Abstract

A recently proposed technique representing a combination of digital imaging laser interferometry with a classical four-point bending method is applied to a canonical nonlinear optical crystal, LiNbO3, to precisely determine a full matrix of its piezo-optic coefficients (POCs). The contribution of a secondary piezo-optic effect to the POCs is investigated experimentally and analyzed theoretically. Based on the POCs thus obtained, a full matrix of strain-optic coefficients (SOCs) is calculated and the appropriate errors are estimated. A comparison of our experimental errors for the POCs and SOCs with the known reference data allows us to claim the present technique as the most precise.

© 2014 Optical Society of America

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  1. I. I. Grakh and A. F. Mozhanskaya, “A type of mechanically anisotropic, optically sensitive material,” Mekhanika Polimerov 5, 835–839 (1971).
  2. Y.-J. Weber, “Determination of internal strain by optical measurements,” Phys. Rev. B 51, 12209–12215 (1995).
    [CrossRef]
  3. T. S. Narasimhamurty, Photoelastic and Electrooptic Properties of Crystals (Plenum, 1981).
  4. I. I. Slezinger, A. N. Alievskaya, and Yu. V. Mironov, “Piezo-optic devices,” Izmeritelnaya Tekhnika 12, 17–19 (1985).
  5. M. Billardon and J. Badoz, “Birefringence modulator,” C. R. Acad. Sci. Ser. B 262, 1672–1675 (1966).
  6. J. C. Kemp, “Piezo-optical birefringence modulators: new use for a long-known effect,” J. Opt. Soc. Am. 59, 950–954 (1969).
  7. B. A. Auld, Acoustic Fields and Waves in Solids (Krieger, 1990).
  8. V. I. Balakshii, V. N. Parygin, and L. E. Chirkov, Physical Fundamentals of Acoustooptics (Radio i Sviaz’, 1985).
  9. J. Xu and R. Stroud, Acousto-Optic Devices: Principles, Design, and Applications (Wiley, 1992).
  10. M. P. Shaskolskaya, Acoustic Crystals (Nauka, 1982).
  11. M. J. Weber, Handbook of Optical Materials (CRC Press, 2003).
  12. F. Pockels, Lehrbuch der Kristallooptik (Teubner Berlin, 1906).
  13. B. H. Mytsyk, “Methods for the studies of the piezo-optical effect in crystals and the analysis of experimental data. Part I. Methodology for the studies of piezo-optical effect,” Ukr. J. Phys. Opt. 4, 1–26 (2003).
    [CrossRef]
  14. Yu. Vasylkiv, O. Kvasnyuk, O. Krupych, O. Mys, O. Maksymuk, and R. Vlokh, “Reconstruction of 3D stress fields basing on piezo-optic experiment,” Ukr. J. Phys. Opt. 10, 22–37 (2009).
    [CrossRef]
  15. I. Skab, I. Smaga, V. Savaryn, Yu. Vasylkiv, and R. Vlokh, “Torsion method for measuring piezo-optic coefficients,” Cryst. Res. Technol. 46, 23–36 (2011).
    [CrossRef]
  16. I. Skab, “Optical anisotropy induced by torsion stresses in the crystals belonging to point symmetry groups 3 and 3¯,” Ukr. J. Phys. Opt. 13, 158–164 (2012).
    [CrossRef]
  17. Yu. Vasylkiv, V. Savaryn, I. Smaga, I. Skab, and R. Vlokh, “On determination of sign of the piezo-optic coefficients using torsion method,” Appl. Opt. 50, 2512–2518 (2011).
    [CrossRef]
  18. O. Krupych, V. Savaryn, I. Skab, and R. Vlokh, “Interferometric measurements of piezo-optic coefficients by means of four-point bending method,” Ukr. J. Phys. Opt. 12, 150–159 (2011).
    [CrossRef]
  19. O. Krupych, V. Savaryn, A. Krupych, I. Klymiv, and R. Vlokh, “Determination of piezo-optic coefficients of crystals by means of four-point bending,” Appl. Opt. 52, 4054–4061 (2013).
    [CrossRef]
  20. S. P. Timoshenko, Strength of Materials (Izdatelstvo NTL, 1965).
  21. R. T. Smith and F. S. Welsh, “Temperature dependence of the elastic, piezoelectric, and dielectric constants of lithium tantalate and lithium niobate,” J. Appl. Phys. 42, 2219–2230 (1971).
    [CrossRef]
  22. Yu. I. Sirotin and M. P. Shaskolskaya, Fundamentals of Crystal Physics (Nauka, 1975).
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  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]
  25. R. S. Weis and T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37, 191–203 (1985).
    [CrossRef]
  26. B. Mytsyk, N. Demyanyshyn, I. Martynyuk-Lototska, and R. Vlokh, “Piezo-optic, photoelastic, and acousto-optic properties of SrB4O7 crystals,” Appl. Opt. 50, 3889–3895 (2011).
    [CrossRef]
  27. A. S. Andrushchak, B. G. Mytsyk, H. P. Laba, O. V. Yurkevych, I. M. Solskii, A. V. Kityk, and B. Sahraoui, “Complete sets of elastic constants and photoelastic coefficients of pure and MgO-doped lithium niobate crystals at room temperature,” J. Appl. Phys. 106, 073510 (2009).
    [CrossRef]
  28. L. P. Avakyants, D. F. Kiselev, and N. N. Shchitkov, “Measurement of the photoelastic coefficients of lithium niobate single crystals,” Sov. Phys. 18, 899–901 (1976).

