Abstract

We present an analysis of the effect of torsion stresses on the spatial distribution of optical birefringence in crystals of different point symmetry groups. The symmetry requirements needed so that the optical beam carries dislocations of the phase front are evaluated for the case when the crystals are twisted and the beam closely corresponds to a plane wave. It is shown that the torsion stresses can produce screw-edge, pure screw, or pure edge dislocations of the phase front in the crystals belonging to cubic and trigonal systems. The conditions for appearance of canonical and noncanonical vortices in the conditions of crystal torsion are analyzed.

© 2011 Optical Society of America

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  1. R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
    [CrossRef]
  2. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
    [CrossRef] [PubMed]
  3. D. P. DiVincenzo, “Quantum computation,” Science 270, 255–261 (1995).
    [CrossRef]
  4. S. Ya. Kilin, “Quantum information,” Phys. Usp. 42435–452 (1999).
    [CrossRef]
  5. D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
    [CrossRef]
  6. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
    [CrossRef] [PubMed]
  7. 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]
  8. E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation of orbital angular momentum eigenmodes of light by thermally tuned q-plates,” Appl. Phys. Lett. 94, 231124 (2009).
    [CrossRef]
  9. B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversation via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
    [CrossRef]
  10. 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] [PubMed]
  11. 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]
  12. R. Vlokh, M. Kostyrko, and I. Skab, “Principle and application of crystallo-optical effects induced by inhomogeneous deformation,” Jpn. J. Appl. Phys. 37, 5418–5420 (1998).
    [CrossRef]
  13. I. Skab, I. Smaga, V. Savaryn, Yu. Vasylkiv, and R. Vlokh, “Torsion method for measuring piezooptic coefficients,” Cryst. Res. Technol. 46, 23–36 (2011).
    [CrossRef]
  14. M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A Pure Appl. Opt. 7, 685–690 (2005).
    [CrossRef]
  15. R. Vlokh, A. Volyar, O. Mys, and O. Krupych, “Appearance of optical vortex at conical refraction. Examples of NaNO2 and YFeO3 crystals,” Ukr. J. Phys. Opt. 4, 90–93 (2003).
    [CrossRef]
  16. M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A Pure Appl. Opt. 6, 289–300 (2004).
    [CrossRef]
  17. Yu. I. Sirotin and M. P. Shaskolskaya, Fundamentals of Crystal Physics (Nauka, 1979).
  18. T. S. Narasimhamurty, Photoelastic and Electrooptic Properties of Crystals (Plenum, 1981).
  19. I. Skab, Yu. Vasylkiv, V. Savaryn, and R. Vlokh, “Relations for optical indicatrix parameters in the conditions of crystal torsion,” Ukr. J. Phys. Opt. 11, 193–240 (2010).
    [CrossRef]
  20. S. Haussühl, Physical Properties of Crystals: An Introduction (Wiley-VCH, 2008).
  21. I. Skab, Yu. Vasylkiv, I. Smaga, V. Savaryn, and R. Vlokh, “On the method for measuring piezooptic coefficients π25 and π14 in the crystals belonging to point symmetry groups 3 and 3¯,” Ukr. J. Phys. Opt. 12, 28–35 (2011).
    [CrossRef]
  22. M. R. Dennis, “Local phase structure of wave dislocation lines: twist and twirl,” J. Opt. A Pure Appl. Opt. 6, S202–S208(2004).
    [CrossRef]

2011 (3)

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, I. Smaga, V. Savaryn, Yu. Vasylkiv, and R. Vlokh, “Torsion method for measuring piezooptic coefficients,” Cryst. Res. Technol. 46, 23–36 (2011).
[CrossRef]

I. Skab, Yu. Vasylkiv, I. Smaga, V. Savaryn, and R. Vlokh, “On the method for measuring piezooptic coefficients π25 and π14 in the crystals belonging to point symmetry groups 3 and 3¯,” Ukr. J. Phys. Opt. 12, 28–35 (2011).
[CrossRef]

2010 (2)

