Abstract

In this work, we analyze the behavior of topological defects of optical indicatrix orientation induced by a conically shaped electric field in crystals in a crossover regime that appears at intermediate fields separating the regimes of prevailing Pockels and Kerr electro-optic nonlinearities. We have found that increases in the electric voltage applied to a crystal induce neither topological defects, with the strengths being not multiples of ½, or the optical vortices with fractional charges. Instead, there appear some additional topological defects of the optical indicatrix orientation, the behavior of which we have studied in detail.

© 2014 Optical Society of America

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    [CrossRef]
  28. I. Skab, Yu. 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]
  29. I. Skab, Yu. 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]
  30. Yu. 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]
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    [CrossRef]
  32. Yu. Vasylkiv, I. Skab, and R. Vlokh, “Double-charged optical vortices generation on the basis of electro-optic Kerr effect,” Appl. Opt. 53, B60–B73 (2014).
    [CrossRef]
  33. 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).
    [CrossRef]
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    [CrossRef]
  37. A. L. Roitburd, “The theory of the formation of a heterophase structure in phase transformations in solids,” Sov. Phys. Usp. 17, 326–344 (1974).
    [CrossRef]
  38. E. F. Dudnik and L. A. Shuvalov, “Domain structure and phase boundaries in ferroelastics,” Ferroelectrics 98, 207–233 (1989).
    [CrossRef]
  39. A. L. Roitburd, “Elastic domains and polydomain phases in solids,” Phase Transit. 45, 1–34 (1993).
    [CrossRef]
  40. A. I. Otko, G. G. Krainyuk, and A. E. Nosenko, “Domain structures and electromechanical effects in inhomogeneously strained Gd2(MoO4)3 crystals,” Ferroelectrics 64, 147–149 (1985).
    [CrossRef]
  41. G. G. Krainyuk, A. I. Otko, and A. E. Nosenko, “Electromechanical effects at the torsion and bending of Gd2(MoO4)3 crystals with the regular domain structures,” Fiz. Tverd. Tela 26, 2611–2614 (1984).
  42. J. Sapriel, “Domain-wall orientations in ferroelastics,” Phys. Rev. B 12, 5128–5140 (1975).
    [CrossRef]

2014 (1)

2013 (3)

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

T. A. Fadeyeva, “Hidden chains of optical vortices generated using a corner of phase wedge,” Ukr. J. Phys. Opt. 14, 57–69 (2013).
[CrossRef]

T. A. Fadeyeva, A. F. Rubass, I. S. Valkov, and A. V. Volyar, “Fractional optical vortices in a uniaxial crystal,” J. Opt. 15, 044020 (2013).
[CrossRef]

2012 (2)

2011 (4)

I. Skab, Yu. 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]

I. Skab, Yu. 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, Yu. 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]

Yu. 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]

2010 (1)

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]

2008 (1)

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).
[CrossRef]

2006 (3)

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]

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

A. Volyar, V. Shvedov, T. Fadeyeva, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, “Generation of single-charge optical vortices with a uniaxial crystal,” Opt. Express 14, 3724–3729 (2006).
[CrossRef]

2004 (7)

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]

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]

W. M. Lee, X.-C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239, 129–135 (2004).
[CrossRef]

S. H. Tao, W. M. Lee, and X.-C. Yuan, “Experimental study of holographic generation of fractional Bessel beams,” Appl. Opt. 43, 122–126 (2004).
[CrossRef]

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

2003 (2)

2002 (1)

G. Tóth, C. Denniston, and J. M. Yeomans, “Hydrodynamics of topological defects in nematic liquid crystals,” Phys. Rev. Lett. 88, 105504 (2002).
[CrossRef]

1998 (2)

M. V. Vasnetsov, I. V. Basistiy, and M. S. Soskin, “Free-space evolution of monochromatic mixed screw-edge wavefront dislocations,” Proc. SPIE 3487, 29–33 (1998).
[CrossRef]

O. D. Lavrentovich, “Topological defects in dispersed liquid crystals, or words and worlds around liquid crystal drops,” Liq. Cryst. 24, 117–126 (1998).
[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 (2)

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

D. P. DiVincenzo, “Quantum computation,” Science 270, 255–261 (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 phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

1993 (1)

A. L. Roitburd, “Elastic domains and polydomain phases in solids,” Phase Transit. 45, 1–34 (1993).
[CrossRef]

1992 (1)

