Abstract

We have found that torsion mechanical stresses induce the optical rotation effect in centrosymmetric NaBi(MoO4)2 crystals. We have suggested a description of the effect on the basis of nonlocal linear elasticity theory. It has been shown that the induced optical gyration is proportional to the stress gradient appearing due to the torsion.

© 2013 Optical Society of America

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Errata

Yuriy Vasylkiv, Oleksiy Kvasnyuk, Yaroslav Shopa, and Rostyslav Vlokh, "Optical activity caused by torsion stresses: the case of NaBi(MoO4)2 crystals: erratum," J. Opt. Soc. Am. A 30, 1380-1380 (2013)
https://www.osapublishing.org/josaa/abstract.cfm?uri=josaa-30-7-1380

References

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  1. F. J. D. Arago, “Memoire sur une modifcation remarquable qu’eprouvent les rayons lumineux dans leur passage a travers certains corps diaphanes et sur quelques autres nouveaux phenomenes d’optique,” Memoires de la classe des sciences math. et phys. de l’Institut Imperial de France 1, 93–134 (1811).
  2. A. Fresnel, “Memoire sur la double refraction que les rayons lumineux eprouvent en traversant les aiguilles de cristal de roche suivant des directions paralleles a l’axe,” Oeuvres 1, 731–751 (1822).
  3. M. Born, “Uber die natufrliche optische Aktivitat von Flussigkeiten und Gasen,” Phys. Z. 16, 251–258 (1915).
  4. C. W. Oseen, “Uber die Wechselwirkung zwischen zwei elektrischen Dipolen und fiber in Kristallen und Flussigkeiten,” Ann. Phys. 353, 1–56 (1915).
    [CrossRef]
  5. F. Gray, “The optical activity of liquids and gases,” Phys. Rev. 7, 472–488 (1916).
    [CrossRef]
  6. V. L. Ginzburg and V. M. Agranovich, “Crystal optics with allowance for spatial dispersion; exciton theory. I,” Sov. Phys. Usp. 5, 323–346 (1962).
    [CrossRef]
  7. V. L. Ginzburg and V. M. Agranovich, “Crystal optics with allowance for spatial dispersion; exciton theory. II,” Sov. Phys. Usp. 5, 649–660 (1963).
    [CrossRef]
  8. L. D. Landau and E. M. Lifshitz, Theoretical Physics. Vol. VIII. Electrodynamics of Continuous Media (Nauka, 1982).
  9. K. Aizu, “Reversal in optical rotatory power—‘gyroelectric’ crystals and ‘hypergyroelectric’ crystals,” Phys. Rev. 133, A1584–A1588 (1964).
    [CrossRef]
  10. I. S. Zheludev, “Axial tensors of the third rank and the physical effects they describe,” Kristallografiya 9, 501–505 (1964). [Sov. Phys. Crystallogr. 9, 418–422 (1965)].
  11. O. G. Vlokh, “Electrooptical activity of quartz crystals,” Ukr. Fiz. Zhurn. 15, 758–762. (1970). [Sov. Phys. Ukr. Fiz. Zhurn. 15, 771–775 (1970)].
  12. O. G. Vlokh, “Electrogyration effects in quartz crystals,” Pisma ZhETF. 13, 118–121 (1971). [Sov. Phys. Pisma. 13, 81–83 (1971)].
  13. O. G. Vlokh and R. O. Vlokh, “The electrogyration effect,” Opt. Photon. News 20, 34–39 (2009).
    [CrossRef]
  14. K. Aizu, “Ferroelectric transformations of tensorial properties in regular ferroelectrics,” Phys. Rev. 133, A1350–A1359 (1964).
    [CrossRef]
  15. O. G. Vlokh and T. D. Krushel’nitskaya, “Axial fourth-rank tensors and quadratic electro-gyration,” Kristallografiya 15, 587–589 (1970).
  16. V. S. Lvov, “Optical activity of deformed crystals,” Fiz. Tverd. Tela. 9, 1273–1275 (1967).
  17. H. J. Weber and S. Haussuhl, “Electrogyration and piezogyration in NaClO3,” Acta Crystallogr. A35, 225–232 (1979).
  18. 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]
  19. R. O. Vlokh, Y. A. Pyatak, and I. P. Skab, “Torsion-gyration effect,” Ukr. Fiz. Zhurn. 34, 845–846 (1989).
  20. R. O. Vlokh, M. E. Kostyrko, and I. P. Skab, “Description of gradients of piezo-gyration and piezo-optics caused by twisting and bending,” Crystallogr. Rep. 42, 1011–1013 (1997).
  21. B. V. Bokut and A. N. Serdyukov, “On the theory of optical activity of the inhomogeneous media,” Zh. Prikl. Spektrosk. 20, 677–681 (1974).
  22. B. V. Bokut, A. N. Serdyukov, F. I. Fedorov, and N. A. Khilo, “On the boundary conditions in the electrodynamics of the optically active media,” Kristallografiya 18, 227–233 (1973).
  23. O. S. Kushnir and L. O. Lokot, “The peculiarities of the optical response of dielectric crystals with incommensurate phases,” Fiz. Tverd. Tela 43, 786–790 (2001).
  24. O. S. Kushnir, “Spatial dispersion in incommensurately modulated insulators,” J. Phys.: Condens. Matter. 16, 1245–1267 (2004).
    [CrossRef]
  25. M. P. Shaskolskaya, Acoustic Crystals (Nauka, 1982).
  26. Yu. I. Sirotin and M. P. Shaskolskaya, Fundamentals of Crystal Physics (Nauka, 1979).
  27. T. S. Narasimhamurty, Photoelastic and Electro-optic Properties of Crystals (Plenum, 1981).
  28. 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]
  29. 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).
  30. 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]
  31. O. G. Vlokh and V. B. Kobylyansky, “Effect of parameters of gyrotropic crystals on the light polarization character,” Ukr. Fiz. Zhurn. 19, 1129–1135 (1974).
  32. A. F. Konstantinova, B. N. Grechushnikov, B. V. Bokut, and E. G. Valyashko, Optical Properties of Crystals (Navuka i Tekhnika, 1995).
  33. http://www.irystyle.com/elent/sbimo.htm .
  34. W. G. Jung, Op Amp Applications Handbook (Elsevier, 2005).
  35. E. Hecht, Optics (Addison–Wesley, 2002).
  36. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).
  37. Yu. I. Sirotin and M. P. Shaskolskaya, Fundamentals of Crystal Physics (Mir, 1982).
  38. R. D. Mindlin and H. F. Tiersten, “Effects of couple-stresses in linear elasticity,” Arch. Ration. Mech. Anal. 11, 415–448 (1962).
    [CrossRef]
  39. R. D. Mindlin, “Micro-structure in linear elasticity,” Arch. Ration. Mech. Anal. 16, 51–78 (1964).
    [CrossRef]
  40. J. F. Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices (Oxford University, 2000).
  41. W. T. Lee, E. K. H. Salje, and U. Bismayer, “Domain-wall structure and domain-wall strain,” J. Appl. Phys. 93, 9890–9897 (2003).
    [CrossRef]
  42. C. G. Grentzelou and H. G. Georgiadis, “Uniqueness for plane crack problems in dipolar gradient elasticity and in couple-stress elasticity,” Int. J. Solids Struct. 42, 6226–6244 (2005).
    [CrossRef]
  43. V. A. Lubarda, “The effects of couple stresses on dislocation strain energy,” Int. J. Solids Struct. 40, 3807–3826 (2003).
    [CrossRef]
  44. F. Yang, A. C. M. Chong, D. C. C. Lam, and P. Tong, “Couple stress based strain gradient theory for elasticity,” Int. J. Solids Struct. 39, 2731–2743 (2002).
    [CrossRef]
  45. A. K. Tagantsev, “Pyroelectric, piezoelectric, flexoelectric, and thermal polarization effects in ionic crystals,” Sov. Phys. Usp. 30, 588–603 (1987).
    [CrossRef]