2013 (1)

2012 (1)

I. Skab, “Optical anisotropy induced by torsion stresses in the crystals belonging to point symmetry groups 3 and 3¯,” Ukr. J. Phys. Opt. 13, 158–164 (2012).
[CrossRef]

2011 (4)

O. Krupych, V. Savaryn, I. Skab, and R. Vlokh, “Interferometric measurements of piezo-optic coefficients by means of four-point bending method,” Ukr. J. Phys. Opt. 12, 150–159 (2011).
[CrossRef]

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

Yu. Vasylkiv, V. Savaryn, I. Smaga, I. Skab, and R. Vlokh, “On determination of sign of the piezo-optic coefficients using torsion method,” Appl. Opt. 50, 2512–2518 (2011).
[CrossRef]

B. Mytsyk, N. Demyanyshyn, I. Martynyuk-Lototska, and R. Vlokh, “Piezo-optic, photoelastic, and acousto-optic properties of SrB4O7 crystals,” Appl. Opt. 50, 3889–3895 (2011).
[CrossRef]

2009 (3)

A. S. Andrushchak, B. G. Mytsyk, H. P. Laba, O. V. Yurkevych, I. M. Solskii, A. V. Kityk, and B. Sahraoui, “Complete sets of elastic constants and photoelastic coefficients of pure and MgO-doped lithium niobate crystals at room temperature,” J. Appl. Phys. 106, 073510 (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]

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

2003 (1)

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

1995 (1)

Y.-J. Weber, “Determination of internal strain by optical measurements,” Phys. Rev. B 51, 12209–12215 (1995).
[CrossRef]

1985 (2)

I. I. Slezinger, A. N. Alievskaya, and Yu. V. Mironov, “Piezo-optic devices,” Izmeritelnaya Tekhnika 12, 17–19 (1985).

R. S. Weis and T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37, 191–203 (1985).
[CrossRef]

1976 (1)

L. P. Avakyants, D. F. Kiselev, and N. N. Shchitkov, “Measurement of the photoelastic coefficients of lithium niobate single crystals,” Sov. Phys. 18, 899–901 (1976).

1971 (2)

I. I. Grakh and A. F. Mozhanskaya, “A type of mechanically anisotropic, optically sensitive material,” Mekhanika Polimerov 5, 835–839 (1971).

R. T. Smith and F. S. Welsh, “Temperature dependence of the elastic, piezoelectric, and dielectric constants of lithium tantalate and lithium niobate,” J. Appl. Phys. 42, 2219–2230 (1971).
[CrossRef]

1969 (1)

1966 (1)

M. Billardon and J. Badoz, “Birefringence modulator,” C. R. Acad. Sci. Ser. B 262, 1672–1675 (1966).

Alievskaya, A. N.