I. Skab, Yu. Vasylkiv, V. Savaryn, and R. Vlokh, “Relations for optical indicatrix parameters in the conditions of crystal torsion,” Ukr. J. Phys. Opt. 11, 193–240 (2010).
[CrossRef]

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversation 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 of orbital angular momentum eigenmodes of light by thermally tuned q-plates,” Appl. Phys. Lett. 94, 231124 (2009).
[CrossRef]

2006 (1)

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] [PubMed]

2005 (1)

M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A Pure Appl. Opt. 7, 685–690 (2005).
[CrossRef]

2004 (2)

M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A Pure Appl. Opt. 6, 289–300 (2004).
[CrossRef]

M. R. Dennis, “Local phase structure of wave dislocation lines: twist and twirl,” J. Opt. A Pure Appl. Opt. 6, S202–S208(2004).
[CrossRef]

2003 (1)

R. Vlokh, A. Volyar, O. Mys, and O. Krupych, “Appearance of optical vortex at conical refraction. Examples of NaNO2 and YFeO3 crystals,” Ukr. J. Phys. Opt. 4, 90–93 (2003).
[CrossRef]

2001 (2)

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

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]

1999 (1)

S. Ya. Kilin, “Quantum information,” Phys. Usp. 42435–452 (1999).
[CrossRef]

1998 (2)

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
[CrossRef]

R. Vlokh, M. Kostyrko, and I. Skab, “Principle and application of crystallo-optical effects induced by inhomogeneous deformation,” Jpn. J. Appl. Phys. 37, 5418–5420 (1998).
[CrossRef]

1995 (1)

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

1936 (1)

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
[CrossRef]

Allen, L.

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

Beijersbergen, M. W.

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] [PubMed]

Berry, M. V.

M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A Pure Appl. Opt. 7, 685–690 (2005).
[CrossRef]

M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A Pure Appl. Opt. 6, 289–300 (2004).
[CrossRef]

Beth, R. A.

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
[CrossRef]

Boschi, D.

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
[CrossRef]

Branca, S.

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
[CrossRef]

D’Ambrosio, V.

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

De Martini, F.

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
[CrossRef]

Dennis, M. R.

M. R. Dennis, “Local phase structure of wave dislocation lines: twist and twirl,” J. Opt. A Pure Appl. Opt. 6, S202–S208(2004).
[CrossRef]

DiVincenzo, D. P.

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

Hardy, L.

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
[CrossRef]

Haussühl, S.

S. Haussühl, Physical Properties of Crystals: An Introduction (Wiley-VCH, 2008).

Jeffrey, M. R.

M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A Pure Appl. Opt. 7, 685–690 (2005).
[CrossRef]

Karimi, E.

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

Kilin, S. Ya.

S. Ya. Kilin, “Quantum information,” Phys. Usp. 42435–452 (1999).
[CrossRef]

Kostyrko, M.

R. Vlokh, M. Kostyrko, and I. Skab, “Principle and application of crystallo-optical effects induced by inhomogeneous deformation,” Jpn. J. Appl. Phys. 37, 5418–5420 (1998).
[CrossRef]

Krupych, O.

R. Vlokh, A. Volyar, O. Mys, and O. Krupych, “Appearance of optical vortex at conical refraction. Examples of NaNO2 and YFeO3 crystals,” Ukr. J. Phys. Opt. 4, 90–93 (2003).
[CrossRef]

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] [PubMed]

Mansuripur, M.

M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A Pure Appl. Opt. 7, 685–690 (2005).
[CrossRef]

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] [PubMed]

Marrucci, L.

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversation 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 of orbital angular momentum eigenmodes of light by thermally tuned q-plates,” Appl. Phys. Lett. 94, 231124 (2009).
[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] [PubMed]

Molina-Terriza, G.

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]

Mys, O.

R. Vlokh, A. Volyar, O. Mys, and O. Krupych, “Appearance of optical vortex at conical refraction. Examples of NaNO2 and YFeO3 crystals,” Ukr. J. Phys. Opt. 4, 90–93 (2003).
[CrossRef]

Nagali, E.

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

Narasimhamurty, T. S.

T. S. Narasimhamurty, Photoelastic and Electrooptic Properties of Crystals (Plenum, 1981).

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] [PubMed]

Piccirillo, B.

