Abstract

We show that double-charged optical vortices can be generated with the help of Kerr electro-optic effect in either single crystals or isotropic media, including gaseous and liquid ones. We analyze possibilities for the vortex generation via the Kerr effect for different point groups of symmetry and formulate the appropriate conditions. We prove that the crystals, textures, and the isotropic media most suitable for the generation of double-charged optical vortices should belong to the symmetry groups 622, 6mm, 6/mmm, 6, 6/m, /m, , 2, mm, /mmm, //mmm, and /2.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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  27. L. Chen and W. She, “Electro-optically forbidden or enhanced spin-to-orbital angular momentum conversion in a focused light beam,” Opt. Lett. 33, 696–698 (2008).
    [CrossRef]
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  32. Y. Fujii and T. Sakudo, “Interferometric determination of the quadratic electro-optic coefficients in SrTiO3 crystal,” J. Appl. Phys. 41, 4118–4120 (1970).
    [CrossRef]
  33. A. V. Volyar, “Do optical quarks exist in the free space? A scalar treatment,” Ukr. J. Phys. Opt. 14, 31–43 (2013).
    [CrossRef]
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    [CrossRef]
  35. I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A 6, S166–S169 (2004).
    [CrossRef]
  36. M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A 6, 259–268 (2004).
    [CrossRef]
  37. S. Chandrasekhar, Liquid Crystals, 2nd ed. (Cambridge University, 1992).
  38. M. V. Berry and J. H. Hannay, “Umbilic points on Gaussian random surfaces,” J. Phys. A 10, 1809–1821 (1977).
    [CrossRef]

2013 (2)

J. Qing Lin, “Heralded generation of symmetric and asymmetric entangled qudits with weak cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 30, 576–581 (2013).
[CrossRef]

A. V. Volyar, “Do optical quarks exist in the free space? A scalar treatment,” Ukr. J. Phys. Opt. 14, 31–43 (2013).
[CrossRef]

2012 (4)

2011 (7)

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

V. G. Shvedov, “Nonparaxial singular beams inside the focal region of a high numerical-aperture lens,” Ukr. J. Phys. Opt. 12, 109–116 (2011).
[CrossRef]

Y. Vasylkiv, O. Krupych, I. Skab, and R. Vlokh, “On the spin-to-orbit momentum conversion operated by electric field in optically active Bi12GeO20 crystals,” Ukr. J. Phys. Opt. 12, 171–179 (2011).
[CrossRef]

I. Skab, Y. Vasylkiv, I. Smaga, and R. Vlokh, “Spin-to-orbital momentum conversion via electro-optic Pockels effect in crystals,” Phys. Rev. A 84, 043815 (2011).
[CrossRef]

J. M. Amjad, H. R. Khalesifard, S. Slussarenko, E. Karimi, L. Marrucci, and E. Santamato, “Laser-induced radial birefringence and spin-to-orbital optical angular momentum conversion in silver-doped glasses,” Appl. Phys. Lett. 99, 011113 (2011).
[CrossRef]

I. Skab, Y. Vasylkiv, B. Zapeka, V. Savaryn, and R. Vlokh, “Appearance of singularities of optical fields under torsion of crystals containing threefold symmetry axes,” J. Opt. Soc. Am. A 28, 1331–1340 (2011).
[CrossRef]

I. Skab, Y. Vasylkiv, V. Savaryn, and R. Vlokh, “Optical anisotropy induced by torsion stresses in LiNbO3 crystals: appearance of an optical vortex,” J. Opt. Soc. Am. A 28, 633–640 (2011).
[CrossRef]

2010 (2)

S. Mosca, B. Canuel, E. Karimi, B. Piccirillo, L. Marrucci, R. De Rosa, E. Genin, L. Milano, and E. Santamato, “Photon self-induced spin-to-orbital conversion in a terbium-gallium-garnet crystal at high laser power,” Phys. Rev. A 82, 043806 (2010).
[CrossRef]

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
[CrossRef]

2009 (1)

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eigenmodes of light by thermally tuned q-plates,” Appl. Phys. Lett. 94, 231124 (2009).
[CrossRef]

2008 (2)

L. Marrucci, “Generation of helical modes of light by spin-to-orbital angular momentum conversion in inhomogeneous liquid crystals,” Mol. Cryst. Liq. Cryst. 488, 148–162 (2008).