2011 (2)

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, “Optical anisotropy induced by torsion stresses in LiNbO3 crystals: appearance of an optical vortex,” J. Opt. Soc. Am. A. 28, 633–640 (2011).

2010 (1)

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]

2009 (1)

O. G. Vlokh and R. O. Vlokh, “The electrogyration effect,” Opt. Photon. News 20, 34–39 (2009).
[CrossRef]

2005 (1)

C. G. Grentzelou and H. G. Georgiadis, “Uniqueness for plane crack problems in dipolar gradient elasticity and in couple-stress elasticity,” Int. J. Solids Struct. 42, 6226–6244 (2005).
[CrossRef]

2004 (1)

O. S. Kushnir, “Spatial dispersion in incommensurately modulated insulators,” J. Phys.: Condens. Matter. 16, 1245–1267 (2004).
[CrossRef]

2003 (2)

W. T. Lee, E. K. H. Salje, and U. Bismayer, “Domain-wall structure and domain-wall strain,” J. Appl. Phys. 93, 9890–9897 (2003).
[CrossRef]

V. A. Lubarda, “The effects of couple stresses on dislocation strain energy,” Int. J. Solids Struct. 40, 3807–3826 (2003).
[CrossRef]

2002 (1)

F. Yang, A. C. M. Chong, D. C. C. Lam, and P. Tong, “Couple stress based strain gradient theory for elasticity,” Int. J. Solids Struct. 39, 2731–2743 (2002).
[CrossRef]

2001 (1)

O. S. Kushnir and L. O. Lokot, “The peculiarities of the optical response of dielectric crystals with incommensurate phases,” Fiz. Tverd. Tela 43, 786–790 (2001).