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversation 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 of orbital angular momentum eigenmodes of light by thermally tuned q-plates,” Appl. Phys. Lett. 94, 231124 (2009).
[CrossRef]

Popescu, S.

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121–1125 (1998).
[CrossRef]

Santamato, E.

B. Piccirillo, V. D’Ambrosio, S. Slussarenko, L. Marrucci, and E. Santamato, “Photon spin-to-orbital angular momentum conversation 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 of orbital angular momentum eigenmodes of light by thermally tuned q-plates,” Appl. Phys. Lett. 94, 231124 (2009).
[CrossRef]

Savaryn, V.

I. Skab, I. Smaga, V. Savaryn, Yu. Vasylkiv, and R. Vlokh, “Torsion method for measuring piezooptic coefficients,” Cryst. Res. Technol. 46, 23–36 (2011).
[CrossRef]

I. Skab, Yu. Vasylkiv, I. Smaga, V. Savaryn, and R. Vlokh, “On the method for measuring piezooptic coefficients π25 and π14 in the crystals belonging to point symmetry groups 3 and 3¯,” Ukr. J. Phys. Opt. 12, 28–35 (2011).
[CrossRef]

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, V. Savaryn, and R. Vlokh, “Relations for optical indicatrix parameters in the conditions of crystal torsion,” Ukr. J. Phys. Opt. 11, 193–240 (2010).
[CrossRef]

Shaskolskaya, M. P.

Yu. I. Sirotin and M. P. Shaskolskaya, Fundamentals of Crystal Physics (Nauka, 1979).

Sirotin, Yu. I.

Yu. I. Sirotin and M. P. Shaskolskaya, Fundamentals of Crystal Physics (Nauka, 1979).

Skab, I.

I. Skab, I. Smaga, V. Savaryn, Yu. Vasylkiv, and R. Vlokh, “Torsion method for measuring piezooptic coefficients,” Cryst. Res. Technol. 46, 23–36 (2011).
[CrossRef]

I. Skab, Yu. Vasylkiv, I. Smaga, V. Savaryn, and R. Vlokh, “On the method for measuring piezooptic coefficients π25 and π14 in the crystals belonging to point symmetry groups 3 and 3¯,” Ukr. J. Phys. Opt. 12, 28–35 (2011).
[CrossRef]

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, V. Savaryn, and R. Vlokh, “Relations for optical indicatrix parameters in the conditions of crystal torsion,” Ukr. J. Phys. Opt. 11, 193–240 (2010).
[CrossRef]

R. Vlokh, M. Kostyrko, and I. Skab, “Principle and application of crystallo-optical effects induced by inhomogeneous deformation,” Jpn. J. Appl. Phys. 37, 5418–5420 (1998).
[CrossRef]

Slussarenko, S.

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

Smaga, I.

I. Skab, I. Smaga, V. Savaryn, Yu. Vasylkiv, and R. Vlokh, “Torsion method for measuring piezooptic coefficients,” Cryst. Res. Technol. 46, 23–36 (2011).
[CrossRef]

I. Skab, Yu. Vasylkiv, I. Smaga, V. Savaryn, and R. Vlokh, “On the method for measuring piezooptic coefficients π25 and π14 in the crystals belonging to point symmetry groups 3 and 3¯,” Ukr. J. Phys. Opt. 12, 28–35 (2011).
[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] [PubMed]

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]

Vasylkiv, Yu.

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, I. Smaga, V. Savaryn, and R. Vlokh, “On the method for measuring piezooptic coefficients π25 and π14 in the crystals belonging to point symmetry groups 3 and 3¯,” Ukr. J. Phys. Opt. 12, 28–35 (2011).
[CrossRef]

I. Skab, I. Smaga, V. Savaryn, Yu. Vasylkiv, and R. Vlokh, “Torsion method for measuring piezooptic coefficients,” Cryst. Res. Technol. 46, 23–36 (2011).
[CrossRef]

I. Skab, Yu. Vasylkiv, V. Savaryn, and R. Vlokh, “Relations for optical indicatrix parameters in the conditions of crystal torsion,” Ukr. J. Phys. Opt. 11, 193–240 (2010).
[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] [PubMed]

Vlokh, R.