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]

1989 (1)

E. F. Dudnik and L. A. Shuvalov, “Domain structure and phase boundaries in ferroelastics,” Ferroelectrics 98, 207–233 (1989).
[CrossRef]

1985 (1)

A. I. Otko, G. G. Krainyuk, and A. E. Nosenko, “Domain structures and electromechanical effects in inhomogeneously strained Gd2(MoO4)3 crystals,” Ferroelectrics 64, 147–149 (1985).
[CrossRef]

1984 (1)

G. G. Krainyuk, A. I. Otko, and A. E. Nosenko, “Electromechanical effects at the torsion and bending of Gd2(MoO4)3 crystals with the regular domain structures,” Fiz. Tverd. Tela 26, 2611–2614 (1984).

1975 (1)

J. Sapriel, “Domain-wall orientations in ferroelastics,” Phys. Rev. B 12, 5128–5140 (1975).
[CrossRef]

1974 (2)

A. L. Roitburd, “The theory of the formation of a heterophase structure in phase transformations in solids,” Sov. Phys. Usp. 17, 326–344 (1974).
[CrossRef]

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

’t Hooft, G. W.

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]

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]

M. V. Vasnetsov, I. V. Basistiy, and M. S. Soskin, “Free-space evolution of monochromatic mixed screw-edge wavefront dislocations,” Proc. SPIE 3487, 29–33 (1998).
[CrossRef]

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[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, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “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]

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

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 phase plate,” Opt. Commun. 112, 321–327 (1994).
[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]

Denniston, C.

G. Tóth, C. Denniston, and J. M. Yeomans, “Hydrodynamics of topological defects in nematic liquid crystals,” Phys. Rev. Lett. 88, 105504 (2002).
[CrossRef]

Desyatnikov, A. S.

Dholakia, K.

W. M. Lee, X.-C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239, 129–135 (2004).
[CrossRef]

DiVincenzo, D. P.

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

Dudnik, E. F.

E. F. Dudnik and L. A. Shuvalov, “Domain structure and phase boundaries in ferroelastics,” Ferroelectrics 98, 207–233 (1989).
[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]

Eliel, E. R.

Fadeyeva, T.

Fadeyeva, T. A.

T. A. Fadeyeva, A. F. Rubass, I. S. Valkov, and A. V. Volyar, “Fractional optical vortices in a uniaxial crystal,” J. Opt. 15, 044020 (2013).
[CrossRef]

T. A. Fadeyeva, “Hidden chains of optical vortices generated using a corner of phase wedge,” Ukr. J. Phys. Opt. 14, 57–69 (2013).
[CrossRef]

Glass, A. M.

M. E. Lines and A. M. Glass, Principles and Application of Ferroelectric and Related Materials (Clarendon, 1977).

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]

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]

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]

Kivshar, Yu. S.

Kloosterboer, J. G.

Krainyuk, G. G.

A. I. Otko, G. G. Krainyuk, and A. E. Nosenko, “Domain structures and electromechanical effects in inhomogeneously strained Gd2(MoO4)3 crystals,” Ferroelectrics 64, 147–149 (1985).
[CrossRef]

G. G. Krainyuk, A. I. Otko, and A. E. Nosenko, “Electromechanical effects at the torsion and bending of Gd2(MoO4)3 crystals with the regular domain structures,” Fiz. Tverd. Tela 26, 2611–2614 (1984).

Kristensen, M.

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

Krolikowski, W.

Krupych, O.

Yu. 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]

Lavrentovich, O. D.

O. D. Lavrentovich, “Topological defects in dispersed liquid crystals, or words and worlds around liquid crystal drops,” Liq. Cryst. 24, 117–126 (1998).
[CrossRef]

Leach, J.

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]

Lee, W. M.

Lines, M. E.

M. E. Lines and A. M. Glass, Principles and Application of Ferroelectric and Related Materials (Clarendon, 1977).

Manzo, C.

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]

Marrucci, L.

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]

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).
[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]

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]

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]

Nay, J. F.

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

Neshev, D. N.

Nosenko, A. E.

A. I. Otko, G. G. Krainyuk, and A. E. Nosenko, “Domain structures and electromechanical effects in inhomogeneously strained Gd2(MoO4)3 crystals,” Ferroelectrics 64, 147–149 (1985).
[CrossRef]

G. G. Krainyuk, A. I. Otko, and A. E. Nosenko, “Electromechanical effects at the torsion and bending of Gd2(MoO4)3 crystals with the regular domain structures,” Fiz. Tverd. Tela 26, 2611–2614 (1984).