L. Chen and W. She, “Electro-optically forbidden or enhanced spin-to-orbital angular momentum conversion in a focused light beam,” Opt. Lett. 33, 696–698 (2008).
[CrossRef]

2006 (1)

S. Groblacher, T. Jennewein, A. Viziri, G. Weihs, and A. Zeillinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[CrossRef]

2005 (1)

2004 (3)

G. Molina-Terriza, A. Vaziri, J. Rehácek, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef]

I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A 6, S166–S169 (2004).
[CrossRef]

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A 6, 259–268 (2004).
[CrossRef]

2003 (2)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

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

2001 (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2001).
[CrossRef]

1997 (1)

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

1995 (1)

D. P. DiVincenzo, “Quantum computation,” Science 270, 255–261 (1995).
[CrossRef]

1994 (1)

M. W. Beijersbergen, “Helical-wavefront laser beams produced with a spiral phase plate,” 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. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef]

1977 (1)

M. V. Berry and J. H. Hannay, “Umbilic points on Gaussian random surfaces,” J. Phys. A 10, 1809–1821 (1977).
[CrossRef]

1974 (1)

J. F. Nay and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. A. 336, 165–190 (1974).
[CrossRef]

1970 (1)

Y. Fujii and T. Sakudo, “Interferometric determination of the quadratic electro-optic coefficients in SrTiO3 crystal,” J. Appl. Phys. 41, 4118–4120 (1970).
[CrossRef]

1965 (1)

O. G. Vlokh, “Deformation of optical indicatrices at quadratic and spontaneous electrooptic effect in crystals,” Ukr. Fiz. Zhurn. 10, 1101–1118 (1965).

Alexeyev, C.

Allen, L.

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

Amjad, J. M.

J. M. Amjad, H. R. Khalesifard, S. Slussarenko, E. Karimi, L. Marrucci, and E. Santamato, “Laser-induced radial birefringence and spin-to-orbital optical angular momentum conversion in silver-doped glasses,” Appl. Phys. Lett. 99, 011113 (2011).
[CrossRef]

Assanto, G.

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, and S. Residori, “Vortex induction via anisotropy stabilized light-matter interaction,” Phys. Rev. Lett. 109, 143901 (2012).
[CrossRef]

Barboza, R.

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, and S. Residori, “Vortex induction via anisotropy stabilized light-matter interaction,” Phys. Rev. Lett. 109, 143901 (2012).
[CrossRef]

Basistiy, I. V.

I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A 6, S166–S169 (2004).
[CrossRef]

Beijersbergen, M.

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

Beijersbergen, M. W.

M. W. Beijersbergen, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Berry, M. V.

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A 6, 259–268 (2004).
[CrossRef]

M. V. Berry and J. H. Hannay, “Umbilic points on Gaussian random surfaces,” J. Phys. A 10, 1809–1821 (1977).
[CrossRef]

J. F. Nay and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. A. 336, 165–190 (1974).
[CrossRef]

Bortolozzo, U.

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, and S. Residori, “Vortex induction via anisotropy stabilized light-matter interaction,” Phys. Rev. Lett. 109, 143901 (2012).
[CrossRef]

Bouwmeester, D.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

Brasselet, E.

Canuel, B.

S. Mosca, B. Canuel, E. Karimi, B. Piccirillo, L. Marrucci, R. De Rosa, E. Genin, L. Milano, and E. Santamato, “Photon self-induced spin-to-orbital conversion in a terbium-gallium-garnet crystal at high laser power,” Phys. Rev. A 82, 043806 (2010).
[CrossRef]

Chandrasekhar, S.

S. Chandrasekhar, Liquid Crystals, 2nd ed. (Cambridge University, 1992).

Chen, L.

Clerc, M. G.

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, and S. Residori, “Vortex induction via anisotropy stabilized light-matter interaction,” Phys. Rev. Lett. 109, 143901 (2012).
[CrossRef]

D’Ambrosio, V.

