Abstract

We have shown that a high-accuracy torsion method recently developed by the authors for measuring piezo-optic coefficients allows determining not only the absolute value of the coefficients but also their sign. The techniques and experimental procedures used for determination of the sign are described in detail and proven based on studies of α-BaB2O4 and LiNbO3 crystals. The piezo-optic coefficients are determined for both crystals, and a combination of the corresponding photoelastic coefficients is determined for the case of α-BaB2O4 crystals.

© 2011 Optical Society of America

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  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]
  2. B. Mytsyk, “Methods for the studies of the piezo-optical effect in crystals and the analysis of experimental data. I. Methodology for the studies of piezo-optical effect,” Ukr. J. Phys. Opt. 4, 1–26 (2003).
    [CrossRef]
  3. A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, B. G. Mytsyk, A. V. Kityk, and W. Schranz, “Two-fold interferometric measurements of piezo-optic constants: application to β-BaB2O4 crystals,” Opt. Laser Technol. 37, 319–328 (2005).
    [CrossRef]
  4. Yu. Vasylkiv, O. Kvasnyuk, O. Krupych, O. Mys, O. Maksymuk, and R. Vlokh, “Reconstruction of 3D stress fields basing on piezooptic experiment,” Ukr. J. Phys. Opt. 10, 22–37 (2009).
    [CrossRef]
  5. “Standard test method for measurement of glass stress—optical coefficient,” ASTM Standard C770-98(2008), ASTM International, West Conshohocken, Pa., 2008, doi:10.1520/C0770-98R08.
  6. R. W. Dixon and M. G. Cohen, “A new technique for measuring magnitudes of photoelastic tensor and its application to lithium niobate,” Appl. Phys. Lett. 8, 205–207 (1966).
    [CrossRef]
  7. R. W. Dixon, “Photoelastic properties of selected materials and their relevance for application to acoustic light modulators and scanners,” J. Appl. Phys. 38, 5149–5153 (1967).
    [CrossRef]
  8. T. S. Narasimhamurty, Photoelastic and Electrooptic Properties of Crystals (Plenum, 1981).
  9. R. O. Vlokh, Y. A. Pyatak, and I. P. Skab, “The elasto-optic effect in LiNbO3 crystals under the torsion,” Fiz. Tverd. Tela 33, 2467–2470 (1991).
  10. 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]
  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. S. G. Lekhnitskii, Torsion of Anisotropic and Inhomogeneous Rods (Nauka, 1971).
  13. S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Body (Nauka, 1971).
  14. Yu. I. Sirotin and M. P. Shaskolskaya, Fundamentals of Crystal Physics (Nauka, 1979).
  15. I. Martynyuk-Lototska, O. Mys, T. Dudok, V. Adamiv, Ye. Smirnov, and R. Vlokh, “Acousto-optic interaction in α-BaB2O4 and Li2B4O7 crystals,” Appl. Opt. 47, 3446–3454(2008).
    [CrossRef] [PubMed]
  16. K. Kato, “Second-harmonic generation to 2048 Å in BaBa2O4,” IEEE J. Quantum Electron. 22, 1013–1014(1986).
    [CrossRef]
  17. Y. Ishida and T. Yajima, “Characteristics of a new-type SHG crystal β-BaB2O4 in the femtosecond region,” Opt. Commun. 62, 197–200 (1987).
    [CrossRef]
  18. L. K. Cheng, W. Bosenberg, and C. L. Tang, “Broadly tunable optical parametric oscillation in β-BaB2O4,” Appl. Phys. Lett. 53, 175–177 (1988).
    [CrossRef]
  19. C. T. Chen, B. C. Wu, A. D. Jiang, and G. M. You, “A new ultraviolet SHG crystal β-BaB2O4,” Sci. Sin. Ser. A B28, 235–243 (1985).
  20. H. Yoshida, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, T. Kamimura, and K. Yoshida, “Dependences of laser-induced bulk damage threshold and crack patterns in several nonlinear crystals on irradiation direction,” Jpn. J. Appl. Phys. 45, 766–769 (2006).
    [CrossRef]
  21. I. Skab, Yu. Vasylkiv, V. Savaryn, and R. Vlokh, “Relations for optical indicatrix parameters at the crystals torsion,” Ukr. J. Phys. Opt. 11, 193–240 (2010).
    [CrossRef]
  22. R. Vlokh, Y. Pyatak, and I. Skab, “On the method of orientation of middle-systems crystals,” Ukr. Fiz. Zh. 37, 207–210(1992).
  23. I. Skab, Yu. Vasylkiv, I. Smaga, V. Savaryn, and R. Vlokh, “On the method for measuring piezooptic coefficients π25 and π14in the crystals belonging to point symmetry groups 3 and 3¯,” Ukr. J. Phys. Opt. 12, 28–35 (2011).
    [CrossRef]
  24. B. G. Mytsyk, A. S. Andrushchak, N. M. Demyanyshyn, Y. P. Kost’, A. V. Kityk, P. Mandracci, and W. Schranz, “Piezo-optic coefficients of MgO-doped LiNbO3 crystals,” Appl. Opt. 48, 1904–1911 (2009).
    [CrossRef] [PubMed]
  25. B. Mytsyk, “Methods for the studies of piezooptic effect in crystals and analysis of the experimental data. II. Analysis of the experimental data,” Ukr. J. Phys. Opt. 4, 105–118(2003).
    [CrossRef]
  26. B. G. Mytsyk and A. S. Andrushchak, “The ambiguity of crystal physics coordinate system choice at study of piezooptic effect on the example of LiNbO3 crystals,” Kristallografiya 35, 1574–1575 (1990).
  27. B. G. Mytsyk and N. M. Dem’yanyshyn, “Piezo-optic surfaces of lithium niobate crystals,” Crystallogr. Rep. 51, 653–660 (2006).
    [CrossRef]

2011 (3)

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).
[CrossRef]

I. Skab, Yu. Vasylkiv, I. Smaga, V. Savaryn, and R. Vlokh, “On the method for measuring piezooptic coefficients π25 and π14in the crystals belonging to point symmetry groups 3 and 3¯,” Ukr. J. Phys. Opt. 12, 28–35 (2011).
[CrossRef]

2010 (1)

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

2009 (2)

Yu. Vasylkiv, O. Kvasnyuk, O. Krupych, O. Mys, O. Maksymuk, and R. Vlokh, “Reconstruction of 3D stress fields basing on piezooptic experiment,” Ukr. J. Phys. Opt. 10, 22–37 (2009).
[CrossRef]

B. G. Mytsyk, A. S. Andrushchak, N. M. Demyanyshyn, Y. P. Kost’, A. V. Kityk, P. Mandracci, and W. Schranz, “Piezo-optic coefficients of MgO-doped LiNbO3 crystals,” Appl. Opt. 48, 1904–1911 (2009).
[CrossRef] [PubMed]

2008 (1)

2006 (2)

H. Yoshida, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, T. Kamimura, and K. Yoshida, “Dependences of laser-induced bulk damage threshold and crack patterns in several nonlinear crystals on irradiation direction,” Jpn. J. Appl. Phys. 45, 766–769 (2006).
[CrossRef]

B. G. Mytsyk and N. M. Dem’yanyshyn, “Piezo-optic surfaces of lithium niobate crystals,” Crystallogr. Rep. 51, 653–660 (2006).
[CrossRef]

2005 (1)

A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, B. G. Mytsyk, A. V. Kityk, and W. Schranz, “Two-fold interferometric measurements of piezo-optic constants: application to β-BaB2O4 crystals,” Opt. Laser Technol. 37, 319–328 (2005).
[CrossRef]

2003 (2)

B. Mytsyk, “Methods for the studies of the piezo-optical effect in crystals and the analysis of experimental data. I. Methodology for the studies of piezo-optical effect,” Ukr. J. Phys. Opt. 4, 1–26 (2003).
[CrossRef]

B. Mytsyk, “Methods for the studies of piezooptic effect in crystals and analysis of the experimental data. II. Analysis of the experimental data,” Ukr. J. Phys. Opt. 4, 105–118(2003).
[CrossRef]

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]

1992 (1)

R. Vlokh, Y. Pyatak, and I. Skab, “On the method of orientation of middle-systems crystals,” Ukr. Fiz. Zh. 37, 207–210(1992).

1991 (1)

R. O. Vlokh, Y. A. Pyatak, and I. P. Skab, “The elasto-optic effect in LiNbO3 crystals under the torsion,” Fiz. Tverd. Tela 33, 2467–2470 (1991).

1990 (1)

B. G. Mytsyk and A. S. Andrushchak, “The ambiguity of crystal physics coordinate system choice at study of piezooptic effect on the example of LiNbO3 crystals,” Kristallografiya 35, 1574–1575 (1990).