I. I. Slezinger, A. N. Alievskaya, and Yu. V. Mironov, “Piezo-optic devices,” Izmeritelnaya Tekhnika 12, 17–19 (1985).

Andrushchak, A. S.

A. S. Andrushchak, B. G. Mytsyk, H. P. Laba, O. V. Yurkevych, I. M. Solskii, A. V. Kityk, and B. Sahraoui, “Complete sets of elastic constants and photoelastic coefficients of pure and MgO-doped lithium niobate crystals at room temperature,” J. Appl. Phys. 106, 073510 (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]

Auld, B. A.

B. A. Auld, Acoustic Fields and Waves in Solids (Krieger, 1990).

Avakyants, L. P.

L. P. Avakyants, D. F. Kiselev, and N. N. Shchitkov, “Measurement of the photoelastic coefficients of lithium niobate single crystals,” Sov. Phys. 18, 899–901 (1976).

Badoz, J.

M. Billardon and J. Badoz, “Birefringence modulator,” C. R. Acad. Sci. Ser. B 262, 1672–1675 (1966).

Balakshii, V. I.

V. I. Balakshii, V. N. Parygin, and L. E. Chirkov, Physical Fundamentals of Acoustooptics (Radio i Sviaz’, 1985).

Billardon, M.

M. Billardon and J. Badoz, “Birefringence modulator,” C. R. Acad. Sci. Ser. B 262, 1672–1675 (1966).

Chirkov, L. E.

V. I. Balakshii, V. N. Parygin, and L. E. Chirkov, Physical Fundamentals of Acoustooptics (Radio i Sviaz’, 1985).

Demyanyshyn, N.

Demyanyshyn, N. M.

Gaylord, T. K.

R. S. Weis and T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37, 191–203 (1985).
[CrossRef]

Grakh, I. I.

I. I. Grakh and A. F. Mozhanskaya, “A type of mechanically anisotropic, optically sensitive material,” Mekhanika Polimerov 5, 835–839 (1971).

Kemp, J. C.

Kiselev, D. F.

L. P. Avakyants, D. F. Kiselev, and N. N. Shchitkov, “Measurement of the photoelastic coefficients of lithium niobate single crystals,” Sov. Phys. 18, 899–901 (1976).

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]

A. S. Andrushchak, B. G. Mytsyk, H. P. Laba, O. V. Yurkevych, I. M. Solskii, A. V. Kityk, and B. Sahraoui, “Complete sets of elastic constants and photoelastic coefficients of pure and MgO-doped lithium niobate crystals at room temperature,” J. Appl. Phys. 106, 073510 (2009).
[CrossRef]

Klymiv, I.

Kost’, Y. P.

Krupych, A.

Krupych, O.

O. Krupych, V. Savaryn, A. Krupych, I. Klymiv, and R. Vlokh, “Determination of piezo-optic coefficients of crystals by means of four-point bending,” Appl. Opt. 52, 4054–4061 (2013).
[CrossRef]

O. Krupych, V. Savaryn, I. Skab, and R. Vlokh, “Interferometric measurements of piezo-optic coefficients by means of four-point bending method,” Ukr. J. Phys. Opt. 12, 150–159 (2011).
[CrossRef]

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

Laba, H. P.

A. S. Andrushchak, B. G. Mytsyk, H. P. Laba, O. V. Yurkevych, I. M. Solskii, A. V. Kityk, and B. Sahraoui, “Complete sets of elastic constants and photoelastic coefficients of pure and MgO-doped lithium niobate crystals at room temperature,” J. Appl. Phys. 106, 073510 (2009).
[CrossRef]

Maksymuk, O.

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

Mandracci, P.

Martynyuk-Lototska, I.

Mironov, Yu. V.

I. I. Slezinger, A. N. Alievskaya, and Yu. V. Mironov, “Piezo-optic devices,” Izmeritelnaya Tekhnika 12, 17–19 (1985).

Mozhanskaya, A. F.

I. I. Grakh and A. F. Mozhanskaya, “A type of mechanically anisotropic, optically sensitive material,” Mekhanika Polimerov 5, 835–839 (1971).