I. Skab, I. Smaga, V. Savaryn, Yu. Vasylkiv, and R. Vlokh, “Torsion method for measuring piezooptic coefficients,” Cryst. Res. Technol. 46, 23–36 (2011).
[CrossRef]

I. Skab, Yu. Vasylkiv, I. Smaga, V. Savaryn, and R. Vlokh, “On the method for measuring piezooptic coefficients π25 and π14 in the crystals belonging to point symmetry groups 3 and 3¯,” Ukr. J. Phys. Opt. 12, 28–35 (2011).
[CrossRef]

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, V. Savaryn, and R. Vlokh, “Relations for optical indicatrix parameters in the conditions of crystal torsion,” Ukr. J. Phys. Opt. 11, 193–240 (2010).
[CrossRef]

R. Vlokh, A. Volyar, O. Mys, and O. Krupych, “Appearance of optical vortex at conical refraction. Examples of NaNO2 and YFeO3 crystals,” Ukr. J. Phys. Opt. 4, 90–93 (2003).
[CrossRef]

R. Vlokh, M. Kostyrko, and I. Skab, “Principle and application of crystallo-optical effects induced by inhomogeneous deformation,” Jpn. J. Appl. Phys. 37, 5418–5420 (1998).
[CrossRef]

Volyar, A.

R. Vlokh, A. Volyar, O. Mys, and O. Krupych, “Appearance of optical vortex at conical refraction. Examples of NaNO2 and YFeO3 crystals,” Ukr. J. Phys. Opt. 4, 90–93 (2003).
[CrossRef]

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] [PubMed]

Woerdman, J. P.

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] [PubMed]

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] [PubMed]

Appl. Phys. Lett. (2)

E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, and E. Santamato, “Efficient generation 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 conversation via an electrically tunable q-plate,” Appl. Phys. Lett. 97, 241104 (2010).
[CrossRef]

Cryst. Res. Technol. (1)

I. Skab, I. Smaga, V. Savaryn, Yu. Vasylkiv, and R. Vlokh, “Torsion method for measuring piezooptic coefficients,” Cryst. Res. Technol. 46, 23–36 (2011).
[CrossRef]

J. Opt. A Pure Appl. Opt. (3)

M. V. Berry, M. R. Jeffrey, and M. Mansuripur, “Orbital and spin angular momentum in conical diffraction,” J. Opt. A Pure Appl. Opt. 7, 685–690 (2005).
[CrossRef]

M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A Pure Appl. Opt. 6, 289–300 (2004).
[CrossRef]

M. R. Dennis, “Local phase structure of wave dislocation lines: twist and twirl,” J. Opt. A Pure Appl. Opt. 6, S202–S208(2004).
[CrossRef]

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

Jpn. J. Appl. Phys. (1)

R. Vlokh, M. Kostyrko, and I. Skab, “Principle and application of crystallo-optical effects induced by inhomogeneous deformation,” Jpn. J. Appl. Phys. 37, 5418–5420 (1998).
[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] [PubMed]

Phys. Rev. (1)

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
[CrossRef]

Phys. Rev. A (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] [PubMed]

Phys. Rev. Lett. (3)

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Supplementary Material (5)

» Media 1: MOV (204 KB)     
» Media 2: MOV (76 KB)     
» Media 3: MOV (254 KB)     
» Media 4: MOV (139 KB)     
» Media 5: MOV (719 KB)     

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Figures (11)

Fig. 1
Fig. 1

Schematic representation of rotation of our working coordinate system with respect to the crystallographic one, which is used to describe the induced birefringence appearing under torsion torque M Z and light propagation given by k Z at different angles Θ.

Fig. 2
Fig. 2

Spatial distribution of induced birefringence for the crystals belonging to the point symmetry groups m3m, 432, and 4 ¯ 3 m (e.g., NaCl crystals), which are twisted around the directions defined by different Θ angles: (a)  Θ = 54.74 deg (i.e., [ 111 ] direction), (b)  Θ = 45 deg , and (c)  Θ = 60 deg (Media 1).

