Abstract

We describe an interferometric technique suitable for determination of piezo-optic coefficients (POCs) in crystals. The method considers real nonparallelism of measured samples, thereby improving the measuring precision of POCs significantly. Corresponding equations are derived for the interferometric half-wave stress method. Using this technique we have determined a complete set of POCs of pure and MgO-doped LiNbO3 crystals. The reliability of the data has been confirmed by comparing the effective POCs expressed through the combinations of measured POCs and the effective POCs determined independently using highly precise optical birefringence measurements. Pure and MgO-doped LiNbO3 crystals reveal nearly the same magnitudes of POCs. However, LiNbO3:MgO exhibits about 4 times higher resistance with respect to powerful light radiation, making it more suitable for application in acousto-optic devices that deal with superpowerful laser radiation.

© 2009 Optical Society of America

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  1. J. F. Nye, Physical Properties of Crystals (Clarendon, 1985), p. 329.
  2. A. S. Sonin and A. S. Vasilevskaya, Electro-Optic Crystals (Atomizdat, 1971), p. 327 [in Russian].
  3. G. Kloos, “On photoelastic and quadratic electrostrictive effect,” J. Phys. D 30, 1536-1539 (1997).
    [CrossRef]
  4. N. Uchida and N. Niizeki, “Acousto-optic deflection materials and techniques,” Proc. IEEE 61, 1073-1094 (1973).
    [CrossRef]
  5. I. M. Silvestrova, A. V. Vinogradov, A. V. Shygorin, T. N. Turskaya, G. S. Belikova, and Ya. V. Pisarevskiy, “Elastic, piezoelectric, acousto-optic and non-linear optical properties of caesium ortosulphobenzoat crystals,” Kristallografiya 35, 906-911 (1990) [in Russian].
  6. D. F. Nelson, Electric, Optic and Acoustic Interactions in Dielectrics (Wiley-Interscience, 1979), p. 539.
  7. A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, B. V. Tybinka, A. V. Kityk, and W. Schranz, “Spatial anisotropy of photoelastic and acousto-optic properties in ??BaB2O4 crystals,” Opt. Mater. 27, 619-624 (2004).
  8. A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, and B. V. Tybinka, “Spatial analysis of isotropic and anisotropic diffraction of light by transverse acoustic waves in barium beta-borate crystals,” Ukr. J. Phys. 50, 26-33 (2005).
  9. D. Yu. Sugak, A. O. Matkovskii, I. M. Solskii, B. M. Kopko, V. Ya. Oliinyk, I. V. Stefanskii, V. M. Gaba, V. V. Grabowskii, I. M. Zaritskii, and L. G. Rakitina, “Growth and optical properties of LiNbO3:MgO single crystals,” Cryst. Res.?echnol. 32, 805-811 (1997).
    [CrossRef]
  10. B. Mytsyk, “Methods for the studies of the piezo-optic effect in crystals and the analysis of experimental data. II. Analysis of the experimental data,” Ukr. J. Phys. Opt. 4, 105-118(2003).
    [CrossRef]
  11. B. Mytsyk, “Methods for the studies of the piezo-optic effect in crystals and the analysis of experimental data. I. Methodology for the studies of piezo-optic effect,” Ukr. J. Phys. Opt. 4, 1-26 (2003).
    [CrossRef]
  12. B. H. Mytsyk, A. S. Andrushchak, and G. I. Gaskevich, “Comprehensive studies of piezo-optic effect in langasite crystals,” Ukr. J. Phys. Opt. 52, 800-809 (2007).
  13. H. P. Laba, O. V. Yurkevych, I. D. Karbovnyk, M. V. Kaidan, S. S. Dumych, I. M. Solskii, and A. S. Andrushchak, “Spatial anisotropy of electro-, piezo- and acousto-optic effects in crystalline materials of solid electronics. Approbation on example of LiNbO3 and LiNbO3:MgO part II. Completing of elastic and piezoelectric coefficients matrix for LiNbO3 and LiNbO3:MgO crystals,” Herald Lviv Polytechnic National Univ. (Electronics) 619, 172-180 (2008).
  14. B. H. Mytsyk, Ya. V. Pryriz, and A. S. Andrushchak, “The lithium niobate piezo-optic features,” Cryst. Res. ?echnol. 26, 931-940 (1991).
    [CrossRef]
  15. M. N. Trainer, “Photoelastic measuring transducer and accelerometer based thereon,” U.S. patent 4,648,274 (3 October 1997).
  16. F. Brandi, E. Polacco, and G. Ruoso, “Stress-optic modulator,” Meas. Sci. Technol. 12, 1503-1508 (2001).
    [CrossRef]
  17. A. S. Andrushchak, B. H. Mytsyk, and B. V. Osyka, “Photoelastic stress transduser,” USSR patent 1,796,936, published in Bulletin No. 7 (1993).
  18. