Abstract

In this study, electrically tunable advanced liquid crystal q-plates (ALCQPs) that combine two q values in one device to generate optical vortex beams were fabricated using a photoalignment method that involves the use of azo dye, a surfactant alignment material. The electrically tunable ALCQP device could be modulated to control the shape and polarization of a circularly polarized Gaussian laser beam that propagated through the device. A Gaussian beam modulated by an ALCQP under suitable applied voltage showed a variation beam shape with helical wavefront, as demonstrated by Michelson’s interference. This helical wavefront beam carries an orbital angular momentum and can be used in an optical tweezers system to trap, move, and rotate particles simultaneously.

© 2013 Optical Society of America

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  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, 8185–8189 (1992).
    [CrossRef]
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  3. A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Shadow effects in spiral phase contrast microscopy,” Phys. Rev. Lett. 94, 233902 (2005).
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  6. J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
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  7. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
    [CrossRef]
  8. L. Aolita and S. P. Walborn, “Quantum communication without alignment using multiple-qubit single-photon states,” Phys. Rev. Lett. 98, 100501 (2007).
    [CrossRef]
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    [CrossRef]
  10. A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Size selective trapping with optical cogwheel tweezers,” Opt. Express 12, 4129–4135 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
    [CrossRef]
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    [CrossRef]
  16. R. Steiger, S. Bernet, and M. Ritsch-Marte, “Mapping of phase singularities with spiral phase contrast microscopy,” Opt. Express 21, 16282–16289 (2013).
    [CrossRef]
  17. 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]
  18. K. Sueda, G. Miyaji, N. Miyanaga, and M. Nakatsuka, “Laguerre-Gaussian beam generated with a multilevel spiral phase plate for high intensity laser pulses,” Opt. Express 12, 3548–3553 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  21. 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]
  22. Y.-H. Huang, S.-W. Ko, M.-S. Li, S.-C. Chu, and A. Y.-G. Fuh, “Modulation of shape and polarization of beam using a liquid crystal q-plate that is fabricated via photo-alignment,” Opt. Express 21, 10954–10961 (2013).
    [CrossRef]
  23. Y.-Y. Tzeng, S.-W. Ke, C.-L. Ting, A. Y.-G. Fuh, and T.-H. Lin, “Axially symmetric polarization converters based on photo-aligned liquid crystal films,” Opt. Express 16, 3768–3775 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  26. J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2004), Chap. 4.

2013 (3)

2012 (1)

2011 (1)

2010 (1)

E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, “Experimental generation and characterization of single-photon hybrid ququarts based on polarization and orbital angular momentum encoding,” Phys. Rev. A 81, 052317 (2010).
[CrossRef]

2008 (1)

2007 (3)

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[CrossRef]

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

L. Aolita and S. P. Walborn, “Quantum communication without alignment using multiple-qubit single-photon states,” Phys. Rev. Lett. 98, 100501 (2007).
[CrossRef]

2006 (3)

F. Tamburini, G. Anzolin, G. Umbriaco, A. Bianchini, and C. Barbieri, “Overcoming the Rayleigh criterion limit with optical vortices,” Phys. Rev. Lett. 97, 163903 (2006).
[CrossRef]

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: switchable helical mode generation,” Appl. Phys. Lett. 88, 221102 (2006).
[CrossRef]

S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, “Residue orbital angular momentum in interferenced double vortex beams with unequal topological charges,” Opt. Express 14, 535–541 (2006).
[CrossRef]

2005 (2)

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Shadow effects in spiral phase contrast microscopy,” Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef]

2004 (5)

2002 (1)

M. J. Padgett and L. Allen, “Orbital angular momentum exchange in cylindrical-lens mode converters,” J. Opt. B Quant. Semiclass. Opt. 4, S17–S19 (2002).
[CrossRef]

2001 (1)

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

1995 (1)

V. I. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[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 (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, 8185–8189 (1992).
[CrossRef]

Allen, L.

