossref]

Berry, M. V.

M. V. Berry, “The adiabatic phase and Pancharatnam’s phase for polarized light,” J. Mod. Opt. 34, 1401–1407 (1987).
[Crossref]

Boyd, R. W.

Bu, J.

R. Cao, Y. Yang, J. G. Wang, J. Bu, M. W. Wang, and X. C. Yuan, “Microfabricated continuous cubic phase plate induced Airy beams for optical manipulation with high power efficiency,” Appl. Phys. Lett. 99, 261106 (2011).
[Crossref]

Buy, C.

M. Granata, C. Buy, R. Ward, and M. Barsuglia, “Higher-order Laguerre-Gauss mode generation and interferometry for gravitational wave detectors,” Phys. Rev. Lett. 105, 231102 (2010).
[Crossref]

Cai, X. D.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom in a single photon,” Nature 518, 516–519 (2015).
[Crossref]

Cao, R.

R. Cao, Y. Yang, J. G. Wang, J. Bu, M. W. Wang, and X. C. Yuan, “Microfabricated continuous cubic phase plate induced Airy beams for optical manipulation with high power efficiency,” Appl. Phys. Lett. 99, 261106 (2011).
[Crossref]

Chen, J.

X. L. Wang, J. Chen, Y. N. Li, J. P. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105, 253602 (2010).
[Crossref]

Chen, L. X.

L. X. Chen, J. J. Lei, and J. Romero, “Quantum digital spiral imaging,” Light Sci. Appl. 3, e153 (2014).
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V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961–968 (2012).
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S. Slussarenko, A. Murauski, T. Du, V. Chigrinov, L. Marrucci, and E. Santamato, “Tunable liquid crystal q-plates with arbitrary topological charge,” Opt. Express 19, 4085–4090 (2011).
[Crossref]

Smith, C. P.

Song, S. H.

H. Choi, J. H. Woo, J. W. Wu, D. W. Kim, T. K. Lim, and S. H. Song, “Holographic inscription of helical wavefronts in a liquid crystal polarization grating,” Appl. Phys. Lett. 91, 141112 (2007).
[Crossref]

Soskin, M. S.

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 429–431 (1990).

Spielmann, C.

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and C. Spielmann, “Strong-field physics with singular light beams,” Nat. Phys. 8, 743–746 (2012).
[Crossref]

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, 8185–8189 (1992).
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Su, Z. E.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom in a single photon,” Nature 518, 516–519 (2015).
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Swartzlander, G. A.

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G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
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Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
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Toyoda, K.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12, 3645–3649 (2012).
[Crossref]

Tur, M.

Y. X. Ren, G. D. Xie, H. Huang, N. Ahmed, Y. Yan, L. Li, C. J. Bao, M. P. J. Lavery, M. Tur, M. A. Neifeld, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive-optics-based simultaneous pre-and post-turbulence compensation of multiple orbital-angular-momentum beams in a bidirectional free-space optical link,” Optica 1, 376–382 (2014).
[Crossref]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
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V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 429–431 (1990).

Voigt, D.

S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref]

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V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961–968 (2012).
[Crossref]