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
[CrossRef]

De Rosa, R.

S. Mosca, B. Canuel, E. Karimi, B. Piccirillo, L. Marrucci, R. De Rosa, E. Genin, L. Milano, and E. Santamato, “Photon self-induced spin-to-orbital conversion in a terbium-gallium-garnet crystal at high laser power,” Phys. Rev. A 82, 043806 (2010).
[CrossRef]

DiVincenzo, D. P.

D. P. DiVincenzo, “Quantum computation,” Science 270, 255–261 (1995).
[CrossRef]

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Eibl, M.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

El Ketara, M.

Fadeyeva, T.

Fujii, Y.

Y. Fujii and T. Sakudo, “Interferometric determination of the quadratic electro-optic coefficients in SrTiO3 crystal,” J. Appl. Phys. 41, 4118–4120 (1970).
[CrossRef]

Genin, E.

S. Mosca, B. Canuel, E. Karimi, B. Piccirillo, L. Marrucci, R. De Rosa, E. Genin, L. Milano, and E. Santamato, “Photon self-induced spin-to-orbital conversion in a terbium-gallium-garnet crystal at high laser power,” Phys. Rev. A 82, 043806 (2010).
[CrossRef]

Grier, D. G.

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

Groblacher, S.

S. Groblacher, T. Jennewein, A. Viziri, G. Weihs, and A. Zeillinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[CrossRef]

Hannay, J. H.

M. V. Berry and J. H. Hannay, “Umbilic points on Gaussian random surfaces,” J. Phys. A 10, 1809–1821 (1977).
[CrossRef]

Heckenberg, N. R.

Hradil, Z.

G. Molina-Terriza, A. Vaziri, J. Rehácek, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef]

Izdebskaya, Ya.

Jennewein, T.

S. Groblacher, T. Jennewein, A. Viziri, G. Weihs, and A. Zeillinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[CrossRef]

Karimi, E.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

J. M. Amjad, H. R. Khalesifard, S. Slussarenko, E. Karimi, L. Marrucci, and E. Santamato, “Laser-induced radial birefringence and spin-to-orbital optical angular momentum conversion in silver-doped glasses,” Appl. Phys. Lett. 99, 011113 (2011).
[CrossRef]

S. Mosca, B. Canuel, E. Karimi, B. Piccirillo, L. Marrucci, R. De Rosa, E. Genin, L. Milano, and E. Santamato, “Photon self-induced spin-to-orbital conversion in a terbium-gallium-garnet crystal at high laser power,” Phys. Rev. A 82, 043806 (2010).
[CrossRef]

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eigenmodes of light by thermally tuned q-plates,” Appl. Phys. Lett. 94, 231124 (2009).
[CrossRef]

Khalesifard, H. R.

J. M. Amjad, H. R. Khalesifard, S. Slussarenko, E. Karimi, L. Marrucci, and E. Santamato, “Laser-induced radial birefringence and spin-to-orbital optical angular momentum conversion in silver-doped glasses,” Appl. Phys. Lett. 99, 011113 (2011).
[CrossRef]

Krupych, O.

Y. Vasylkiv, O. Krupych, I. Skab, and R. Vlokh, “On the spin-to-orbit momentum conversion operated by electric field in optically active Bi12GeO20 crystals,” Ukr. J. Phys. Opt. 12, 171–179 (2011).
[CrossRef]

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Lide, D. R.

D. R. Lide, CRC Handbook of Chemistry and Physics, 90th ed. (Taylor & Francis, 2010).

Marrucci, L.

J. M. Amjad, H. R. Khalesifard, S. Slussarenko, E. Karimi, L. Marrucci, and E. Santamato, “Laser-induced radial birefringence and spin-to-orbital optical angular momentum conversion in silver-doped glasses,” Appl. Phys. Lett. 99, 011113 (2011).
[CrossRef]

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

S. Mosca, B. Canuel, E. Karimi, B. Piccirillo, L. Marrucci, R. De Rosa, E. Genin, L. Milano, and E. Santamato, “Photon self-induced spin-to-orbital conversion in a terbium-gallium-garnet crystal at high laser power,” Phys. Rev. A 82, 043806 (2010).
[CrossRef]

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
[CrossRef]

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eigenmodes of light by thermally tuned q-plates,” Appl. Phys. Lett. 94, 231124 (2009).
[CrossRef]

L. Marrucci, “Generation of helical modes of light by spin-to-orbital angular momentum conversion in inhomogeneous liquid crystals,” Mol. Cryst. Liq. Cryst. 488, 148–162 (2008).