M. J. Padgett and L. Allen, “Orbital angular momentum exchange in cylindrical-lens mode converters,” J. Opt. B Quant. Semiclass. Opt. 4, S17–S19 (2002).
[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]

Anzolin, G.

F. Tamburini, G. Anzolin, G. Umbriaco, A. Bianchini, and C. Barbieri, “Overcoming the Rayleigh criterion limit with optical vortices,” Phys. Rev. Lett. 97, 163903 (2006).
[CrossRef]

Aolita, L.

L. Aolita and S. P. Walborn, “Quantum communication without alignment using multiple-qubit single-photon states,” Phys. Rev. Lett. 98, 100501 (2007).
[CrossRef]

Barbieri, C.

F. Tamburini, G. Anzolin, G. Umbriaco, A. Bianchini, and C. Barbieri, “Overcoming the Rayleigh criterion limit with optical vortices,” Phys. Rev. Lett. 97, 163903 (2006).
[CrossRef]

Barnett, S. M.

Barreiro, J. T.

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

Basistiy, V. I.

V. I. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[CrossRef]

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]

Bernet, S.

R. Steiger, S. Bernet, and M. Ritsch-Marte, “Mapping of phase singularities with spiral phase contrast microscopy,” Opt. Express 21, 16282–16289 (2013).
[CrossRef]

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[CrossRef]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Shadow effects in spiral phase contrast microscopy,” Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Size selective trapping with optical cogwheel tweezers,” Opt. Express 12, 4129–4135 (2004).
[CrossRef]

Bianchini, A.

F. Tamburini, G. Anzolin, G. Umbriaco, A. Bianchini, and C. Barbieri, “Overcoming the Rayleigh criterion limit with optical vortices,” Phys. Rev. Lett. 97, 163903 (2006).
[CrossRef]

Block, S. M.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809 (2004).
[CrossRef]

Boyd, R. W.

Burge, R. E.

Cao, W.

Cheng, K.-T.

C.-R. Lee, T.-L. Fu, K.-T. Cheng, T.-S. Mo, and A. Y.-G. Fuh, “Surface-assisted photoalignment in dye-doped liquid-crystal films,” Phys. Rev. E 69, 031704 (2004).
[CrossRef]

Chigrinov, V.

Chu, S.-C.

Coerwinkel, R. P. C.

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]

Courtial, J.

Du, T.

Franke-Arnold, S.

Fu, T.-L.

C.-R. Lee, T.-L. Fu, K.-T. Cheng, T.-S. Mo, and A. Y.-G. Fuh, “Surface-assisted photoalignment in dye-doped liquid-crystal films,” Phys. Rev. E 69, 031704 (2004).
[CrossRef]

Fuh, A. Y.-G.

Fürhapter, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[CrossRef]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Shadow effects in spiral phase contrast microscopy,” Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Size selective trapping with optical cogwheel tweezers,” Opt. Express 12, 4129–4135 (2004).
[CrossRef]

Gibson, G.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2004), Chap. 4.

Hu, A.

Huang, Y.-H.

Jesacher, A.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[CrossRef]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Shadow effects in spiral phase contrast microscopy,” Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Size selective trapping with optical cogwheel tweezers,” Opt. Express 12, 4129–4135 (2004).
[CrossRef]

Jia, W.

Karimi, E.

Ke, S.-W.

Ko, S.-W.

Kristensen, M.

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]

Kwiat, P. G.

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

Langford, N. K.

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

Lee, C.-R.

C.-R. Lee, T.-L. Fu, K.-T. Cheng, T.-S. Mo, and A. Y.-G. Fuh, “Surface-assisted photoalignment in dye-doped liquid-crystal films,” Phys. Rev. E 69, 031704 (2004).
[CrossRef]

Li, M.-S.

Lin, J.

Lin, T.-H.

Machula, T.

Mair, A.

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

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: switchable helical mode generation,” Appl. Phys. Lett. 88, 221102 (2006).
[CrossRef]

Marrucci, L.