1998 (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]

1997 (1)

R. O. Vlokh, M. E. Kostyrko, and I. P. Skab, “Description of gradients of piezo-gyration and piezo-optics caused by twisting and bending,” Crystallogr. Rep. 42, 1011–1013 (1997).

1989 (1)

R. O. Vlokh, Y. A. Pyatak, and I. P. Skab, “Torsion-gyration effect,” Ukr. Fiz. Zhurn. 34, 845–846 (1989).

1987 (1)

A. K. Tagantsev, “Pyroelectric, piezoelectric, flexoelectric, and thermal polarization effects in ionic crystals,” Sov. Phys. Usp. 30, 588–603 (1987).
[CrossRef]

1979 (1)

H. J. Weber and S. Haussuhl, “Electrogyration and piezogyration in NaClO3,” Acta Crystallogr. A35, 225–232 (1979).

1974 (2)

B. V. Bokut and A. N. Serdyukov, “On the theory of optical activity of the inhomogeneous media,” Zh. Prikl. Spektrosk. 20, 677–681 (1974).

O. G. Vlokh and V. B. Kobylyansky, “Effect of parameters of gyrotropic crystals on the light polarization character,” Ukr. Fiz. Zhurn. 19, 1129–1135 (1974).

1973 (1)

B. V. Bokut, A. N. Serdyukov, F. I. Fedorov, and N. A. Khilo, “On the boundary conditions in the electrodynamics of the optically active media,” Kristallografiya 18, 227–233 (1973).

1971 (1)

O. G. Vlokh, “Electrogyration effects in quartz crystals,” Pisma ZhETF. 13, 118–121 (1971). [Sov. Phys. Pisma. 13, 81–83 (1971)].

1970 (2)

O. G. Vlokh and T. D. Krushel’nitskaya, “Axial fourth-rank tensors and quadratic electro-gyration,” Kristallografiya 15, 587–589 (1970).

O. G. Vlokh, “Electrooptical activity of quartz crystals,” Ukr. Fiz. Zhurn. 15, 758–762. (1970). [Sov. Phys. Ukr. Fiz. Zhurn. 15, 771–775 (1970)].

1967 (1)

V. S. Lvov, “Optical activity of deformed crystals,” Fiz. Tverd. Tela. 9, 1273–1275 (1967).

1964 (4)

K. Aizu, “Ferroelectric transformations of tensorial properties in regular ferroelectrics,” Phys. Rev. 133, A1350–A1359 (1964).
[CrossRef]

K. Aizu, “Reversal in optical rotatory power—‘gyroelectric’ crystals and ‘hypergyroelectric’ crystals,” Phys. Rev. 133, A1584–A1588 (1964).
[CrossRef]

I. S. Zheludev, “Axial tensors of the third rank and the physical effects they describe,” Kristallografiya 9, 501–505 (1964). [Sov. Phys. Crystallogr. 9, 418–422 (1965)].

R. D. Mindlin, “Micro-structure in linear elasticity,” Arch. Ration. Mech. Anal. 16, 51–78 (1964).
[CrossRef]

1963 (1)

V. L. Ginzburg and V. M. Agranovich, “Crystal optics with allowance for spatial dispersion; exciton theory. II,” Sov. Phys. Usp. 5, 649–660 (1963).
[CrossRef]

1962 (2)

V. L. Ginzburg and V. M. Agranovich, “Crystal optics with allowance for spatial dispersion; exciton theory. I,” Sov. Phys. Usp. 5, 323–346 (1962).
[CrossRef]

R. D. Mindlin and H. F. Tiersten, “Effects of couple-stresses in linear elasticity,” Arch. Ration. Mech. Anal. 11, 415–448 (1962).
[CrossRef]

1916 (1)

F. Gray, “The optical activity of liquids and gases,” Phys. Rev. 7, 472–488 (1916).
[CrossRef]

1915 (2)

M. Born, “Uber die natufrliche optische Aktivitat von Flussigkeiten und Gasen,” Phys. Z. 16, 251–258 (1915).

C. W. Oseen, “Uber die Wechselwirkung zwischen zwei elektrischen Dipolen und fiber in Kristallen und Flussigkeiten,” Ann. Phys. 353, 1–56 (1915).
[CrossRef]

1822 (1)

A. Fresnel, “Memoire sur la double refraction que les rayons lumineux eprouvent en traversant les aiguilles de cristal de roche suivant des directions paralleles a l’axe,” Oeuvres 1, 731–751 (1822).