1988 (1)

L. K. Cheng, W. Bosenberg, and C. L. Tang, “Broadly tunable optical parametric oscillation in β-BaB2O4,” Appl. Phys. Lett. 53, 175–177 (1988).
[CrossRef]

1987 (1)

Y. Ishida and T. Yajima, “Characteristics of a new-type SHG crystal β-BaB2O4 in the femtosecond region,” Opt. Commun. 62, 197–200 (1987).
[CrossRef]

1986 (1)

K. Kato, “Second-harmonic generation to 2048 Å in BaBa2O4,” IEEE J. Quantum Electron. 22, 1013–1014(1986).
[CrossRef]

1985 (1)

C. T. Chen, B. C. Wu, A. D. Jiang, and G. M. You, “A new ultraviolet SHG crystal β-BaB2O4,” Sci. Sin. Ser. A B28, 235–243 (1985).

1967 (1)

R. W. Dixon, “Photoelastic properties of selected materials and their relevance for application to acoustic light modulators and scanners,” J. Appl. Phys. 38, 5149–5153 (1967).
[CrossRef]

1966 (1)

R. W. Dixon and M. G. Cohen, “A new technique for measuring magnitudes of photoelastic tensor and its application to lithium niobate,” Appl. Phys. Lett. 8, 205–207 (1966).
[CrossRef]

Adamiv, V.

Andrushchak, A. S.

B. G. Mytsyk, A. S. Andrushchak, N. M. Demyanyshyn, Y. P. Kost’, A. V. Kityk, P. Mandracci, and W. Schranz, “Piezo-optic coefficients of MgO-doped LiNbO3 crystals,” Appl. Opt. 48, 1904–1911 (2009).
[CrossRef] [PubMed]

A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, B. G. Mytsyk, A. V. Kityk, and W. Schranz, “Two-fold interferometric measurements of piezo-optic constants: application to β-BaB2O4 crystals,” Opt. Laser Technol. 37, 319–328 (2005).
[CrossRef]

B. G. Mytsyk and A. S. Andrushchak, “The ambiguity of crystal physics coordinate system choice at study of piezooptic effect on the example of LiNbO3 crystals,” Kristallografiya 35, 1574–1575 (1990).

Bobitski, Ya. V.

A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, B. G. Mytsyk, A. V. Kityk, and W. Schranz, “Two-fold interferometric measurements of piezo-optic constants: application to β-BaB2O4 crystals,” Opt. Laser Technol. 37, 319–328 (2005).
[CrossRef]

Bosenberg, W.

L. K. Cheng, W. Bosenberg, and C. L. Tang, “Broadly tunable optical parametric oscillation in β-BaB2O4,” Appl. Phys. Lett. 53, 175–177 (1988).
[CrossRef]

Chen, C. T.

C. T. Chen, B. C. Wu, A. D. Jiang, and G. M. You, “A new ultraviolet SHG crystal β-BaB2O4,” Sci. Sin. Ser. A B28, 235–243 (1985).

Cheng, L. K.

L. K. Cheng, W. Bosenberg, and C. L. Tang, “Broadly tunable optical parametric oscillation in β-BaB2O4,” Appl. Phys. Lett. 53, 175–177 (1988).
[CrossRef]

Cohen, M. G.

R. W. Dixon and M. G. Cohen, “A new technique for measuring magnitudes of photoelastic tensor and its application to lithium niobate,” Appl. Phys. Lett. 8, 205–207 (1966).
[CrossRef]

Dem’yanyshyn, N. M.

B. G. Mytsyk and N. M. Dem’yanyshyn, “Piezo-optic surfaces of lithium niobate crystals,” Crystallogr. Rep. 51, 653–660 (2006).
[CrossRef]

Demyanyshyn, N. M.

Dixon, R. W.

R. W. Dixon, “Photoelastic properties of selected materials and their relevance for application to acoustic light modulators and scanners,” J. Appl. Phys. 38, 5149–5153 (1967).
[CrossRef]

R. W. Dixon and M. G. Cohen, “A new technique for measuring magnitudes of photoelastic tensor and its application to lithium niobate,” Appl. Phys. Lett. 8, 205–207 (1966).
[CrossRef]

Dudok, T.

Fujita, H.