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]

E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, “Experimental generation and characterization of single-photon hybrid ququarts based on polarization and orbital angular momentum encoding,” Phys. Rev. A 81, 052317 (2010).
[CrossRef]

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: switchable helical mode generation,” Appl. Phys. Lett. 88, 221102 (2006).
[CrossRef]

Maurer, C.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[CrossRef]

Miyaji, G.

Miyanaga, N.

Mo, T.-S.

C.-R. Lee, T.-L. Fu, K.-T. Cheng, T.-S. Mo, and A. Y.-G. Fuh, “Surface-assisted photoalignment in dye-doped liquid-crystal films,” Phys. Rev. E 69, 031704 (2004).
[CrossRef]

Molina-Terriza, G.

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

Murauski, A.

Nagali, E.

E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, “Experimental generation and characterization of single-photon hybrid ququarts based on polarization and orbital angular momentum encoding,” Phys. Rev. A 81, 052317 (2010).
[CrossRef]

Nakatsuka, M.

Neuman, K. C.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787–2809 (2004).
[CrossRef]

Padgett, M. J.

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: switchable helical mode generation,” Appl. Phys. Lett. 88, 221102 (2006).
[CrossRef]

Pasko, V.

Peters, N. A.

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

Ritsch-Marte, M.

R. Steiger, S. Bernet, and M. Ritsch-Marte, “Mapping of phase singularities with spiral phase contrast microscopy,” Opt. Express 21, 16282–16289 (2013).
[CrossRef]

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[CrossRef]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Shadow effects in spiral phase contrast microscopy,” Phys. Rev. Lett. 94, 233902 (2005).
[CrossRef]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Size selective trapping with optical cogwheel tweezers,” Opt. Express 12, 4129–4135 (2004).
[CrossRef]

Sansoni, L.

E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, “Experimental generation and characterization of single-photon hybrid ququarts based on polarization and orbital angular momentum encoding,” Phys. Rev. A 81, 052317 (2010).
[CrossRef]

Santamato, E.

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]

E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, “Experimental generation and characterization of single-photon hybrid ququarts based on polarization and orbital angular momentum encoding,” Phys. Rev. A 81, 052317 (2010).
[CrossRef]

Schulz, S. A.

Sciarrino, F.

E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, “Experimental generation and characterization of single-photon hybrid ququarts based on polarization and orbital angular momentum encoding,” Phys. Rev. A 81, 052317 (2010).
[CrossRef]

Slussarenko, S.

Soskin, M. S.

V. I. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[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).
[CrossRef]

Steiger, R.

Sueda, K.

Tamburini, F.

F. Tamburini, G. Anzolin, G. Umbriaco, A. Bianchini, and C. Barbieri, “Overcoming the Rayleigh criterion limit with optical vortices,” Phys. Rev. Lett. 97, 163903 (2006).
[CrossRef]

Tao, S. H.

Ting, C.-L.

Torner, L.

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

Torres, J. P.

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

Tzeng, Y.-Y.

Umbriaco, G.

F. Tamburini, G. Anzolin, G. Umbriaco, A. Bianchini, and C. Barbieri, “Overcoming the Rayleigh criterion limit with optical vortices,” Phys. Rev. Lett. 97, 163903 (2006).
[CrossRef]

Vasnetsov, M.

Vasnetsov, M. V.

V. I. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[CrossRef]

Vaziri, A.

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

Walborn, S. P.

L. Aolita and S. P. Walborn, “Quantum communication without alignment using multiple-qubit single-photon states,” Phys. Rev. Lett. 98, 100501 (2007).
[CrossRef]

Wang, S.

Weihs, G.

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

Woerdman, J. P.

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]

Wu, J.

Yu, J.

Yuan, X. C.

Zeilinger, A.