1811 (1)

F. J. D. Arago, “Memoire sur une modifcation remarquable qu’eprouvent les rayons lumineux dans leur passage a travers certains corps diaphanes et sur quelques autres nouveaux phenomenes d’optique,” Memoires de la classe des sciences math. et phys. de l’Institut Imperial de France 1, 93–134 (1811).

Agranovich, V. M.

V. L. Ginzburg and V. M. Agranovich, “Crystal optics with allowance for spatial dispersion; exciton theory. II,” Sov. Phys. Usp. 5, 649–660 (1963).
[CrossRef]

V. L. Ginzburg and V. M. Agranovich, “Crystal optics with allowance for spatial dispersion; exciton theory. I,” Sov. Phys. Usp. 5, 323–346 (1962).
[CrossRef]

Aizu, K.

K. Aizu, “Reversal in optical rotatory power—‘gyroelectric’ crystals and ‘hypergyroelectric’ crystals,” Phys. Rev. 133, A1584–A1588 (1964).
[CrossRef]

K. Aizu, “Ferroelectric transformations of tensorial properties in regular ferroelectrics,” Phys. Rev. 133, A1350–A1359 (1964).
[CrossRef]

Arago, F. J. D.

F. J. D. Arago, “Memoire sur une modifcation remarquable qu’eprouvent les rayons lumineux dans leur passage a travers certains corps diaphanes et sur quelques autres nouveaux phenomenes d’optique,” Memoires de la classe des sciences math. et phys. de l’Institut Imperial de France 1, 93–134 (1811).

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Bismayer, U.

W. T. Lee, E. K. H. Salje, and U. Bismayer, “Domain-wall structure and domain-wall strain,” J. Appl. Phys. 93, 9890–9897 (2003).
[CrossRef]

Bokut, B. V.

B. V. Bokut and A. N. Serdyukov, “On the theory of optical activity of the inhomogeneous media,” Zh. Prikl. Spektrosk. 20, 677–681 (1974).

B. V. Bokut, A. N. Serdyukov, F. I. Fedorov, and N. A. Khilo, “On the boundary conditions in the electrodynamics of the optically active media,” Kristallografiya 18, 227–233 (1973).

A. F. Konstantinova, B. N. Grechushnikov, B. V. Bokut, and E. G. Valyashko, Optical Properties of Crystals (Navuka i Tekhnika, 1995).

Born, M.

M. Born, “Uber die natufrliche optische Aktivitat von Flussigkeiten und Gasen,” Phys. Z. 16, 251–258 (1915).

Chong, A. C. M.

F. Yang, A. C. M. Chong, D. C. C. Lam, and P. Tong, “Couple stress based strain gradient theory for elasticity,” Int. J. Solids Struct. 39, 2731–2743 (2002).
[CrossRef]

Fedorov, F. I.

B. V. Bokut, A. N. Serdyukov, F. I. Fedorov, and N. A. Khilo, “On the boundary conditions in the electrodynamics of the optically active media,” Kristallografiya 18, 227–233 (1973).

Fresnel, A.

A. Fresnel, “Memoire sur la double refraction que les rayons lumineux eprouvent en traversant les aiguilles de cristal de roche suivant des directions paralleles a l’axe,” Oeuvres 1, 731–751 (1822).

Georgiadis, H. G.

C. G. Grentzelou and H. G. Georgiadis, “Uniqueness for plane crack problems in dipolar gradient elasticity and in couple-stress elasticity,” Int. J. Solids Struct. 42, 6226–6244 (2005).
[CrossRef]

Ginzburg, V. L.

V. L. Ginzburg and V. M. Agranovich, “Crystal optics with allowance for spatial dispersion; exciton theory. II,” Sov. Phys. Usp. 5, 649–660 (1963).
[CrossRef]

V. L. Ginzburg and V. M. Agranovich, “Crystal optics with allowance for spatial dispersion; exciton theory. I,” Sov. Phys. Usp. 5, 323–346 (1962).
[CrossRef]

Gray, F.

F. Gray, “The optical activity of liquids and gases,” Phys. Rev. 7, 472–488 (1916).
[CrossRef]

Grechushnikov, B. N.

A. F. Konstantinova, B. N. Grechushnikov, B. V. Bokut, and E. G. Valyashko, Optical Properties of Crystals (Navuka i Tekhnika, 1995).

Grentzelou, C. G.

C. G. Grentzelou and H. G. Georgiadis, “Uniqueness for plane crack problems in dipolar gradient elasticity and in couple-stress elasticity,” Int. J. Solids Struct. 42, 6226–6244 (2005).
[CrossRef]

Haussuhl, S.

H. J. Weber and S. Haussuhl, “Electrogyration and piezogyration in NaClO3,” Acta Crystallogr. A35, 225–232 (1979).

Hecht, E.

E. Hecht, Optics (Addison–Wesley, 2002).

Jung, W. G.