Fig. 3
Fig. 3

Spatial distribution of optical indicatrix rotation angle for the crystals belonging to the point symmetry groups m3m, 432, and 4 ¯ 3 m (e.g., NaCl crystals), which are twisted around the direction defined by different Θ angles in the ( 110 ) plane: (a)  Θ = 54.74 deg , (b)  Θ = 15 deg , and (c)  Θ = 85 deg (Media 2).

Fig. 4
Fig. 4

Spatial distribution of induced birefringence for the crystals belonging to the point symmetry groups 23 and m3 (e.g., KAl ( SO 4 ) 2 × 12 H 2 O crystals), which are twisted around the direction defined by different Θ angles: (a)  Θ = 54.74 deg (i.e., [ 111 ] direction) and (b)  Θ = 90 deg (Media 3).

Fig. 5
Fig. 5

Spatial distribution of optical indicatrix rotation angle for the crystals belonging to the point symmetry groups 23 and m3 (e.g., KAl ( SO 4 ) 2 × 12 H 2 O crystals), which are twisted around the direction defined by different Θ angles in ( 110 ) plane: (a)  Θ = 54.74 deg , (b)  Θ = 15 deg , (c)  Θ = 85 deg , and (d)  Θ = 90 deg (Media 4).

Fig. 6
Fig. 6

Dependences of piezo-optic coefficients on the Θ angle for (a) NaCl illustrating crystals of m3m, 432, and 4 ¯ 3 m symmetry groups ( π 14 , solid circles and π 15 , open circles) and (b)  KAl ( SO 4 ) 2 × 12 H 2 O illustrating crystals of 23 and m3 symmetry groups ( π 14 , solid triangles; π 15 , solid circles; π 24 , open triangles; π 25 , open circles; π 64 , solid diamonds, and π 65 , open diamonds).

Fig. 7
Fig. 7

Spatial distributions of optical indicatrix rotation angle for crystals of 3m, 32, and 3 ¯ m symmetry groups, under torsion around the Z axis.

Fig. 8
Fig. 8

Spatial distributions of birefringence ( Δ n X Y ) and optical indicatrix orientation ( ζ Z ) in the X Y plane for the crystals belonging to symmetry groups 3 and 3 ¯ at different ratios of piezo-optic coefficients K = π 15 / π 14 : (a), (b)  K = 1 ; (c), (d)  K = 100 ( M z = 0.05 N × m , n o = 2.0 , π 14 = 10 12 m 2 / N , R = 3 × 10 3 m ).

Fig. 9
Fig. 9

(a) Dependence of the birefringence on the X coordinate along the solid line at Y = 0 and (b) spatial distribution of the birefringence in the X Y plane for the case K = 100 .

Fig. 10
Fig. 10

Spatial distributions of phase retardation simulated with Eq. (39) for the case of KAl ( SO 4 ) 2 × 12 H 2 O crystals: (a)  Θ = 54.74 deg (i.e., [ 111 ] direction), (b)  Θ = 45 deg , (c)  Θ = 60 deg , and (d)  Θ = 90 deg .

Fig. 11
Fig. 11

Spatial distributions of light intensity transmitted through the system of circular polarizers and twisted crystal with the symmetry 23 in between, as obtained on the example of KAl ( SO 4 ) 2 × 12 H 2 O : (a)  Θ = 54.74 deg (i.e., [ 111 ] direction), (b)  Θ = 45 deg , (c)  Θ = 60 deg , and (d)  Θ = 90 deg (Media 5).