Oemrawsingh, S. S. R.

Otko, A. I.

A. I. Otko, G. G. Krainyuk, and A. E. Nosenko, “Domain structures and electromechanical effects in inhomogeneously strained Gd2(MoO4)3 crystals,” Ferroelectrics 64, 147–149 (1985).
[CrossRef]

G. G. Krainyuk, A. I. Otko, and A. E. Nosenko, “Electromechanical effects at the torsion and bending of Gd2(MoO4)3 crystals with the regular domain structures,” Fiz. Tverd. Tela 26, 2611–2614 (1984).

Padgett, M. J.

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]

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]

Paparo, D.

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]

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.

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]

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]

Roitburd, A. L.

A. L. Roitburd, “Elastic domains and polydomain phases in solids,” Phase Transit. 45, 1–34 (1993).
[CrossRef]

A. L. Roitburd, “The theory of the formation of a heterophase structure in phase transformations in solids,” Sov. Phys. Usp. 17, 326–344 (1974).
[CrossRef]

Rubass, A.

Rubass, A. F.

T. A. Fadeyeva, A. F. Rubass, I. S. Valkov, and A. V. Volyar, “Fractional optical vortices in a uniaxial crystal,” J. Opt. 15, 044020 (2013).
[CrossRef]

Santamato, E.

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]

Sapriel, J.

J. Sapriel, “Domain-wall orientations in ferroelastics,” Phys. Rev. B 12, 5128–5140 (1975).
[CrossRef]

Savaryn, V.

Shaskolskaya, M. P.

M. P. Shaskolskaya, Acoustic Crystals (Nauka, 1982).

Shuvalov, L. A.

E. F. Dudnik and L. A. Shuvalov, “Domain structure and phase boundaries in ferroelastics,” Ferroelectrics 98, 207–233 (1989).
[CrossRef]

Shvedov, V.

Skab, I.

Slussarenko, S.

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, Yu. 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]

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]

M. V. Vasnetsov, I. V. Basistiy, and M. S. Soskin, “Free-space evolution of monochromatic mixed screw-edge wavefront dislocations,” Proc. SPIE 3487, 29–33 (1998).
[CrossRef]

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

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2001), Vol. 42, pp. 219–276.

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]

Tao, S. H.

Tóth, G.

G. Tóth, C. Denniston, and J. M. Yeomans, “Hydrodynamics of topological defects in nematic liquid crystals,” Phys. Rev. Lett. 88, 105504 (2002).
[CrossRef]

Valkov, I. S.

T. A. Fadeyeva, A. F. Rubass, I. S. Valkov, and A. V. Volyar, “Fractional optical vortices in a uniaxial crystal,” J. Opt. 15, 044020 (2013).
[CrossRef]

van Houwelingen, J. A. W.

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]

M. V. Vasnetsov, I. V. Basistiy, and M. S. Soskin, “Free-space evolution of monochromatic mixed screw-edge wavefront dislocations,” Proc. SPIE 3487, 29–33 (1998).
[CrossRef]

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

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2001), Vol. 42, pp. 219–276.

Vasylkiv, Yu.

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]

Verstegen, E. J. K.

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]

Vlokh, R.

Volyar, A.

Volyar, A. V.

T. A. Fadeyeva, A. F. Rubass, I. S. Valkov, and A. V. Volyar, “Fractional optical vortices in a uniaxial crystal,” J. Opt. 15, 044020 (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]

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]

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]

Woerdman, J. P.

S. S. R. Oemrawsingh, J. A. W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Production and characterization of spiral phase plates for optical wavelengths,” Appl. Opt. 43, 688–694 (2004).
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M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Yao, E.

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]

Yeomans, J. M.

G. Tóth, C. Denniston, and J. M. Yeomans, “Hydrodynamics of topological defects in nematic liquid crystals,” Phys. Rev. Lett. 88, 105504 (2002).
[CrossRef]

Yuan, X.-C.