W. G. Jung, Op Amp Applications Handbook (Elsevier, 2005).

Khilo, N. A.

B. V. Bokut, A. N. Serdyukov, F. I. Fedorov, and N. A. Khilo, “On the boundary conditions in the electrodynamics of the optically active media,” Kristallografiya 18, 227–233 (1973).

Kobylyansky, V. B.

O. G. Vlokh and V. B. Kobylyansky, “Effect of parameters of gyrotropic crystals on the light polarization character,” Ukr. Fiz. Zhurn. 19, 1129–1135 (1974).

Konstantinova, A. F.

A. F. Konstantinova, B. N. Grechushnikov, B. V. Bokut, and E. G. Valyashko, Optical Properties of Crystals (Navuka i Tekhnika, 1995).

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]

Kostyrko, M. E.

R. O. Vlokh, M. E. Kostyrko, and I. P. Skab, “Description of gradients of piezo-gyration and piezo-optics caused by twisting and bending,” Crystallogr. Rep. 42, 1011–1013 (1997).

Krushel’nitskaya, T. D.

O. G. Vlokh and T. D. Krushel’nitskaya, “Axial fourth-rank tensors and quadratic electro-gyration,” Kristallografiya 15, 587–589 (1970).

Kushnir, O. S.

O. S. Kushnir, “Spatial dispersion in incommensurately modulated insulators,” J. Phys.: Condens. Matter. 16, 1245–1267 (2004).
[CrossRef]

O. S. Kushnir and L. O. Lokot, “The peculiarities of the optical response of dielectric crystals with incommensurate phases,” Fiz. Tverd. Tela 43, 786–790 (2001).

Lam, D. C. C.

F. Yang, A. C. M. Chong, D. C. C. Lam, and P. Tong, “Couple stress based strain gradient theory for elasticity,” Int. J. Solids Struct. 39, 2731–2743 (2002).
[CrossRef]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Theoretical Physics. Vol. VIII. Electrodynamics of Continuous Media (Nauka, 1982).

Lee, W. T.

W. T. Lee, E. K. H. Salje, and U. Bismayer, “Domain-wall structure and domain-wall strain,” J. Appl. Phys. 93, 9890–9897 (2003).
[CrossRef]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Theoretical Physics. Vol. VIII. Electrodynamics of Continuous Media (Nauka, 1982).

Lokot, L. O.

O. S. Kushnir and L. O. Lokot, “The peculiarities of the optical response of dielectric crystals with incommensurate phases,” Fiz. Tverd. Tela 43, 786–790 (2001).

Lubarda, V. A.

V. A. Lubarda, “The effects of couple stresses on dislocation strain energy,” Int. J. Solids Struct. 40, 3807–3826 (2003).
[CrossRef]

Lvov, V. S.

V. S. Lvov, “Optical activity of deformed crystals,” Fiz. Tverd. Tela. 9, 1273–1275 (1967).

Mindlin, R. D.

R. D. Mindlin, “Micro-structure in linear elasticity,” Arch. Ration. Mech. Anal. 16, 51–78 (1964).
[CrossRef]

R. D. Mindlin and H. F. Tiersten, “Effects of couple-stresses in linear elasticity,” Arch. Ration. Mech. Anal. 11, 415–448 (1962).
[CrossRef]

Narasimhamurty, T. S.

T. S. Narasimhamurty, Photoelastic and Electro-optic Properties of Crystals (Plenum, 1981).

Nye, J. F.

J. F. Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices (Oxford University, 2000).

Oseen, C. W.

C. W. Oseen, “Uber die Wechselwirkung zwischen zwei elektrischen Dipolen und fiber in Kristallen und Flussigkeiten,” Ann. Phys. 353, 1–56 (1915).
[CrossRef]

Pyatak, Y. A.

R. O. Vlokh, Y. A. Pyatak, and I. P. Skab, “Torsion-gyration effect,” Ukr. Fiz. Zhurn. 34, 845–846 (1989).

Salje, E. K. H.

W. T. Lee, E. K. H. Salje, and U. Bismayer, “Domain-wall structure and domain-wall strain,” J. Appl. Phys. 93, 9890–9897 (2003).
[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, 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).

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]

Serdyukov, A. N.

B. V. Bokut and A. N. Serdyukov, “On the theory of optical activity of the inhomogeneous media,” Zh. Prikl. Spektrosk. 20, 677–681 (1974).

B. V. Bokut, A. N. Serdyukov, F. I. Fedorov, and N. A. Khilo, “On the boundary conditions in the electrodynamics of the optically active media,” Kristallografiya 18, 227–233 (1973).

Shaskolskaya, M. P.

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

Yu. I. Sirotin and M. P. Shaskolskaya, Fundamentals of Crystal Physics (Mir, 1982).