H. Yoshida, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, T. Kamimura, and K. Yoshida, “Dependences of laser-induced bulk damage threshold and crack patterns in several nonlinear crystals on irradiation direction,” Jpn. J. Appl. Phys. 45, 766–769 (2006).
[CrossRef]

Ishida, Y.

Y. Ishida and T. Yajima, “Characteristics of a new-type SHG crystal β-BaB2O4 in the femtosecond region,” Opt. Commun. 62, 197–200 (1987).
[CrossRef]

Jiang, A. D.

C. T. Chen, B. C. Wu, A. D. Jiang, and G. M. You, “A new ultraviolet SHG crystal β-BaB2O4,” Sci. Sin. Ser. A B28, 235–243 (1985).

Kaidan, M. V.

A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, B. G. Mytsyk, A. V. Kityk, and W. Schranz, “Two-fold interferometric measurements of piezo-optic constants: application to β-BaB2O4 crystals,” Opt. Laser Technol. 37, 319–328 (2005).
[CrossRef]

Kamimura, T.

H. Yoshida, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, T. Kamimura, and K. Yoshida, “Dependences of laser-induced bulk damage threshold and crack patterns in several nonlinear crystals on irradiation direction,” Jpn. J. Appl. Phys. 45, 766–769 (2006).
[CrossRef]

Kato, K.

K. Kato, “Second-harmonic generation to 2048 Å in BaBa2O4,” IEEE J. Quantum Electron. 22, 1013–1014(1986).
[CrossRef]

Kityk, A. V.

B. G. Mytsyk, A. S. Andrushchak, N. M. Demyanyshyn, Y. P. Kost’, A. V. Kityk, P. Mandracci, and W. Schranz, “Piezo-optic coefficients of MgO-doped LiNbO3 crystals,” Appl. Opt. 48, 1904–1911 (2009).
[CrossRef] [PubMed]

A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, B. G. Mytsyk, A. V. Kityk, and W. Schranz, “Two-fold interferometric measurements of piezo-optic constants: application to β-BaB2O4 crystals,” Opt. Laser Technol. 37, 319–328 (2005).
[CrossRef]

Kost’, Y. P.

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.

Yu. Vasylkiv, O. Kvasnyuk, O. Krupych, O. Mys, O. Maksymuk, and R. Vlokh, “Reconstruction of 3D stress fields basing on piezooptic experiment,” Ukr. J. Phys. Opt. 10, 22–37 (2009).
[CrossRef]

Kvasnyuk, O.

Yu. Vasylkiv, O. Kvasnyuk, O. Krupych, O. Mys, O. Maksymuk, and R. Vlokh, “Reconstruction of 3D stress fields basing on piezooptic experiment,” Ukr. J. Phys. Opt. 10, 22–37 (2009).
[CrossRef]

Lekhnitskii, S. G.

S. G. Lekhnitskii, Torsion of Anisotropic and Inhomogeneous Rods (Nauka, 1971).

S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Body (Nauka, 1971).

Maksymuk, O.

Yu. Vasylkiv, O. Kvasnyuk, O. Krupych, O. Mys, O. Maksymuk, and R. Vlokh, “Reconstruction of 3D stress fields basing on piezooptic experiment,” Ukr. J. Phys. Opt. 10, 22–37 (2009).
[CrossRef]

Mandracci, P.

Martynyuk-Lototska, I.

Mys, O.

Yu. Vasylkiv, O. Kvasnyuk, O. Krupych, O. Mys, O. Maksymuk, and R. Vlokh, “Reconstruction of 3D stress fields basing on piezooptic experiment,” Ukr. J. Phys. Opt. 10, 22–37 (2009).
[CrossRef]

I. Martynyuk-Lototska, O. Mys, T. Dudok, V. Adamiv, Ye. Smirnov, and R. Vlokh, “Acousto-optic interaction in α-BaB2O4 and Li2B4O7 crystals,” Appl. Opt. 47, 3446–3454(2008).
[CrossRef] [PubMed]

Mytsyk, B.

B. Mytsyk, “Methods for the studies of the piezo-optical effect in crystals and the analysis of experimental data. I. Methodology for the studies of piezo-optical effect,” Ukr. J. Phys. Opt. 4, 1–26 (2003).
[CrossRef]

B. Mytsyk, “Methods for the studies of piezooptic effect in crystals and analysis of the experimental data. II. Analysis of the experimental data,” Ukr. J. Phys. Opt. 4, 105–118(2003).
[CrossRef]

Mytsyk, B. G.