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X. L. Wang, J. Chen, Y. N. Li, J. P. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105, 253602 (2010).
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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
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B. Y. Wei, W. Hu, Y. Ming, F. Xu, S. Rubin, J. G. Wang, V. Chigrinov, and Y. Q. Lu, “Generating switchable and reconfigurable optical vortices via photopatterning of liquid crystals,” Adv. Mater. 26, 1590–1595 (2014).
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R. Cao, Y. Yang, J. G. Wang, J. Bu, M. W. Wang, and X. C. Yuan, “Microfabricated continuous cubic phase plate induced Airy beams for optical manipulation with high power efficiency,” Appl. Phys. Lett. 99, 261106 (2011).
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L. Wang, X. W. Lin, W. Hu, G. H. Shao, P. Chen, L. J. Liang, B. B. Jin, P. H. Wu, H. Qian, Y. N. Lu, X. Liang, Z. G. Zheng, and Y. Q. Lu, “Broadband tunable liquid crystal terahertz waveplates driven with porous graphene electrodes,” Light Sci. Appl. 4, e253 (2015).
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R. Cao, Y. Yang, J. G. Wang, J. Bu, M. W. Wang, and X. C. Yuan, “Microfabricated continuous cubic phase plate induced Airy beams for optical manipulation with high power efficiency,” Appl. Phys. Lett. 99, 261106 (2011).
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Wang, X. L.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom in a single photon,” Nature 518, 516–519 (2015).
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D. S. Ding, W. Zhang, Z. Y. Zhou, S. Shi, G. Y. Xiang, X. S. Wang, Y. K. Jiang, B. S. Shi, and G. C. Guo, “Quantum storage of orbital angular momentum entanglement in an atomic ensemble,” Phys. Rev. Lett. 114, 050502 (2015).
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H. Choi, J. H. Woo, J. W. Wu, D. W. Kim, T. K. Lim, and S. H. Song, “Holographic inscription of helical wavefronts in a liquid crystal polarization grating,” Appl. Phys. Lett. 91, 141112 (2007).
[Crossref]

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X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom in a single photon,” Nature 518, 516–519 (2015).
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Wu, J. W.

H. Choi, J. H. Woo, J. W. Wu, D. W. Kim, T. K. Lim, and S. H. Song, “Holographic inscription of helical wavefronts in a liquid crystal polarization grating,” Appl. Phys. Lett. 91, 141112 (2007).
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L. Wang, X. W. Lin, W. Hu, G. H. Shao, P. Chen, L. J. Liang, B. B. Jin, P. H. Wu, H. Qian, Y. N. Lu, X. Liang, Z. G. Zheng, and Y. Q. Lu, “Broadband tunable liquid crystal terahertz waveplates driven with porous graphene electrodes,” Light Sci. Appl. 4, e253 (2015).
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S. T. Wu, “Birefringence dispersions of liquid crystals,” Phys. Rev. A 33, 1270–1274 (1986).
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D. S. Ding, W. Zhang, Z. Y. Zhou, S. Shi, G. Y. Xiang, X. S. Wang, Y. K. Jiang, B. S. Shi, and G. C. Guo, “Quantum storage of orbital angular momentum entanglement in an atomic ensemble,” Phys. Rev. Lett. 114, 050502 (2015).
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X. T. Gan, P. Zhang, S. Liu, F. J. Xiao, and J. L. Zhao, “Beam steering and topological transformations driven by interactions between a discrete vortex soliton and a discrete fundamental soliton,” Phys. Rev. A 89, 013844 (2014).
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Xu, F.

B. Y. Wei, W. Hu, Y. Ming, F. Xu, S. Rubin, J. G. Wang, V. Chigrinov, and Y. Q. Lu, “Generating switchable and reconfigurable optical vortices via photopatterning of liquid crystals,” Adv. Mater. 26, 1590–1595 (2014).
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T. Lei, M. Zhang, Y. R. Li, P. Jia, G. N. Liu, X. G. Xu, Z. H. Li, C. J. Min, J. Lin, C. Y. Yu, H. B. Niu, and X. C. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4, e257 (2015).
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Y. X. Ren, G. D. Xie, H. Huang, N. Ahmed, Y. Yan, L. Li, C. J. Bao, M. P. J. Lavery, M. Tur, M. A. Neifeld, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive-optics-based simultaneous pre-and post-turbulence compensation of multiple orbital-angular-momentum beams in a bidirectional free-space optical link,” Optica 1, 376–382 (2014).
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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