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

Sirotin, Yu. I.

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

Yu. I. Sirotin and M. P. Shaskolskaya, Fundamentals of Crystal Physics (Mir, 1982).

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, 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).

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]

Skab, I. P.

R. O. Vlokh, M. E. Kostyrko, and I. P. Skab, “Description of gradients of piezo-gyration and piezo-optics caused by twisting and bending,” Crystallogr. Rep. 42, 1011–1013 (1997).

R. O. Vlokh, Y. A. Pyatak, and I. P. Skab, “Torsion-gyration effect,” Ukr. Fiz. Zhurn. 34, 845–846 (1989).

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]

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A. K. Tagantsev, “Pyroelectric, piezoelectric, flexoelectric, and thermal polarization effects in ionic crystals,” Sov. Phys. Usp. 30, 588–603 (1987).
[CrossRef]

Tiersten, H. F.

R. D. Mindlin and H. F. Tiersten, “Effects of couple-stresses in linear elasticity,” Arch. Ration. Mech. Anal. 11, 415–448 (1962).
[CrossRef]

Tong, P.

F. Yang, A. C. M. Chong, D. C. C. Lam, and P. Tong, “Couple stress based strain gradient theory for elasticity,” Int. J. Solids Struct. 39, 2731–2743 (2002).
[CrossRef]

Valyashko, E. G.

A. F. Konstantinova, B. N. Grechushnikov, B. V. Bokut, and E. G. Valyashko, Optical Properties of Crystals (Navuka i Tekhnika, 1995).

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).

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]

Vlokh, O. G.

O. G. Vlokh and R. O. Vlokh, “The electrogyration effect,” Opt. Photon. News 20, 34–39 (2009).
[CrossRef]

O. G. Vlokh and V. B. Kobylyansky, “Effect of parameters of gyrotropic crystals on the light polarization character,” Ukr. Fiz. Zhurn. 19, 1129–1135 (1974).

O. G. Vlokh, “Electrogyration effects in quartz crystals,” Pisma ZhETF. 13, 118–121 (1971). [Sov. Phys. Pisma. 13, 81–83 (1971)].

O. G. Vlokh, “Electrooptical activity of quartz crystals,” Ukr. Fiz. Zhurn. 15, 758–762. (1970). [Sov. Phys. Ukr. Fiz. Zhurn. 15, 771–775 (1970)].

O. G. Vlokh and T. D. Krushel’nitskaya, “Axial fourth-rank tensors and quadratic electro-gyration,” Kristallografiya 15, 587–589 (1970).

Vlokh, R.

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).

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]

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]

Vlokh, R. O.

O. G. Vlokh and R. O. Vlokh, “The electrogyration effect,” Opt. Photon. News 20, 34–39 (2009).
[CrossRef]

R. O. Vlokh, M. E. Kostyrko, and I. P. Skab, “Description of gradients of piezo-gyration and piezo-optics caused by twisting and bending,” Crystallogr. Rep. 42, 1011–1013 (1997).

R. O. Vlokh, Y. A. Pyatak, and I. P. Skab, “Torsion-gyration effect,” Ukr. Fiz. Zhurn. 34, 845–846 (1989).

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H. J. Weber and S. Haussuhl, “Electrogyration and piezogyration in NaClO3,” Acta Crystallogr. A35, 225–232 (1979).

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F. Yang, A. C. M. Chong, D. C. C. Lam, and P. Tong, “Couple stress based strain gradient theory for elasticity,” Int. J. Solids Struct. 39, 2731–2743 (2002).
[CrossRef]

Zheludev, I. S.

I. S. Zheludev, “Axial tensors of the third rank and the physical effects they describe,” Kristallografiya 9, 501–505 (1964). [Sov. Phys. Crystallogr. 9, 418–422 (1965)].

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H. J. Weber and S. Haussuhl, “Electrogyration and piezogyration in NaClO3,” Acta Crystallogr. A35, 225–232 (1979).

Ann. Phys. (1)

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[CrossRef]

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R. D. Mindlin and H. F. Tiersten, “Effects of couple-stresses in linear elasticity,” Arch. Ration. Mech. Anal. 11, 415–448 (1962).
[CrossRef]

R. D. Mindlin, “Micro-structure in linear elasticity,” Arch. Ration. Mech. Anal. 16, 51–78 (1964).
[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]

Crystallogr. Rep. (1)

R. O. Vlokh, M. E. Kostyrko, and I. P. Skab, “Description of gradients of piezo-gyration and piezo-optics caused by twisting and bending,” Crystallogr. Rep. 42, 1011–1013 (1997).

Fiz. Tverd. Tela (1)

O. S. Kushnir and L. O. Lokot, “The peculiarities of the optical response of dielectric crystals with incommensurate phases,” Fiz. Tverd. Tela 43, 786–790 (2001).