Mys, O.

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

Mytsyk, B.

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]

A. S. Andrushchak, B. G. Mytsyk, H. P. Laba, O. V. Yurkevych, I. M. Solskii, A. V. Kityk, and B. Sahraoui, “Complete sets of elastic constants and photoelastic coefficients of pure and MgO-doped lithium niobate crystals at room temperature,” J. Appl. Phys. 106, 073510 (2009).
[CrossRef]

Mytsyk, B. H.

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

Narasimhamurty, T. S.

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

Parygin, V. N.

V. I. Balakshii, V. N. Parygin, and L. E. Chirkov, Physical Fundamentals of Acoustooptics (Radio i Sviaz’, 1985).

Pockels, F.

F. Pockels, Lehrbuch der Kristallooptik (Teubner Berlin, 1906).

Sahraoui, B.

A. S. Andrushchak, B. G. Mytsyk, H. P. Laba, O. V. Yurkevych, I. M. Solskii, A. V. Kityk, and B. Sahraoui, “Complete sets of elastic constants and photoelastic coefficients of pure and MgO-doped lithium niobate crystals at room temperature,” J. Appl. Phys. 106, 073510 (2009).
[CrossRef]

Savaryn, V.

O. Krupych, V. Savaryn, A. Krupych, I. Klymiv, and R. Vlokh, “Determination of piezo-optic coefficients of crystals by means of four-point bending,” Appl. Opt. 52, 4054–4061 (2013).
[CrossRef]

O. Krupych, V. Savaryn, I. Skab, and R. Vlokh, “Interferometric measurements of piezo-optic coefficients by means of four-point bending method,” Ukr. J. Phys. Opt. 12, 150–159 (2011).
[CrossRef]

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

Yu. Vasylkiv, V. Savaryn, I. Smaga, I. Skab, and R. Vlokh, “On determination of sign of the piezo-optic coefficients using torsion method,” Appl. Opt. 50, 2512–2518 (2011).
[CrossRef]

Schranz, W.

Shaskolskaya, M. P.

Yu. I. Sirotin and M. P. Shaskolskaya, Fundamentals of Crystal Physics (Nauka, 1975).

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

Shchitkov, N. N.

L. P. Avakyants, D. F. Kiselev, and N. N. Shchitkov, “Measurement of the photoelastic coefficients of lithium niobate single crystals,” Sov. Phys. 18, 899–901 (1976).

Sirotin, Yu. I.

Yu. I. Sirotin and M. P. Shaskolskaya, Fundamentals of Crystal Physics (Nauka, 1975).

Skab, I.

I. Skab, “Optical anisotropy induced by torsion stresses in the crystals belonging to point symmetry groups 3 and 3¯,” Ukr. J. Phys. Opt. 13, 158–164 (2012).
[CrossRef]

Yu. Vasylkiv, V. Savaryn, I. Smaga, I. Skab, and R. Vlokh, “On determination of sign of the piezo-optic coefficients using torsion method,” Appl. Opt. 50, 2512–2518 (2011).
[CrossRef]

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

O. Krupych, V. Savaryn, I. Skab, and R. Vlokh, “Interferometric measurements of piezo-optic coefficients by means of four-point bending method,” Ukr. J. Phys. Opt. 12, 150–159 (2011).
[CrossRef]

Slezinger, I. I.

I. I. Slezinger, A. N. Alievskaya, and Yu. V. Mironov, “Piezo-optic devices,” Izmeritelnaya Tekhnika 12, 17–19 (1985).

Smaga, I.

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

Yu. Vasylkiv, V. Savaryn, I. Smaga, I. Skab, and R. Vlokh, “On determination of sign of the piezo-optic coefficients using torsion method,” Appl. Opt. 50, 2512–2518 (2011).
[CrossRef]

Smith, R. T.

R. T. Smith and F. S. Welsh, “Temperature dependence of the elastic, piezoelectric, and dielectric constants of lithium tantalate and lithium niobate,” J. Appl. Phys. 42, 2219–2230 (1971).
[CrossRef]

Solskii, I. M.