Mattle, K.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

McDuff, R.

Milano, L.

S. Mosca, B. Canuel, E. Karimi, B. Piccirillo, L. Marrucci, R. De Rosa, E. Genin, L. Milano, and E. Santamato, “Photon self-induced spin-to-orbital conversion in a terbium-gallium-garnet crystal at high laser power,” Phys. Rev. A 82, 043806 (2010).
[CrossRef]

Molina-Terriza, G.

G. Molina-Terriza, A. Vaziri, J. Rehácek, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2001).
[CrossRef]

Mosca, S.

S. Mosca, B. Canuel, E. Karimi, B. Piccirillo, L. Marrucci, R. De Rosa, E. Genin, L. Milano, and E. Santamato, “Photon self-induced spin-to-orbital conversion in a terbium-gallium-garnet crystal at high laser power,” Phys. Rev. A 82, 043806 (2010).
[CrossRef]

Nagali, E.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eigenmodes of light by thermally tuned q-plates,” Appl. Phys. Lett. 94, 231124 (2009).
[CrossRef]

Nay, J. F.

J. F. Nay and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. A. 336, 165–190 (1974).
[CrossRef]

Newnham, R. E.

R. E. Newnham, Properties of Materials: Anisotropy, Symmetry, Structure (Oxford University, 2005).

Pan, J.-W.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

Pas’ko, V. A.

I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A 6, S166–S169 (2004).
[CrossRef]

Piccirillo, B.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
[CrossRef]

S. Mosca, B. Canuel, E. Karimi, B. Piccirillo, L. Marrucci, R. De Rosa, E. Genin, L. Milano, and E. Santamato, “Photon self-induced spin-to-orbital conversion in a terbium-gallium-garnet crystal at high laser power,” Phys. Rev. A 82, 043806 (2010).
[CrossRef]

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eigenmodes of light by thermally tuned q-plates,” Appl. Phys. Lett. 94, 231124 (2009).
[CrossRef]

Qing Lin, J.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Rehácek, J.

G. Molina-Terriza, A. Vaziri, J. Rehácek, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef]

Residori, S.

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, and S. Residori, “Vortex induction via anisotropy stabilized light-matter interaction,” Phys. Rev. Lett. 109, 143901 (2012).
[CrossRef]

Rubass, A.

Sakudo, T.

Y. Fujii and T. Sakudo, “Interferometric determination of the quadratic electro-optic coefficients in SrTiO3 crystal,” J. Appl. Phys. 41, 4118–4120 (1970).
[CrossRef]

Santamato, E.

J. M. Amjad, H. R. Khalesifard, S. Slussarenko, E. Karimi, L. Marrucci, and E. Santamato, “Laser-induced radial birefringence and spin-to-orbital optical angular momentum conversion in silver-doped glasses,” Appl. Phys. Lett. 99, 011113 (2011).
[CrossRef]

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
[CrossRef]

S. Mosca, B. Canuel, E. Karimi, B. Piccirillo, L. Marrucci, R. De Rosa, E. Genin, L. Milano, and E. Santamato, “Photon self-induced spin-to-orbital conversion in a terbium-gallium-garnet crystal at high laser power,” Phys. Rev. A 82, 043806 (2010).
[CrossRef]

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eigenmodes of light by thermally tuned q-plates,” Appl. Phys. Lett. 94, 231124 (2009).
[CrossRef]

Savaryn, V.

Sciarrino, F.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

She, W.

Shvedov, V.

Shvedov, V. G.

V. G. Shvedov, “Nonparaxial singular beams inside the focal region of a high numerical-aperture lens,” Ukr. J. Phys. Opt. 12, 109–116 (2011).
[CrossRef]

Skab, I.