Fiz. Tverd. Tela. (1)

V. S. Lvov, “Optical activity of deformed crystals,” Fiz. Tverd. Tela. 9, 1273–1275 (1967).

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C. G. Grentzelou and H. G. Georgiadis, “Uniqueness for plane crack problems in dipolar gradient elasticity and in couple-stress elasticity,” Int. J. Solids Struct. 42, 6226–6244 (2005).
[CrossRef]

V. A. Lubarda, “The effects of couple stresses on dislocation strain energy,” Int. J. Solids Struct. 40, 3807–3826 (2003).
[CrossRef]

F. Yang, A. C. M. Chong, D. C. C. Lam, and P. Tong, “Couple stress based strain gradient theory for elasticity,” Int. J. Solids Struct. 39, 2731–2743 (2002).
[CrossRef]

J. Appl. Phys. (1)

W. T. Lee, E. K. H. Salje, and U. Bismayer, “Domain-wall structure and domain-wall strain,” J. Appl. Phys. 93, 9890–9897 (2003).
[CrossRef]

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

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).

J. Phys.: Condens. Matter. (1)

O. S. Kushnir, “Spatial dispersion in incommensurately modulated insulators,” J. Phys.: Condens. Matter. 16, 1245–1267 (2004).
[CrossRef]

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]

Kristallografiya (3)

O. G. Vlokh and T. D. Krushel’nitskaya, “Axial fourth-rank tensors and quadratic electro-gyration,” Kristallografiya 15, 587–589 (1970).

I. S. Zheludev, “Axial tensors of the third rank and the physical effects they describe,” Kristallografiya 9, 501–505 (1964). [Sov. Phys. Crystallogr. 9, 418–422 (1965)].

B. V. Bokut, A. N. Serdyukov, F. I. Fedorov, and N. A. Khilo, “On the boundary conditions in the electrodynamics of the optically active media,” Kristallografiya 18, 227–233 (1973).

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F. J. D. Arago, “Memoire sur une modifcation remarquable qu’eprouvent les rayons lumineux dans leur passage a travers certains corps diaphanes et sur quelques autres nouveaux phenomenes d’optique,” Memoires de la classe des sciences math. et phys. de l’Institut Imperial de France 1, 93–134 (1811).

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A. Fresnel, “Memoire sur la double refraction que les rayons lumineux eprouvent en traversant les aiguilles de cristal de roche suivant des directions paralleles a l’axe,” Oeuvres 1, 731–751 (1822).

Opt. Photon. News (1)

O. G. Vlokh and R. O. Vlokh, “The electrogyration effect,” Opt. Photon. News 20, 34–39 (2009).
[CrossRef]

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K. Aizu, “Ferroelectric transformations of tensorial properties in regular ferroelectrics,” Phys. Rev. 133, A1350–A1359 (1964).
[CrossRef]

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[CrossRef]

F. Gray, “The optical activity of liquids and gases,” Phys. Rev. 7, 472–488 (1916).
[CrossRef]

Phys. Z. (1)

M. Born, “Uber die natufrliche optische Aktivitat von Flussigkeiten und Gasen,” Phys. Z. 16, 251–258 (1915).

Pisma ZhETF. (1)

O. G. Vlokh, “Electrogyration effects in quartz crystals,” Pisma ZhETF. 13, 118–121 (1971). [Sov. Phys. Pisma. 13, 81–83 (1971)].

Sov. Phys. Usp. (3)

V. L. Ginzburg and V. M. Agranovich, “Crystal optics with allowance for spatial dispersion; exciton theory. I,” Sov. Phys. Usp. 5, 323–346 (1962).
[CrossRef]

V. L. Ginzburg and V. M. Agranovich, “Crystal optics with allowance for spatial dispersion; exciton theory. II,” Sov. Phys. Usp. 5, 649–660 (1963).
[CrossRef]

A. K. Tagantsev, “Pyroelectric, piezoelectric, flexoelectric, and thermal polarization effects in ionic crystals,” Sov. Phys. Usp. 30, 588–603 (1987).
[CrossRef]

Ukr. Fiz. Zhurn. (3)

O. G. Vlokh, “Electrooptical activity of quartz crystals,” Ukr. Fiz. Zhurn. 15, 758–762. (1970). [Sov. Phys. Ukr. Fiz. Zhurn. 15, 771–775 (1970)].

R. O. Vlokh, Y. A. Pyatak, and I. P. Skab, “Torsion-gyration effect,” Ukr. Fiz. Zhurn. 34, 845–846 (1989).

O. G. Vlokh and V. B. Kobylyansky, “Effect of parameters of gyrotropic crystals on the light polarization character,” Ukr. Fiz. Zhurn. 19, 1129–1135 (1974).