A. S. Andrushchak, B. G. Mytsyk, H. P. Laba, O. V. Yurkevych, I. M. Solskii, A. V. Kityk, and B. Sahraoui, “Complete sets of elastic constants and photoelastic coefficients of pure and MgO-doped lithium niobate crystals at room temperature,” J. Appl. Phys. 106, 073510 (2009).
[CrossRef]

Stroud, R.

J. Xu and R. Stroud, Acousto-Optic Devices: Principles, Design, and Applications (Wiley, 1992).

Timoshenko, S. P.

S. P. Timoshenko, Strength of Materials (Izdatelstvo NTL, 1965).

Vasylkiv, Yu.

Yu. Vasylkiv, V. Savaryn, I. Smaga, I. Skab, and R. Vlokh, “On determination of sign of the piezo-optic coefficients using torsion method,” Appl. Opt. 50, 2512–2518 (2011).
[CrossRef]

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

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

Vlokh, R.

O. Krupych, V. Savaryn, A. Krupych, I. Klymiv, and R. Vlokh, “Determination of piezo-optic coefficients of crystals by means of four-point bending,” Appl. Opt. 52, 4054–4061 (2013).
[CrossRef]

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

O. Krupych, V. Savaryn, I. Skab, and R. Vlokh, “Interferometric measurements of piezo-optic coefficients by means of four-point bending method,” Ukr. J. Phys. Opt. 12, 150–159 (2011).
[CrossRef]

Yu. Vasylkiv, V. Savaryn, I. Smaga, I. Skab, and R. Vlokh, “On determination of sign of the piezo-optic coefficients using torsion method,” Appl. Opt. 50, 2512–2518 (2011).
[CrossRef]

B. Mytsyk, N. Demyanyshyn, I. Martynyuk-Lototska, and R. Vlokh, “Piezo-optic, photoelastic, and acousto-optic properties of SrB4O7 crystals,” Appl. Opt. 50, 3889–3895 (2011).
[CrossRef]

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

Weber, M. J.

M. J. Weber, Handbook of Optical Materials (CRC Press, 2003).

Weber, Y.-J.

Y.-J. Weber, “Determination of internal strain by optical measurements,” Phys. Rev. B 51, 12209–12215 (1995).
[CrossRef]

Weis, R. S.

R. S. Weis and T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37, 191–203 (1985).
[CrossRef]

Welsh, F. S.

R. T. Smith and F. S. Welsh, “Temperature dependence of the elastic, piezoelectric, and dielectric constants of lithium tantalate and lithium niobate,” J. Appl. Phys. 42, 2219–2230 (1971).
[CrossRef]

Xu, J.

J. Xu and R. Stroud, Acousto-Optic Devices: Principles, Design, and Applications (Wiley, 1992).

Yurkevych, O. V.

A. S. Andrushchak, B. G. Mytsyk, H. P. Laba, O. V. Yurkevych, I. M. Solskii, A. V. Kityk, and B. Sahraoui, “Complete sets of elastic constants and photoelastic coefficients of pure and MgO-doped lithium niobate crystals at room temperature,” J. Appl. Phys. 106, 073510 (2009).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. A (1)

R. S. Weis and T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37, 191–203 (1985).
[CrossRef]

C. R. Acad. Sci. Ser. B (1)

M. Billardon and J. Badoz, “Birefringence modulator,” C. R. Acad. Sci. Ser. B 262, 1672–1675 (1966).

Cryst. Res. Technol. (1)

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

Izmeritelnaya Tekhnika (1)

I. I. Slezinger, A. N. Alievskaya, and Yu. V. Mironov, “Piezo-optic devices,” Izmeritelnaya Tekhnika 12, 17–19 (1985).

J. Appl. Phys. (2)

R. T. Smith and F. S. Welsh, “Temperature dependence of the elastic, piezoelectric, and dielectric constants of lithium tantalate and lithium niobate,” J. Appl. Phys. 42, 2219–2230 (1971).
[CrossRef]

A. S. Andrushchak, B. G. Mytsyk, H. P. Laba, O. V. Yurkevych, I. M. Solskii, A. V. Kityk, and B. Sahraoui, “Complete sets of elastic constants and photoelastic coefficients of pure and MgO-doped lithium niobate crystals at room temperature,” J. Appl. Phys. 106, 073510 (2009).
[CrossRef]

J. Opt. Soc. Am. (1)

Mekhanika Polimerov (1)

I. I. Grakh and A. F. Mozhanskaya, “A type of mechanically anisotropic, optically sensitive material,” Mekhanika Polimerov 5, 835–839 (1971).