B. G. Mytsyk, A. S. Andrushchak, N. M. Demyanyshyn, Y. P. Kost’, A. V. Kityk, P. Mandracci, and W. Schranz, “Piezo-optic coefficients of MgO-doped LiNbO3 crystals,” Appl. Opt. 48, 1904–1911 (2009).
[CrossRef] [PubMed]

B. G. Mytsyk and N. M. Dem’yanyshyn, “Piezo-optic surfaces of lithium niobate crystals,” Crystallogr. Rep. 51, 653–660 (2006).
[CrossRef]

A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, B. G. Mytsyk, A. V. Kityk, and W. Schranz, “Two-fold interferometric measurements of piezo-optic constants: application to β-BaB2O4 crystals,” Opt. Laser Technol. 37, 319–328 (2005).
[CrossRef]

B. G. Mytsyk and A. S. Andrushchak, “The ambiguity of crystal physics coordinate system choice at study of piezooptic effect on the example of LiNbO3 crystals,” Kristallografiya 35, 1574–1575 (1990).

Nakatsuka, M.

H. Yoshida, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, T. Kamimura, and K. Yoshida, “Dependences of laser-induced bulk damage threshold and crack patterns in several nonlinear crystals on irradiation direction,” Jpn. J. Appl. Phys. 45, 766–769 (2006).
[CrossRef]

Narasimhamurty, T. S.

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

Pyatak, Y.

R. Vlokh, Y. Pyatak, and I. Skab, “On the method of orientation of middle-systems crystals,” Ukr. Fiz. Zh. 37, 207–210(1992).

Pyatak, Y. A.

R. O. Vlokh, Y. A. Pyatak, and I. P. Skab, “The elasto-optic effect in LiNbO3 crystals under the torsion,” Fiz. Tverd. Tela 33, 2467–2470 (1991).

Sasaki, T.

H. Yoshida, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, T. Kamimura, and K. Yoshida, “Dependences of laser-induced bulk damage threshold and crack patterns in several nonlinear crystals on irradiation direction,” Jpn. J. Appl. Phys. 45, 766–769 (2006).
[CrossRef]

Savaryn, V.

I. Skab, Yu. Vasylkiv, I. Smaga, V. Savaryn, and R. Vlokh, “On the method for measuring piezooptic coefficients π25 and π14in 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, 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 at the crystals torsion,” Ukr. J. Phys. Opt. 11, 193–240 (2010).
[CrossRef]

Schranz, W.

B. G. Mytsyk, A. S. Andrushchak, N. M. Demyanyshyn, Y. P. Kost’, A. V. Kityk, P. Mandracci, and W. Schranz, “Piezo-optic coefficients of MgO-doped LiNbO3 crystals,” Appl. Opt. 48, 1904–1911 (2009).
[CrossRef] [PubMed]

A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, B. G. Mytsyk, A. V. Kityk, and W. Schranz, “Two-fold interferometric measurements of piezo-optic constants: application to β-BaB2O4 crystals,” Opt. Laser Technol. 37, 319–328 (2005).
[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, 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 π14in 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, “Relations for optical indicatrix parameters at the crystals 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]

R. Vlokh, Y. Pyatak, and I. Skab, “On the method of orientation of middle-systems crystals,” Ukr. Fiz. Zh. 37, 207–210(1992).

Skab, I. P.

R. O. Vlokh, Y. A. Pyatak, and I. P. Skab, “The elasto-optic effect in LiNbO3 crystals under the torsion,” Fiz. Tverd. Tela 33, 2467–2470 (1991).

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 π14in the crystals belonging to point symmetry groups 3 and 3¯,” Ukr. J. Phys. Opt. 12, 28–35 (2011).
[CrossRef]

Smirnov, Ye.

Tang, C. L.

L. K. Cheng, W. Bosenberg, and C. L. Tang, “Broadly tunable optical parametric oscillation in β-BaB2O4,” Appl. Phys. Lett. 53, 175–177 (1988).
[CrossRef]

Vasylkiv, Yu.