Slussarenko, S.

J. M. Amjad, H. R. Khalesifard, S. Slussarenko, E. Karimi, L. Marrucci, and E. Santamato, “Laser-induced radial birefringence and spin-to-orbital optical angular momentum conversion in silver-doped glasses,” Appl. Phys. Lett. 99, 011113 (2011).
[CrossRef]

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
[CrossRef]

Slyusar, V. V.

I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A 6, S166–S169 (2004).
[CrossRef]

Smaga, I.

I. Skab, Y. Vasylkiv, I. Smaga, and R. Vlokh, “Spin-to-orbital momentum conversion via electro-optic Pockels effect in crystals,” Phys. Rev. A 84, 043815 (2011).
[CrossRef]

Smith, C. P.

Soskin, M. S.

I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A 6, S166–S169 (2004).
[CrossRef]

Spreeuw, R.

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

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2001).
[CrossRef]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2001).
[CrossRef]

Vasnetsov, M. V.

I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A 6, S166–S169 (2004).
[CrossRef]

Vasylkiv, Y.

Vaziri, A.

G. Molina-Terriza, A. Vaziri, J. Rehácek, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef]

Vidal-Henriquez, E.

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, and S. Residori, “Vortex induction via anisotropy stabilized light-matter interaction,” Phys. Rev. Lett. 109, 143901 (2012).
[CrossRef]

Viziri, A.

S. Groblacher, T. Jennewein, A. Viziri, G. Weihs, and A. Zeillinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[CrossRef]

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O. G. Vlokh, “Deformation of optical indicatrices at quadratic and spontaneous electrooptic effect in crystals,” Ukr. Fiz. Zhurn. 10, 1101–1118 (1965).

Vlokh, R.

Volyar, A.

Volyar, A. V.

A. V. Volyar, “Do optical quarks exist in the free space? A scalar treatment,” Ukr. J. Phys. Opt. 14, 31–43 (2013).
[CrossRef]

Weihs, G.

S. Groblacher, T. Jennewein, A. Viziri, G. Weihs, and A. Zeillinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[CrossRef]

Weinfurter, H.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

White, A. G.

Woerdman, J.

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

Zapeka, B.

Zeilinger, A.

G. Molina-Terriza, A. Vaziri, J. Rehácek, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef]

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

Zeillinger, A.

S. Groblacher, T. Jennewein, A. Viziri, G. Weihs, and A. Zeillinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

J. M. Amjad, H. R. Khalesifard, S. Slussarenko, E. Karimi, L. Marrucci, and E. Santamato, “Laser-induced radial birefringence and spin-to-orbital optical angular momentum conversion in silver-doped glasses,” Appl. Phys. Lett. 99, 011113 (2011).
[CrossRef]

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation and sorting of orbital angular momentum eigenmodes of light by thermally tuned q-plates,” Appl. Phys. Lett. 94, 231124 (2009).
[CrossRef]

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversion via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
[CrossRef]

J. Appl. Phys. (1)

Y. Fujii and T. Sakudo, “Interferometric determination of the quadratic electro-optic coefficients in SrTiO3 crystal,” J. Appl. Phys. 41, 4118–4120 (1970).
[CrossRef]

J. Opt. (1)

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

J. Opt. A (2)

I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A 6, S166–S169 (2004).
[CrossRef]

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A 6, 259–268 (2004).
[CrossRef]

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[CrossRef]

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L. Marrucci, “Generation of helical modes of light by spin-to-orbital angular momentum conversion in inhomogeneous liquid crystals,” Mol. Cryst. Liq. Cryst. 488, 148–162 (2008).