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

Zhou, C.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: switchable helical mode generation,” Appl. Phys. Lett. 88, 221102 (2006).
[CrossRef]

J. Opt. B Quant. Semiclass. Opt. (1)

M. J. Padgett and L. Allen, “Orbital angular momentum exchange in cylindrical-lens mode converters,” J. Opt. B Quant. Semiclass. Opt. 4, S17–S19 (2002).
[CrossRef]

Nat. Phys. (1)

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

Nature (1)

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

New J. Phys. (1)

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[CrossRef]

Opt. Commun. (2)

V. I. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[CrossRef]

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]

Opt. Express (9)

Y.-H. Huang, S.-W. Ko, M.-S. Li, S.-C. Chu, and A. Y.-G. Fuh, “Modulation of shape and polarization of beam using a liquid crystal q-plate that is fabricated via photo-alignment,” Opt. Express 21, 10954–10961 (2013).
[CrossRef]

S. A. Schulz, T. Machula, E. Karimi, and R. W. Boyd, “Integrated multi vector vortex beam generator,” Opt. Express 21, 16130–16141 (2013).
[CrossRef]

R. Steiger, S. Bernet, and M. Ritsch-Marte, “Mapping of phase singularities with spiral phase contrast microscopy,” Opt. Express 21, 16282–16289 (2013).
[CrossRef]

K. Sueda, G. Miyaji, N. Miyanaga, and M. Nakatsuka, “Laguerre-Gaussian beam generated with a multilevel spiral phase plate for high intensity laser pulses,” Opt. Express 12, 3548–3553 (2004).
[CrossRef]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Size selective trapping with optical cogwheel tweezers,” Opt. Express 12, 4129–4135 (2004).
[CrossRef]

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S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, “Residue orbital angular momentum in interferenced double vortex beams with unequal topological charges,” Opt. Express 14, 535–541 (2006).
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Y.-Y. Tzeng, S.-W. Ke, C.-L. Ting, A. Y.-G. Fuh, and T.-H. Lin, “Axially symmetric polarization converters based on photo-aligned liquid crystal films,” Opt. Express 16, 3768–3775 (2008).
[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]

Phys. Rev. A (2)

E. Nagali, L. Sansoni, L. Marrucci, E. Santamato, and F. Sciarrino, “Experimental generation and characterization of single-photon hybrid ququarts based on polarization and orbital angular momentum encoding,” Phys. Rev. A 81, 052317 (2010).
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[CrossRef]

Phys. Rev. E (1)

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[CrossRef]

Phys. Rev. Lett. (4)

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[CrossRef]

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[CrossRef]

Other (1)

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2004), Chap. 4.

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Figures (5)

Fig. 1.
Fig. 1.

Sample fabrication setup.

Fig. 2.
Fig. 2.

(a) Cross-POM images. (b) Numerically simulated POM images. (c) Schematics of LC director of LC QPs with (q1,q2)=(1,3), (q1,q2)=(1,3), and (q1,q2)=(2,4).

Fig. 3.
Fig. 3.

(a) Various beam shapes obtained by ALCQP modulation with q values of (q1,q2)=(1,3), (q1,q2)=(1,3), and (q1,q2)=(2,4) when suitable voltages were applied. (b) Simulated intensity distributions of the probe beam after being modulated by ALCQPs with (q1,q2)=(1,3), (q1,q2)=(1,3), and (q1,q2)=(2,4)).

Fig. 4.
Fig. 4.

(a) Test setup for the helical wavefront. (b) Interference patterns of the outgoing beam from the LC QP and ALCQPs. (c) Interference patterns of the signal beam through the LC QP with (q1,q2)=(1,3) under various applied voltages, and without LC QP.

Fig. 5.
Fig. 5.

Response time of ALCQP of q values of (q1,q2)=(2,4).

Equations (3)

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α(x,y)=α(ϕ)=qϕ+α(0),
M(ϕ,V)=[cos(qϕ)sin(qϕ)sin(qϕ)cos(qϕ)][exp(i2πd·neff(V)/λ)00exp(i2πd·no/λ)][cos(qϕ)sin(qϕ)sin(qϕ)cos(qϕ)].
U(ε,η)=ejkzejk(ε2+η2)/2zjλzU(x,y)exp[j2πλz(εx+ηy)]dxdy,

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