I. Skab, Yu. Vasylkiv, I. Smaga, V. Savaryn, and R. Vlokh, “On the method for measuring piezooptic coefficients π25 and π14in 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, “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 at the crystals torsion,” Ukr. J. Phys. Opt. 11, 193–240 (2010).
[CrossRef]

Yu. Vasylkiv, O. Kvasnyuk, O. Krupych, O. Mys, O. Maksymuk, and R. Vlokh, “Reconstruction of 3D stress fields basing on piezooptic experiment,” Ukr. J. Phys. Opt. 10, 22–37 (2009).
[CrossRef]

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, 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 π14in 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, “Relations for optical indicatrix parameters at the crystals torsion,” Ukr. J. Phys. Opt. 11, 193–240 (2010).
[CrossRef]

Yu. Vasylkiv, O. Kvasnyuk, O. Krupych, O. Mys, O. Maksymuk, and R. Vlokh, “Reconstruction of 3D stress fields basing on piezooptic experiment,” Ukr. J. Phys. Opt. 10, 22–37 (2009).
[CrossRef]

I. Martynyuk-Lototska, O. Mys, T. Dudok, V. Adamiv, Ye. Smirnov, and R. Vlokh, “Acousto-optic interaction in α-BaB2O4 and Li2B4O7 crystals,” Appl. Opt. 47, 3446–3454(2008).
[CrossRef] [PubMed]

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]

R. Vlokh, Y. Pyatak, and I. Skab, “On the method of orientation of middle-systems crystals,” Ukr. Fiz. Zh. 37, 207–210(1992).

Vlokh, R. O.

R. O. Vlokh, Y. A. Pyatak, and I. P. Skab, “The elasto-optic effect in LiNbO3 crystals under the torsion,” Fiz. Tverd. Tela 33, 2467–2470 (1991).

Wu, B. C.

C. T. Chen, B. C. Wu, A. D. Jiang, and G. M. You, “A new ultraviolet SHG crystal β-BaB2O4,” Sci. Sin. Ser. A B28, 235–243 (1985).

Yajima, T.

Y. Ishida and T. Yajima, “Characteristics of a new-type SHG crystal β-BaB2O4 in the femtosecond region,” Opt. Commun. 62, 197–200 (1987).
[CrossRef]

Yoshida, H.

H. Yoshida, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, T. Kamimura, and K. Yoshida, “Dependences of laser-induced bulk damage threshold and crack patterns in several nonlinear crystals on irradiation direction,” Jpn. J. Appl. Phys. 45, 766–769 (2006).
[CrossRef]

Yoshida, K.

H. Yoshida, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, T. Kamimura, and K. Yoshida, “Dependences of laser-induced bulk damage threshold and crack patterns in several nonlinear crystals on irradiation direction,” Jpn. J. Appl. Phys. 45, 766–769 (2006).
[CrossRef]

Yoshimura, M.

H. Yoshida, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, T. Kamimura, and K. Yoshida, “Dependences of laser-induced bulk damage threshold and crack patterns in several nonlinear crystals on irradiation direction,” Jpn. J. Appl. Phys. 45, 766–769 (2006).
[CrossRef]

You, G. M.

C. T. Chen, B. C. Wu, A. D. Jiang, and G. M. You, “A new ultraviolet SHG crystal β-BaB2O4,” Sci. Sin. Ser. A B28, 235–243 (1985).

Appl. Opt. (2)

Appl. Phys. Lett. (2)

L. K. Cheng, W. Bosenberg, and C. L. Tang, “Broadly tunable optical parametric oscillation in β-BaB2O4,” Appl. Phys. Lett. 53, 175–177 (1988).
[CrossRef]

R. W. Dixon and M. G. Cohen, “A new technique for measuring magnitudes of photoelastic tensor and its application to lithium niobate,” Appl. Phys. Lett. 8, 205–207 (1966).
[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)

B. G. Mytsyk and N. M. Dem’yanyshyn, “Piezo-optic surfaces of lithium niobate crystals,” Crystallogr. Rep. 51, 653–660 (2006).
[CrossRef]

Fiz. Tverd. Tela (1)

R. O. Vlokh, Y. A. Pyatak, and I. P. Skab, “The elasto-optic effect in LiNbO3 crystals under the torsion,” Fiz. Tverd. Tela 33, 2467–2470 (1991).