Equations (39)

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σ μ = 2 M Z π R 4 ( X δ 4 μ Y δ 5 μ ) .
Δ B i = B i B i 0 = π i μ σ μ ,
π i μ = | π 11 π 12 π 13 π 14 π 15 π 16 π 21 π 22 π 23 π 24 π 25 π 26 π 31 π 32 π 33 π 34 π 35 π 36 π 41 π 42 π 43 π 44 π 45 π 46 π 51 π 52 π 53 π 54 π 55 π 56 π 61 π 62 π 63 π 64 π 65 π 66 | ,
( B 1 0 + π 14 σ 4 + π 15 σ 5 ) X 2 + ( B 1 0 + π 24 σ 4 + π 25 σ 5 ) Y 2 + 2 ( π 64 σ 4 + π 65 σ 5 ) X Y = 0 .
π i μ = | π 11 π 12 π 12 0 0 0 π 12 π 11 π 12 0 0 0 π 12 π 12 π 11 0 0 0 0 0 0 π 44 0 0 0 0 0 0 π 44 0 0 0 0 0 0 π 44 | , π i μ = | π 11 π 12 π 21 0 0 0 π 21 π 11 π 12 0 0 0 π 12 π 21 π 11 0 0 0 0 0 0 π 44 0 0 0 0 0 0 π 44 0 0 0 0 0 0 π 44 | .
Δ n X Y = n 3 M Z π R 4 ( ( π 14 π 24 ) X + ( π 15 π 25 ) Y ) 2 + 4 A ( π 15 X + π 24 Y ) 2 , tan 2 ζ Z = 2 A ( π 15 X + π 24 Y ) ( π 14 π 24 ) X + ( π 15 π 25 ) Y ,
A = 3 sin 2 Θ 1 + 3 cos 2 Θ ,
π 14 = 3 2 4 sin 3 Θ cos Θ ( π 11 π 44 1 2 ( π 12 + π 21 ) ) + 2 8 sin Θ ( 1 9 cos 2 Θ ) ( π 12 π 21 ) ,
π 24 = 2 4 sin Θ ( 1 + 3 cos 2 Θ ) ( ( π 11 π 44 ) cos Θ 1 2 π 12 ( 1 + cos Θ ) + 1 2 π 21 ( 1 cos Θ ) ) ,
π 15 = 2 4 sin Θ ( 1 + 3 cos 2 Θ ) ( ( π 11 π 44 ) cos Θ + 1 2 π 12 ( 1 cos Θ ) 1 2 π 21 ( 1 + cos Θ ) ) ,
π 25 = 3 2 4 sin 3 Θ cos Θ ( π 11 π 44 1 2 ( π 12 + π 21 ) ) 2 8 sin Θ ( 1 9 cos 2 Θ ) ( π 12 π 21 ) .
Δ n X Y = 2 n 3 M Z 2 π R 4 ( π 11 π 44 π 12 ) sin Θ cos Θ 4 ( X Y ) 2 + 9 sin 4 Θ ( X + Y ) 2 , tan 2 ζ Z = 3 ( X + Y ) 2 ( X Y ) sin 2 Θ .
Δ n X Y = n 0 3 ( π 14 2 + π 15 2 ) ( σ 4 2 + σ 5 2 ) = 2 n 0 3 M Z π 14 2 + π 15 2 π R 4 X 2 + Y 2 ,
tan 2 ζ Z = π 14 σ 5 π 15 σ 4 π 14 σ 4 π 15 σ 5 = π 14 Y π 15 X π 14 X + π 15 Y = Y K X X + K Y ,
Δ n X Y = 2 n 0 3 M Z π 14 2 + π 15 2 π R 4 ρ ,
tan 2 ζ Z = π 14 sin φ π 15 cos φ π 14 cos φ + π 15 sin φ = tan ( 2 φ 0 + φ ) , ζ Z = φ 0 + φ / 2 ,
Δ n X Y = n 0 3 2 π 14 σ 4 2 + σ 5 2 = 2 2 n 0 3 ( π 11 π 44 π 12 ) M Z 3 π R 4 X 2 + Y 2 = 2 2 n 0 3 ( π 11 π 44 π 12 ) M Z 3 π R 4 ρ ,
tan 2 ζ Z = σ 4 + σ 5 σ 4 σ 5 = X + Y X Y = cos φ + sin φ cos φ sin φ = tan ( 45 ° + φ ) , ζ Z = φ 0 + φ / 2 ,