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. (4)

Appl. Phys. Lett. (1)

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]

Ferroelectrics (2)

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[CrossRef]

E. F. Dudnik and L. A. Shuvalov, “Domain structure and phase boundaries in ferroelastics,” Ferroelectrics 98, 207–233 (1989).
[CrossRef]

Fiz. Tverd. Tela (1)

G. G. Krainyuk, A. I. Otko, and A. E. Nosenko, “Electromechanical effects at the torsion and bending of Gd2(MoO4)3 crystals with the regular domain structures,” Fiz. Tverd. Tela 26, 2611–2614 (1984).

J. Opt. (1)

T. A. Fadeyeva, A. F. Rubass, I. S. Valkov, and A. V. Volyar, “Fractional optical vortices in a uniaxial crystal,” J. Opt. 15, 044020 (2013).
[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]

J. Opt. Soc. Am. A (2)

Liq. Cryst. (1)

O. D. Lavrentovich, “Topological defects in dispersed liquid crystals, or words and worlds around liquid crystal drops,” Liq. Cryst. 24, 117–126 (1998).
[CrossRef]

Mol. Cryst. Liq. Cryst. (1)

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).
[CrossRef]

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. (2)

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

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]

Opt. Commun. (3)

W. M. Lee, X.-C. Yuan, and K. Dholakia, “Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step,” Opt. Commun. 239, 129–135 (2004).
[CrossRef]

I. V. 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 phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phase Transit. (1)

A. L. Roitburd, “Elastic domains and polydomain phases in solids,” Phase Transit. 45, 1–34 (1993).
[CrossRef]

Phys. Rev. A (2)

I. Skab, Yu. 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]

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. B (1)

J. Sapriel, “Domain-wall orientations in ferroelastics,” Phys. Rev. B 12, 5128–5140 (1975).
[CrossRef]

Phys. Rev. Lett. (3)

G. Tóth, C. Denniston, and J. M. Yeomans, “Hydrodynamics of topological defects in nematic liquid crystals,” Phys. Rev. Lett. 88, 105504 (2002).
[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]

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]

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]

Proc. SPIE (1)

M. V. Vasnetsov, I. V. Basistiy, and M. S. Soskin, “Free-space evolution of monochromatic mixed screw-edge wavefront dislocations,” Proc. SPIE 3487, 29–33 (1998).
[CrossRef]

Science (1)

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

Sov. Phys. Usp. (1)

A. L. Roitburd, “The theory of the formation of a heterophase structure in phase transformations in solids,” Sov. Phys. Usp. 17, 326–344 (1974).
[CrossRef]

Ukr. J. Phys. Opt. (3)

Yu. 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]

T. A. Fadeyeva, “Hidden chains of optical vortices generated using a corner of phase wedge,” Ukr. J. Phys. Opt. 14, 57–69 (2013).
[CrossRef]

Other (3)

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2001), Vol. 42, pp. 219–276.

M. P. Shaskolskaya, Acoustic Crystals (Nauka, 1982).

M. E. Lines and A. M. Glass, Principles and Application of Ferroelectric and Related Materials (Clarendon, 1977).

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Figures (6)

Fig. 1.
Fig. 1.

Schematic representation of a crystalline plate with circularly shaped electrodes e1 and e2, and a conical spatial distribution of the electric field produced by these electrodes.

Fig. 2.
Fig. 2.

XY distributions of the effective OI orientation angle [panels (a), (d), (g), (j), (m)], the effective phase difference [panels (b), (i), (h), (k), (n)], and the emergent light intensity for the crystalline sample placed between the crossed circular polarizers [panels (c), (f), (i), (l), (o)]. Calculations are performed for the crystals of the point group 6¯m2 subjected to the “conical” electric field. The electric voltages are U=1.0 [panels (a)–(c)], 5.0 kV (d)–(f), 15.0 kV (g)–(i), 20.5 kV (j)–(l), and 50.0 kV (m)–(o). The other parameters are specified in the text.

Fig. 3.
Fig. 3.

Dependences of OI rotation angle in the vicinities of central TD [panel (a)] and lateral TDs [TD1,panel (b); TD2,panel (c);, and TD3,panel (d)] on the tracing angle calculated at different voltages, indicated in the legend. See also explanations in the text (ρ is the chosen radius around the lateral TDs).

Fig. 4.
Fig. 4.

Spatial distributions of OI orientation angle calculated for the sample thicknesses equal to (a) d/3, (b) 2d/3, and (c) d. The electric voltage is equal to U=50kV.

Fig. 5.
Fig. 5.