IEEE J. Quantum Electron. (1)

K. Kato, “Second-harmonic generation to 2048 Å in BaBa2O4,” IEEE J. Quantum Electron. 22, 1013–1014(1986).
[CrossRef]

J. Appl. Phys. (1)

R. W. Dixon, “Photoelastic properties of selected materials and their relevance for application to acoustic light modulators and scanners,” J. Appl. Phys. 38, 5149–5153 (1967).
[CrossRef]

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

Jpn. J. Appl. Phys. (2)

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]

H. Yoshida, H. Fujita, M. Nakatsuka, M. Yoshimura, T. Sasaki, T. Kamimura, and K. Yoshida, “Dependences of laser-induced bulk damage threshold and crack patterns in several nonlinear crystals on irradiation direction,” Jpn. J. Appl. Phys. 45, 766–769 (2006).
[CrossRef]

Kristallografiya (1)

B. G. Mytsyk and A. S. Andrushchak, “The ambiguity of crystal physics coordinate system choice at study of piezooptic effect on the example of LiNbO3 crystals,” Kristallografiya 35, 1574–1575 (1990).

Opt. Commun. (1)

Y. Ishida and T. Yajima, “Characteristics of a new-type SHG crystal β-BaB2O4 in the femtosecond region,” Opt. Commun. 62, 197–200 (1987).
[CrossRef]

Opt. Laser Technol. (1)

A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, B. G. Mytsyk, A. V. Kityk, and W. Schranz, “Two-fold interferometric measurements of piezo-optic constants: application to β-BaB2O4 crystals,” Opt. Laser Technol. 37, 319–328 (2005).
[CrossRef]

Sci. Sin. Ser. A (1)

C. T. Chen, B. C. Wu, A. D. Jiang, and G. M. You, “A new ultraviolet SHG crystal β-BaB2O4,” Sci. Sin. Ser. A B28, 235–243 (1985).

Ukr. Fiz. Zh. (1)

R. Vlokh, Y. Pyatak, and I. Skab, “On the method of orientation of middle-systems crystals,” Ukr. Fiz. Zh. 37, 207–210(1992).

Ukr. J. Phys. Opt. (5)

I. Skab, Yu. Vasylkiv, I. Smaga, V. Savaryn, and R. Vlokh, “On the method for measuring piezooptic coefficients π25 and π14in 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, “Relations for optical indicatrix parameters at the crystals torsion,” Ukr. J. Phys. Opt. 11, 193–240 (2010).
[CrossRef]

B. Mytsyk, “Methods for the studies of piezooptic effect in crystals and analysis of the experimental data. II. Analysis of the experimental data,” Ukr. J. Phys. Opt. 4, 105–118(2003).
[CrossRef]

Yu. Vasylkiv, O. Kvasnyuk, O. Krupych, O. Mys, O. Maksymuk, and R. Vlokh, “Reconstruction of 3D stress fields basing on piezooptic experiment,” Ukr. J. Phys. Opt. 10, 22–37 (2009).
[CrossRef]

B. Mytsyk, “Methods for the studies of the piezo-optical effect in crystals and the analysis of experimental data. I. Methodology for the studies of piezo-optical effect,” Ukr. J. Phys. Opt. 4, 1–26 (2003).
[CrossRef]

Other (5)

“Standard test method for measurement of glass stress—optical coefficient,” ASTM Standard C770-98(2008), ASTM International, West Conshohocken, Pa., 2008, doi:10.1520/C0770-98R08.

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

S. G. Lekhnitskii, Torsion of Anisotropic and Inhomogeneous Rods (Nauka, 1971).

S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Body (Nauka, 1971).

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

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Figures (6)

Fig. 1
Fig. 1

Distributions of angle of (a) optical indicatrix rotation and (b) birefringence in the X Y cross section of α - BaB 2 O 4 crystals, induced by the torsion moment | M z | = 0.058 N × m at the light wavelength of λ = 632.8 nm .

Fig. 2
Fig. 2

(a) Dependences of birefringence induced by the torsion moment | M z | = 0.058 N × m upon distance ρ at different angles φ and (b) the respective dependence of piezo-optic coefficients π 14 on angle φ in α - BaB 2 O 4 crystals ( λ = 632.8 nm ).

Fig. 3
Fig. 3

Experimental distribution of birefringence induced by the torsion moment | M z | = 63.77 × 10 3 N × m in the X Y plane of LiNbO 3 crystals ( λ = 632.8 nm ) [11].

Fig. 4
Fig. 4

Fresnel ellipsoid for optically biaxial crystals and a right-handed Cartesian coordinate system (OA1 and OA2 are the optical axes).

Fig. 5
Fig. 5

Orientations of samples, torsion moments and the changes in the conoscopic fringes observed for the (a)  α - BaB 2 O 4 and (b)  LiNbO 3 crystals (OA, outlets of the optical axes).