Phys. Rev. B (1)

Y.-J. Weber, “Determination of internal strain by optical measurements,” Phys. Rev. B 51, 12209–12215 (1995).
[CrossRef]

Sov. Phys. (1)

L. P. Avakyants, D. F. Kiselev, and N. N. Shchitkov, “Measurement of the photoelastic coefficients of lithium niobate single crystals,” Sov. Phys. 18, 899–901 (1976).

Ukr. J. Phys. Opt. (4)

O. Krupych, V. Savaryn, I. Skab, and R. Vlokh, “Interferometric measurements of piezo-optic coefficients by means of four-point bending method,” Ukr. J. Phys. Opt. 12, 150–159 (2011).
[CrossRef]

I. Skab, “Optical anisotropy induced by torsion stresses in the crystals belonging to point symmetry groups 3 and 3¯,” Ukr. J. Phys. Opt. 13, 158–164 (2012).
[CrossRef]

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

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

Other (10)

B. A. Auld, Acoustic Fields and Waves in Solids (Krieger, 1990).

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J. Xu and R. Stroud, Acousto-Optic Devices: Principles, Design, and Applications (Wiley, 1992).

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

M. J. Weber, Handbook of Optical Materials (CRC Press, 2003).

F. Pockels, Lehrbuch der Kristallooptik (Teubner Berlin, 1906).

Yu. I. Sirotin and M. P. Shaskolskaya, Fundamentals of Crystal Physics (Nauka, 1975).

“Standards on piezoelectric crystals,” Proc. Inst. Radio Eng.37, 1378–1395 (1949).

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

S. P. Timoshenko, Strength of Materials (Izdatelstvo NTL, 1965).

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Figures (2)

Fig. 1.
Fig. 1.

Scheme of sample-loading geometry according to a four-point bending technique, with a Cartesian coordinate system chosen. P is a loading force and light beam propagates along Z direction (see [12]).

Fig. 2.
Fig. 2.

Spatial distributions of electric-field vector induced by piezo-electric effect in the central part of LN samples under four-point bending: sample No. 1, Z-cut (a); sample No. 2, Y-cut (b).

Tables (4)

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Table 1. Dimensions of Samples (in mm) and Orientation of their Faces Written in Terms of Miller Indices

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Table 2. Effective POCs under Measurement and Parameters of the Corresponding Experimental Geometries

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Table 3. POCs of the LN Crystals as Obtained Here and as Known from the Literature

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Table 4. SOCs (dimensionless) for LN Crystals as Obtained Here and as Known from the Literature

Equations (11)

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δBλ=πλμσμ(λ,μ=16),
δBλ=pλμεμ(λ,μ=16)
σmσX=6Pabh3y;σqσY=0;σlσZ=0,
πqm=(π11π12π13π14π15π16π21π22π23π24π25π26π31π32π33π34π35π36π41π42π43π44π45π46π51π52π53π54π55π56π61π62π63π64π65π66)=(ABCD).
A=(π11π12π13π21π22π23π31π32π33),B=(π14π15π16π24π25π26π34π35π36),C=(π41π42π43π51π52π53π61π62π63),D=(π44π45π46π54π55π56π64π65π66).
πqm=(π11π12π13π1400π12π11π13π1400π31π31π33000π41π410π44000000π442π410000π14(π11π12)).
Ceff=K+D=(12nq3πqm)+[Slm(nq1)],
πλμ=πλμE+πλμ*=πλμE+rλidiμε0χii(i=13,λ,μ=16),
E1=0;E2=d22σ1ε0χ11=2.84×102σ1;E3=d31σ1ε0χ33=0.38×102σ1.
E1=0;E2=0;E3=d33σ3ε0χ33=4.67×102σ3.
pλμ=πλθCθμ,

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