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R. Cao, Y. Yang, J. G. Wang, J. Bu, M. W. Wang, and X. C. Yuan, “Microfabricated continuous cubic phase plate induced Airy beams for optical manipulation with high power efficiency,” Appl. Phys. Lett. 99, 261106 (2011).
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Z. C. Zhang, Z. You, and D. P. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light Sci. Appl. 3, e213 (2014).
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T. Lei, M. Zhang, Y. R. Li, P. Jia, G. N. Liu, X. G. Xu, Z. H. Li, C. J. Min, J. Lin, C. Y. Yu, H. B. Niu, and X. C. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4, e257 (2015).
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T. Lei, M. Zhang, Y. R. Li, P. Jia, G. N. Liu, X. G. Xu, Z. H. Li, C. J. Min, J. Lin, C. Y. Yu, H. B. Niu, and X. C. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4, e257 (2015).
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R. Cao, Y. Yang, J. G. Wang, J. Bu, M. W. Wang, and X. C. Yuan, “Microfabricated continuous cubic phase plate induced Airy beams for optical manipulation with high power efficiency,” Appl. Phys. Lett. 99, 261106 (2011).
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J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. X. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
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T. Lei, M. Zhang, Y. R. Li, P. Jia, G. N. Liu, X. G. Xu, Z. H. Li, C. J. Min, J. Lin, C. Y. Yu, H. B. Niu, and X. C. Yuan, “Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings,” Light Sci. Appl. 4, e257 (2015).
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Zhang, P.

X. T. Gan, P. Zhang, S. Liu, F. J. Xiao, and J. L. Zhao, “Beam steering and topological transformations driven by interactions between a discrete vortex soliton and a discrete fundamental soliton,” Phys. Rev. A 89, 013844 (2014).
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D. S. Ding, W. Zhang, Z. Y. Zhou, S. Shi, G. Y. Xiang, X. S. Wang, Y. K. Jiang, B. S. Shi, and G. C. Guo, “Quantum storage of orbital angular momentum entanglement in an atomic ensemble,” Phys. Rev. Lett. 114, 050502 (2015).
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Z. C. Zhang, Z. You, and D. P. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light Sci. Appl. 3, e213 (2014).
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X. T. Gan, P. Zhang, S. Liu, F. J. Xiao, and J. L. Zhao, “Beam steering and topological transformations driven by interactions between a discrete vortex soliton and a discrete fundamental soliton,” Phys. Rev. A 89, 013844 (2014).
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L. Wang, X. W. Lin, W. Hu, G. H. Shao, P. Chen, L. J. Liang, B. B. Jin, P. H. Wu, H. Qian, Y. N. Lu, X. Liang, Z. G. Zheng, and Y. Q. Lu, “Broadband tunable liquid crystal terahertz waveplates driven with porous graphene electrodes,” Light Sci. Appl. 4, e253 (2015).
[Crossref]

Zhou, Z. Y.

D. S. Ding, W. Zhang, Z. Y. Zhou, S. Shi, G. Y. Xiang, X. S. Wang, Y. K. Jiang, B. S. Shi, and G. C. Guo, “Quantum storage of orbital angular momentum entanglement in an atomic ensemble,” Phys. Rev. Lett. 114, 050502 (2015).
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M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and C. Spielmann, “Strong-field physics with singular light beams,” Nat. Phys. 8, 743–746 (2012).
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Adv. Mater. (1)

B. Y. Wei, W. Hu, Y. Ming, F. Xu, S. Rubin, J. G. Wang, V. Chigrinov, and Y. Q. Lu, “Generating switchable and reconfigurable optical vortices via photopatterning of liquid crystals,” Adv. Mater. 26, 1590–1595 (2014).
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R. Cao, Y. Yang, J. G. Wang, J. Bu, M. W. Wang, and X. C. Yuan, “Microfabricated continuous cubic phase plate induced Airy beams for optical manipulation with high power efficiency,” Appl. Phys. Lett. 99, 261106 (2011).
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Nano Lett. (1)

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12, 3645–3649 (2012).
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Nat. Commun. (1)

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961–968 (2012).
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Nat. Photonics (1)

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

Nat. Phys. (2)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[Crossref]