Nature (2)

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[CrossRef]

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

New J. Phys. (1)

S. Groblacher, T. Jennewein, A. Viziri, G. Weihs, and A. Zeillinger, “Experimental quantum cryptography with qutrits,” New J. Phys. 8, 75 (2006).
[CrossRef]

Opt. Commun. (1)

M. W. Beijersbergen, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. A (3)

I. Skab, Y. Vasylkiv, I. Smaga, and R. Vlokh, “Spin-to-orbital momentum conversion via electro-optic Pockels effect in crystals,” Phys. Rev. A 84, 043815 (2011).
[CrossRef]

S. Mosca, B. Canuel, E. Karimi, B. Piccirillo, L. Marrucci, R. De Rosa, E. Genin, L. Milano, and E. Santamato, “Photon self-induced spin-to-orbital conversion in a terbium-gallium-garnet crystal at high laser power,” Phys. Rev. A 82, 043806 (2010).
[CrossRef]

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

Phys. Rev. Lett. (4)

G. Molina-Terriza, A. Vaziri, J. Rehácek, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[CrossRef]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, and S. Residori, “Vortex induction via anisotropy stabilized light-matter interaction,” Phys. Rev. Lett. 109, 143901 (2012).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2001).
[CrossRef]

Proc. R. Soc. A. (1)

J. F. Nay and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. A. 336, 165–190 (1974).
[CrossRef]

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[CrossRef]

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Y. Vasylkiv, O. Krupych, I. Skab, and R. Vlokh, “On the spin-to-orbit momentum conversion operated by electric field in optically active Bi12GeO20 crystals,” Ukr. J. Phys. Opt. 12, 171–179 (2011).
[CrossRef]

A. V. Volyar, “Do optical quarks exist in the free space? A scalar treatment,” Ukr. J. Phys. Opt. 14, 31–43 (2013).
[CrossRef]

V. G. Shvedov, “Nonparaxial singular beams inside the focal region of a high numerical-aperture lens,” Ukr. J. Phys. Opt. 12, 109–116 (2011).
[CrossRef]

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R. E. Newnham, Properties of Materials: Anisotropy, Symmetry, Structure (Oxford University, 2005).

D. R. Lide, CRC Handbook of Chemistry and Physics, 90th ed. (Taylor & Francis, 2010).

Supplementary Material (1)

» Media 1: AVI (435 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Schematic representation of electro-optic cell with circular electrodes El1 and El2, and a conical spatial distribution of electric field produced by these electrodes.

Fig. 2.
Fig. 2.

(a) Calculated dependence of the effective angle of optical indicatrix rotation on the tracing angle at the constant module ρ; (b) spatial XY distribution of the effective angle of optical indicatrix rotation; (c) induced effective phase difference; (d) appearance of the doughnut mode; and (e) dependence of the effective phase difference on the coordinate X, as calculated following from the Jones matrix approach (open circles) and formula (11) (solid curve). A nitrobenzene Kerr cell is assumed under the conical electric field U/d=1.98×107V/m (d=5mm, the radius of the El2 electrode R=5mm, and the light wavelength λ=632.8nm).

Fig. 3.
Fig. 3.

Optical scheme of vortex generation: 1, light source (e.g., laser); 2 and 3, objective lenses; 4 and 8, linear polarizers; 5 and 7, quarter-wave plates; 6, sample (cuvette with a Kerr liquid); and 9, CCD camera.

Fig. 4.
Fig. 4.

(a) Calculated XY distribution of the effective angle of optical indicatrix rotation at R44/(R11R12)=0.1; (b) induced effective phase difference at R44/(R11R12)=0.1 (R11=1.09×1018m2/V2, R12=0.29×1018m2/V2, and R44=0.08×1018m2/V2) under the conical electric field U/d=16×106m/V; (c) dependence of the phase of outgoing light beam on the tracing angle at different ratios R44/(R11R12) (1, stars; 0.1, full circles; 10, semi-open circles; and 100, open circles); and (d) intensity distribution for the outgoing beam at R44/(R11R12)=0.1 (d=5mm, R=5mm and λ=632.8nm—see the notation in Fig. 2).

Fig. 5.
Fig. 5.

Calculated distributions of the effective phase difference (a) and the effective angle of optical indicatrix rotation (b), and light intensity behind the circular analyzer (c). A conical electric field U/d=1.01×107V/m is applied along the Z direction in SrTiO3 crystals (d=5mm, R=5mm, and λ=632.8nm—see the notation in Fig. 2).

Fig. 6.
Fig. 6.