( B 11 + π 14 ( σ 4 σ 5 ) ) X 2 + ( B 11 + π 14 ( σ 4 σ 5 ) ) Y 2 + 6 π 14 ( σ 4 σ 5 ) X Y = 1 ,
Δ n X Y = 3 n 3 π 14 ( σ 4 σ 5 ) = 6 n 3 π 14 M Z π R 4 ( X Y ) .
Δ n X Y = n o 3 π 14 σ 5 2 + σ 4 2 = 2 n o 3 π 14 M Z π R 4 Y 2 + X 2 = 2 n o 3 π 14 M Z π R 4 ρ ,
tan 2 ζ z = σ 5 σ 4 = Y X = sin φ cos φ = tan φ ( or     ζ Z = φ / 2 ) ,
( B 11 + π 14 σ 4 + π 15 σ 5 ) X 2 + ( B 11 π 14 σ 4 π 15 σ 5 ) Y 2 + B 33 Z 2 + 2 ( π 44 σ 4 + π 45 σ 5 ) Y Z + 2 ( π 44 σ 5 π 45 σ 4 ) X Z + 2 ( π 14 σ 5 π 15 σ 4 ) X Y = 1 .
Δ n X Y = n o 3 π 14 2 σ 4 2 + ( π 15 σ 4 + π 14 σ 5 ) 2 = 2 n o 3 M Z π R 4 π 14 2 X 2 + ( π 15 X + π 14 Y ) 2 ,
tan 2 ζ Z = π 15 σ 4 + π 14 σ 5 π 14 σ 4 = π 15 X + π 14 Y π 14 X .
Δ n X Y = 2 n o 3 M Z π R 4 π 14 2 X 2 + π 15 2 X 2 + π 14 2 Y 2 + 2 π 14 π 15 X Y = 2 n o 3 M Z π R 4 ρ π 14 2 + π 15 2 cos 2 φ + π 15 π 14 sin 2 φ ,
tan 2 ζ Z = π 15 X + π 14 Y π 14 X = π 15 cos φ + π 14 sin φ π 14 cos φ .
Δ n X Y = 2 n o 3 M Z π R 4 π 14 X 2 + Y 2 = 2 n o 3 M Z π R 4 π 14 ρ ,
tan 2 ζ Z = Y X = tan φ .
tan 2 ζ Z = ± , ζ Z = ± 45 ° ,
tan ζ Z = π 15 π 14 ,
β = 1 2 arctan π 14 π 15 = 1 2 arctan 1 K ,
e = 1 ( a b ) 2 = 1 2 π 14 2 + π 15 2 + π 15 π 15 2 + 4 π 14 2 2 π 14 2 + π 15 2 π 15 π 15 2 + 4 π 14 2 ,
Δ n X Y = ± 2 n o 3 M z π R 4 π 25 X = ± 2 n o 3 M z π R 4 ρ π 25 cos φ .
J k l = | ( e i Δ Γ k l / 2 cos 2 ζ k l Z + e i Δ Γ k l / 2 sin 2 ζ k l Z ) i sin ( Δ Γ k l / 2 ) sin 2 ζ k l Z i sin ( Δ Γ k l / 2 ) sin 2 ζ k l Z ( e i Δ Γ k l / 2 sin 2 ζ k l Z + e i Δ Γ k l / 2 cos 2 ζ k l Z ) | ,
( σ 4 ) k l = 2 M Z π R 4 ( k 30 ) × 10 4 , ( σ 5 ) k l = 2 M Z π R 4 ( k 30 ) × 10 4 , Δ Γ k l = 2 π Δ n X Y / λ , ζ k l Z = 1 2 arctan ( σ 4 ) k l ( σ 5 ) k l ,
| E 1 k l E 2 k l | = J A J QWP J k l J QWP + | E 1 E 2 | ,
E 1 = 1 , E 2 = 0 , J A = ( 0 0 0 1 ) , J QWP = ( 1 2 e i π 4 1 2 e i π 4 1 2 e i π 4 1 2 e i π 4 ) , J QWP + = ( 1 2 e i π 4 1 2 e i π 4 1 2 e i π 4 1 2 e i π 4 ) .
Δ Γ k l = arctan ( Im E 1 k l Re E 1 k l ) arctan ( Im E 2 k l Re E 2 k l ) .

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