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and C. Spielmann, “Strong-field physics with singular light beams,” Nat. Phys. 8, 743–746 (2012).
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J. Leach, E. Yao, and M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71–78 (2004).
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X. T. Gan, P. Zhang, S. Liu, F. J. Xiao, and J. L. Zhao, “Beam steering and topological transformations driven by interactions between a discrete vortex soliton and a discrete fundamental soliton,” Phys. Rev. A 89, 013844 (2014).
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M. Granata, C. Buy, R. Ward, and M. Barsuglia, “Higher-order Laguerre-Gauss mode generation and interferometry for gravitational wave detectors,” Phys. Rev. Lett. 105, 231102 (2010).
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S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. 95, 240501 (2005).
[Crossref]

X. L. Wang, J. Chen, Y. N. Li, J. P. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105, 253602 (2010).
[Crossref]

D. S. Ding, W. Zhang, Z. Y. Zhou, S. Shi, G. Y. Xiang, X. S. Wang, Y. K. Jiang, B. S. Shi, and G. C. Guo, “Quantum storage of orbital angular momentum entanglement in an atomic ensemble,” Phys. Rev. Lett. 114, 050502 (2015).
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Figures (5)

Fig. 1.
Fig. 1.

Schematic diagram and diffraction property of a director-varying LC fork grating with m=1. The color variation from blue to red indicates the director varying from 0 to π continuously, and the gray sticks label the local director orientations. The polarization vectors observed along the light propagation direction are marked with arrows. LCP, left circularly polarized; LP, linearly polarized; RCP, right circularly polarized.

Fig. 2.
Fig. 2.

DMD-based micro-lithography setup consists of a light emission component, a dynamic pattern generation component, an image focusing component, and a monitor component. Three out of all 18 exposure sum-regions from FPGs with m=2, as well as with m=1 and p=1, are shown as examples, with corresponding polarizer angles listed below.

Fig. 3.
Fig. 3.

(a) Theoretical, (b) measured director distribution, and (c) POM micrograph of an FPG with m=2. (d) Micrograph of a reconfigured FPG with m=10. The color bars indicate the director varying from 0 to π continuously, and the scale bars are all 100 μm.

Fig. 4.
Fig. 4.

Dependencies of diffraction efficiency on (a) applied voltage and (b) incident polarization at 2.31Vrms. Top images are the diffraction patterns on different polarization conditions marked with circles in corresponding color on the curves. The color bar indicates the relative optical intensity in all diffraction patterns.

Fig. 5.
Fig. 5.

Theoretical director distributions, micrographs, measured director distributions, and diffraction patterns of samples with (a) m=1 and p=1, (b) m=1 and p=2, (c) m=2.5, and (d) m=2.5 and p=1. The scale bars are all 100 μm. Incident polarizations are labeled in the images; clockwise/counterclockwise indicates left/right circularly polarized light.

Equations (8)

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Φ(x,y)=12mϕ(x,y)πx/Λ+Φ0.
Φ(x,y)=12mϕ(x,y)πx/Λ+Φ0+π2θ[Lp|m|(2r2/w02)],
J(x,y)=R(Φ)·[exp(iΓ/2)00exp(iΓ/2)]·R(Φ)=cosζIisinζ[cos2Φ(x,y)sin2Φ(x,y)sin2Φ(x,y)cos2Φ(x,y)].
D(x,y)=J(x,y)Ein(x,y)=cosζ·χ(±)isinζ·exp{±im·ϕ(x,y)i2πx/Λ±iπθ[Lp|m|(2r2/w02)]}·χ().
Dn=1Λ0ΛD(x,y)ei2πnx/Λdx=cosζδnχ(±)isinζδn±1exp{±im·ϕ(x,y)±iπθ[Lp|m|(2r2/w02)]}χ().
η0=cos2ζ,
η±1=|χ()|Ψ|2sin2ζ,
ηn=0(n0,±1),

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