Calculated spatial distributions of effective phase difference (a)–(d) and effective angle of optical indicatrix rotation (e)–(h); light intensity behind a circular analyzer (i)–(l) (Media 1) and schemes of topological defects (m)–(p) induced by a conical electric field applied along the direction [111] in crystals belonging to the point symmetry groups m3m and 432. The ratio is R14/R66=0 (a), (e), (i), (m), U=45kV, R14/R66=0.01 (b), (f), (j), (n), U=43.5kV and R14/R66=0.25 (c), (g), (k), (o), and U=30kV and R14/R66=0.99 (d), (h), (l), (p) at U=18kV.

Equations (52)

Equations on this page are rendered with MathJax. Learn more.

Bij=rijkEk+RijklEkEl,
E1=UdZX2+Y2+Z2X=mX,E2=UdZX2+Y2+Z2Y=mY,E3=UdZX2+Y2+Z2Z=mZ.
E1=UdtanΘ1+tan2Θcosφ,
E2=UdtanΘ1+tan2Θsinφ,
E3=Ud(1+tan2Θ).
(B1+R11E12+R12E22+R12E32)X2+(B1+R12E12+R11E22+R12E32)Y2+2(R11R12)E1E2XY=1.
ΔnXY=12n3(R11R12)(E12+E22)=12n3m2(R11R12)(X2+Y2),
tan2ζZ=2E1E2E12E22=2XYX2Y2=tan2φ,orζZ=φ.
Jkl=|(eiΔΓklef/2cos2ζklef+eiΔΓklef/2sin2ζklef)isin(ΔΓklef/2)sin2ζklefisin(ΔΓklef/2)sin2ζklef(eiΔΓklef/2sin2ζklef+eiΔΓklef/2cos2ζklef)|=n=1Nmax|(eiΔΓkln/2cos2ζkln+eiΔΓkln/2sin2ζkln)isin(ΔΓkln/2)sin2ζklnisin(ΔΓkln/2)sin2ζkln(eiΔΓkln/2sin2ζkln+eiΔΓkln/2cos2ζkln)|,
Eout(X,Y)=E0cosΔΓklef2[1±i]+iE0sinΔΓklef2e±i2pφ±i2ζ0[1i],
ΔΓklef=πn3U2(R11R12)ρ2λd2[d(R(ρ2+d2)ρ(R2+d2))(R2+d2)(ρ2+d2)+arctan(d(Rρ)ρRd2)].
(E1klE2kl)=JAJQWPJklJQWP+(E1E2),
E1=1,E2=0,JA=(0001),JQWP=(12eiπ412eiπ412eiπ412eiπ4),JQWP+=(12eiπ412eiπ412eiπ412eiπ4).
(Ikl)lout=(E1klE2kl)(E1kl*E2kl*).
ΔnXY=12n3(R11R12)2(E12E22)2+4R442E12E22=12n3m2(R11R12)2(X2Y2)2+4R442X2Y2,
tan2ζZ=2R44E1E2(R11R12)(E12E22)=2R44XY(R11R12)(X2Y2)=R44R11R12tan2φ.
E1E1E2E2E3E3E2E3E1E3E1E2ΔB1R11R12R13R14R140ΔB2R12R11R13R14R140ΔB3R13R13R33000ΔB412R1412R140R440R14ΔB512R1412R1400R44R14ΔB6000R14R14R66,
ΔnXY=n32([R66(E12E22)2R14E3(E1E2)]2+4[R14E3(E1+E2)+R66E1E2]2)1/2=n36([(R11+2R44R12)(E12E22)2(R11R44R12)E3(E1E2)]2+4[(R11R44R12)E3(E1+E2)+(R11+2R44R12)E1E2]2)1/2
tan2ζZ=2(R14E3(E1+E2)+R66E1E2)R66(E12E22)2R14E3(E1E2)=2((R11R44R12)E3(E1+E2)+(R11+2R44R12)E1E2)(R11+2R44R12)(E12E22)2(R11R44R12)E3(E1E2),