Fig. 6
Fig. 6

Schematic representation of shear strains appearing at the coordinates ( X c , 0 ) and ( X c , 0 ) in the LiNbO 3 crystals when the torsion moment is applied as shown in Fig. 5.

Equations (23)

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Δ B λ = B λ B λ 0 = π λ μ σ μ ,
σ μ = 2 M z π R 4 ( X δ 4 μ Y δ 5 μ ) ,
σ 4 = 2 M z π R 4 X ,
σ 5 = 2 M z π R 4 Y ,
σ 1 σ 2 σ 3 σ 4 σ 5 σ 6 Δ B 1 π 11 π 12 π 13 π 14 0 0 Δ B 2 π 12 π 11 π 13 π 14 0 0 Δ B 3 π 31 π 31 π 33 0 0 0 Δ B 4 π 41 π 41 0 π 44 0 0 Δ B 5 0 0 0 0 π 44 2 π 41 Δ B 6 0 0 0 0 π 14 π 66 .
( B 1 + π 14 σ 4 ( X ) ) X 2 + ( B 1 π 14 σ 4 ( X ) ) Y 2 = 1.
Δ n = n 0 3 π 14 σ ( Y ) 5 2 + σ ( X ) 4 2 = n 0 3 π 14 2 M z π R 4 Y 2 + X 2 ,
π 14 = Δ n 2 n 0 3 M z Y 2 + X 2 π R 4 ,
Δ n = n 0 3 π 14 2 M z π R 4 ρ ,
π 14 = Δ n 2 n 0 3 M z ρ π R 4 .
tan 2 ζ z = σ 5 σ 4 = Y X = sin φ cos φ = tan φ , or ζ z = φ / 2.
π 14 = π R 4 2 n 0 3 M z ( + Δ n ) ( σ 4 ) | ( X c , 0 ) = π R 4 2 n 0 3 M z ( Δ n ) ( + σ 4 ) | ( X c , 0 ) = ( 1.77 ± 0.17 ) × 10 12 m 2 / N < 0 ,
π 14 = π R 4 2 n 0 3 M z ( + Δ n ) ( + σ 4 ) | ( X c , 0 ) = π R 4 2 n 0 3 M z ( Δ n ) ( σ 4 ) | ( X c , 0 ) = ( 8.87 ± 0.28 ) × 10 13 m 2 / N > 0 ,
δ Δ k = δ Δ n k d k Δ n k δ d k , or π k m pure = π k m meas + 2 Δ n k S k m .
e 1 = 2 M z π R 4 S 14 X , e 2 = 2 M z π R 4 S 14 X , e 3 = 0 , e 4 = 2 M z π R 4 S 44 X , e 5 = 2 M z π R 4 S 55 Y , e 6 = 4 M z π R 4 S 14 Y .
B 1 X 2 + B 1 Y 2 + B 3 Z 2 + 2 p 44 e 5 Z X + 2 p 41 e 6 Z X + 2 p 14 e 5 X Y + 2 p 66 e 6 X Y = 1 ,
( B 1 + p 11 e 1 + p 12 e 2 + p 14 e 4 ) X 2 + ( B 1 + p 12 e 1 + p 11 e 2 p 14 e 4 ) Y 2 + B 3 Z 2 + 2 p 41 e 1 Z Y 2 p 41 e 2 Z Y + 2 p 14 e 4 Z Y = 1 ,
B 1 X 2 + B 1 Y 2 + 2 p 14 e 5 X Y + 2 p 66 e 6 X Y = 1 ,
( B 1 + p 11 e 1 + p 12 e 2 + p 14 e 4 ) X 2 + ( B 1 + p 12 e 1 + p 11 e 2 p 14 e 4 ) Y 2 = 1 .
Δ n = n 0 3 ( p 14 e 5 + p 66 e 6 ) = 2 n 0 3 ( p 14 S 55 + 2 p 66 S 14 ) M z π R 4 Y ,
Δ n = 1 2 n 0 3 [ ( p 11 p 12 ) ( e 1 e 2 ) + 2 p 14 e 4 ] .
Δ n = 2 n 0 3 ( p 14 S 55 + 2 p 66 S 14 ) M z π R 4 X .
p 14 S 44 + 2 p 66 S 14 = Δ n π R 4 2 M z X n 0 3 = π 14 .

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