Ukr. J. Phys. Opt. (1)

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]

Zh. Prikl. Spektrosk. (1)

B. V. Bokut and A. N. Serdyukov, “On the theory of optical activity of the inhomogeneous media,” Zh. Prikl. Spektrosk. 20, 677–681 (1974).

Other (11)

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

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

T. S. Narasimhamurty, Photoelastic and Electro-optic Properties of Crystals (Plenum, 1981).

A. F. Konstantinova, B. N. Grechushnikov, B. V. Bokut, and E. G. Valyashko, Optical Properties of Crystals (Navuka i Tekhnika, 1995).

http://www.irystyle.com/elent/sbimo.htm .

W. G. Jung, Op Amp Applications Handbook (Elsevier, 2005).

E. Hecht, Optics (Addison–Wesley, 2002).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Yu. I. Sirotin and M. P. Shaskolskaya, Fundamentals of Crystal Physics (Mir, 1982).

J. F. Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices (Oxford University, 2000).

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Figures (4)

Fig. 1.
Fig. 1.

Experimental setup for measuring optical activity appearing under torsion stresses (1) laser, (2) objective lens, (3, 6) polarizer and analyzer with rotation units, (4) sample placed into an apparatus 5 for applying torsion stresses, and (7) photodiode.

Fig. 2.
Fig. 2.

Sample of NaBi(MoO4)2 crystals: 1–6 are points through which laser beams propagate parallel to the Z axis.

Fig. 3.
Fig. 3.

Distribution of residual linear birefringence in the XY cross section of NaBi(MoO4)2 crystals. Circles correspond to light beams referred to in Fig. 2, while diameters of these circles are equal to those of the beams.

Fig. 4.
Fig. 4.

Specific rotation of polarization plane in NaBi(MoO4)2 crystals (at λ=532nm) versus torsion moment as measured for the points (a) No. 1, (b) No. 2, (c) No. 3, (d) No. 4, (e) No. 5, and (f) No. 6. Data points correspond to experiment and lines to linear fitting.

Tables (2)

Tables Icon

Table 1. Coordinates of Points in the Incident XY Face of a Sample, Through Which the Laser Beams Propagate, and the Appropriate Values of Residual Linear Birefringence

Tables Icon

Table 2. Fitting Parameters Describing Dependences of Specific Polarization Plane Rotation on Torsion Moment

Equations (31)

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

Di(k,ω)=εij(ω,k)Ej(k,ω),
Di(r,t)=tdtdrε^ij(tt,rr)Ej(r,t)
εij(ω,k)=0dτdRe(kRωτ)ε^ij(τ,R).
εij(ω,k)=εij0(ω)+iδijlglnkn+τijntknkt+,
εij(ω,r,r)=εij(ω,r+a,r+a),
εij(ω,r,r)=bfb(ω,rr)ei2πbr,
Di(ω,k)=εijb=0(ω,k)Ej(ω,k)+b0εijb(ω,k)Ej(ω,k+2πb).
Di=εij0(ω)Ej+αijkrotEj=εij0(ω)Ej+αijkEj/Xk,
Di=εij0(ω)Ej+iαijk[kkBj]=εij0(ω)Ej+αijkEj/Xk.
Δgln=γlnkEk,
Δgln=ϑlnkmσkm,
Δgln=βlnkmvσkm/Xv,
Δgln=ΩlnimMim,
Di=εijEj+αijkEj/xk+(χijkEj)/xk,
σkm=σμ=2MZπR4(Xδ4μYδ5μ).
ΔBij=BijBij0=πijkmσkm,
B110X2+B110Y2+B330Z2+2(π3232σ32+π3231σ31)YZ+2(π3232σ31π3231σ32)XZ=1.
B110X2+B110Y2=1,
tan2γ=tan2αcosΔ2κ1+κ2sinΔ(1κ21+κ2)2+(2κ1+κ2)2cosΔ+2κ1+κ2tan2αsinΔ,
tan2γ=tan2αcosΔsinΔcosΔ+tan2αsinΔ=tan(2αΔ).
γ=πdλ(n2n1)=πdg33λno=ρd,
I(γ)=I0(sin2ψ+a),
I(γ)=C0+C1ψ+C2ψ2.
g33=β33321σ32/X+β33312σ31/Y.
g33=4β33321MZ/πR4.
β33321=14λnoR4ρMZ.
σkmΩ=CkmpteptΩ+ΘkmptνeptΩXν,
σkmΩ=CkmpteptΩ+iΘkmptνmνeptΩ,
σkm=Ckmptept+ΘkmptνeptXν,
Δgln=ϑlnkmσkm=ϑlnkmCkmptept+ϑlnkmΘkmptνeptXν.
Δgln=ϑlnptept+βlnptreptXr.

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