Dependences of coordinates of the TDs on the applied voltage, as calculated at Z=d=5mm.

Fig. 6.
Fig. 6.

Spatial map of OI orientation that would have been observed if a hypothetical TD with the strength equal to 1/4 appeared.

Equations (30)

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

Eout(X,Y)=E0cosΔΓklef2[1±i]+iE0sinΔΓklef2e±i2pφ±i2ζ0[1i],
E1=kX,E2=kY,E3=kZ,
k=UdZX2+Y2+Z2.
E1=UdtanΘ1+tan2Θcosφ,
E2=UdtanΘ1+tan2Θsinφ,
E3=Ud(1+tan2Θ),
Bij=Bij0+rijkEk+RijklEkEl,
Jkl=|(eiΔΓklef/2cos2ζklef+eiΔΓklef/2sin2ζklef)isin(ΔΓklef/2)sin2ζklefisin(ΔΓklef/2)sin2ζklef(eiΔΓklef/2sin2ζklef+eiΔΓklef/2cos2ζklef)|=s=1Smax|(eiΔΓkls/2cos2ζkls+eiΔΓkls/2sin2ζkls)isin(ΔΓkls/2)sin2ζklsisin(ΔΓkls/2)sin2ζkls(eiΔΓkls/2sin2ζkls+eiΔΓkls/2cos2ζkls)|,
(E1klE2kl)=JAJQWPJklJQWP+(E1E2),
E1=1,E2=0,JA=(0001),JQWP=(12eiπ412eiπ412eiπ412eiπ4),JQWP+=(12eiπ412eiπ412eiπ412eiπ4).
(Ikl)lout=(E1klE2kl)(E1kl*E2kl*).
ΔnXY=no324r112(E12+E22)+R662(E12+E22)2+4r11R66E1(E128E22),
tan2ζZ=2(R66E1E2r11E2)2r11E1+R66(E12E22),
ΔnXY=no32[2(r11E1r22E2)+R66(E12E22)+4R62E1E2]2+4[R66E1E2R62(E12E22)r22E1r11E2]2,
tan2ζZ=2(R66E1E2R62(E12E22)r22E1r11E2)2(r11E1r22E2)+R66(E12E22)+4R62E1E2.
ΔnXY=no32[2r11E1+R66(E12E22)+2R14E3E2]2+4[R14E3E2+R66E1E2]2,
tan2ζZ=2(R14E3E1R66E1E2r11E2)2r11E1+R66(E12E22)+2R14E3E2.
ΔnXY=no32[2(r11E1r22E2)+R66(E12E22)+2R14E3E22R25E3E1+4R62E1E2]2+4[R62(E22E12)+R25E2E3+R14E3E1+R66E1E2r22E1r11E2]2,
tan2ζZ=2(R62(E22E12)+R25E2E3+R14E3E1+R66E1E2r22E1r11E2)2(r11E1r22E2)+R66(E12E22)+2R14E3E22R25E3E1+4R62E1E2.
ΔnXY=n32(R11R12)2(E12E22)+4(r41E3+R44E1E2)2,
tan2ζZ=2(r41E3+R44E1E2)(R11R12)(E12E22)=2r41E3(R11R12)(E12E22)+R44R11R12tan2φ=2r41(ρ2+Z2)E0(R11R12)ρ2cos2φ+R44R11R12tan2φ=2r41(X2+Y2+Z2)E0(R11R12)(X2Y2)+R44R11R12tan2φ.
ΔnXY=n32[(R11R12)E12+(R12R11)E22+(R21R12)E32]2+4(r41E3+R44E1E2)2,
tan2ζZ=2(r41E3+R44E1E2)(R11R21)E12+(R12R11)E22+(R21R12)E32.
ΔnXY=no32[2r13E3+(R11R12)(E12E22)+2R16E1E2]2+4[r63E3+R61(E12E22)+R66E1E2]2,
tan2ζZ=2(r63E3+R61(E12E22)+R66E1E2)2r13E3+(R11R21)(E12E22)+2R16E1E2.
{R66E1E2r11E2=02r11E1+R66(E12E22)=0.
X1,2=12Z[R664r11E0±R66216r112E021],
Y1,2=±R66r11E0ZXX2Z2,
X3=Z[R664r11E0±R66216r112E021],Y3=0.
tan2ζZ=2E1E2E12E22=tan2φ,orζZ=φ.

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