ΔnXY=n32R44(E12+E22)=n32R44m2(X2+Y2),
tan2ζZ=2E1E2E12E22=2XYX2Y2=tan2φζZ=φ.
(B1+R11E12+R12E22+R21E32)X2+(B1+R21E12+R11E22+R12E32)Y2+2R44E1E2XY=1.
ΔnXY=12n3[(R11R21)E12(R11R12)E22+(R21R12)E32]2+4R442E12E22=12n3m2[(R11R21)X2(R11R12)Y2+(R21R12)Z2]2+4R442X2Y2,
tan2ζZ=2R44E1E2(R11R21)E12(R11R12)E22+(R21R12)E32=2R44XY(R11R21)X2(R11R12)Y2+(R21R12)Z2.
ΔnXY=12n3R44(E12+E22)=12n3m2R44(X2+Y2)
tan2ζZ=2E1E2E12E22=2XYX2Y2=tan2φorζZ=φ.
ΔnXY=12n3(R11R12)2(E12E22)2+4R442E12E22=12n3m2(R11R12)(X2Y2)2+4R442X2Y2
tan2ζZ=R44(R11R12)2E1E2(E12E22)=R44(R11R12)2XY(X2Y2)=R44R11R12tan2φ,
ΔnXY=n32[(R66(E12E22)+2R14E3E2+2R15E3E1+2R16E1E2)2+4(12R16(E22E12)R15E3E2+R14E3E1+R66E1E2)2]1/2,
tan2ζZ=R16(E22E12)2R15E3E2+2R14E3E1+2R66E1E2R66(E12E22)+2R14E3E2+2R15E3E1+2R16E1E2.
R14=13(R11R44)1+36R12136R21,R15=13(R11R44)+136R12+1+36R21.
ΔnXY=n32R162+R662(E12+E22)=n32m2R162+R662(X2+Y2),
tan2ζZ=R16(E22E12)+2R66E1E2R66(E12E22)+2R16E1E2=tan2φR16R661+R16R66tan2φ=tan(2φ2ζ0),tan2ζ0=R16R66.
ΔnXY=12no3(R11R12)(E12+E22)=12no3m2(R11R12)(X2+Y2)
tan2ζZ=tan2φorζZ=φ.
ΔnXY=12no3R662+4R622(E12+E22)=12no3m2R662+4R622(X2+Y2)
tan2ζZ=tan2(φζ0),ζZ=φζ0,ζ0=12arctan2R62R66,
ΔnXY=12no3R662+4R612(E12+E22)=12no3m2R662+4R612(X2+Y2),
tan2ζZ=tan2(φ+ζ0),ζZ=φ+ζ0,ζ0=12arctan2R61R66.
ΔnXY=12no3(R11R12)2(E12E22)2+4R662E12E22=12no3m2(R11R12)2(X2Y2)2+4R662X2Y2,
tan2ζZ=R66R11R12tan2φ.
ΔnXY=12no3[(R11R12)(E12E22)+2R16E1E2]2+4[R61(E12E22)+R66E1E2]2=12no3m2[(R11R12)(X2Y2)+2R16XY]2+4[R61(X2Y2)+R66XY]2,
tan2ζZ=2R61+R66tan2φ(R11R12)+R16tan2φ.
ΔnXY=12no3m2R66(X2+Y2).
ΔnXY=12no3R662(E12+E22)2+4R66R14E2E3(3E12E22)+4R142E32(E12+E22),
tan2ζZ=2(R14E3E1+R66E1E2)R66(E12E22)+2R14E2E3.
ΔnXY=12no3R66(E12+E22)=12no3R66m2(X2+Y2),
tan2ζZ=2E1E2E12E22=tan2φ,ζZ=φ.
ΔnXY=12no3[R66(E12E22)+2R14E2E32R25E3E1+4R62E1E2]2+4[R25E2E3+R14E3E1+R66E1E2R62(E12E22)]2,
tan2ζZ=2(R62(E22E12)+R25E2E3+R14E3E1+R66E1E2)R66(E12E22)+2R14E2E32R25E3E1+4R62E1E2.
ΔnXY=12no3R66(E12+E22)=12no3R66m2(X2+Y2),
tan2ζZ=2E1E2E12E22=tan2φ,ζZ=φ.

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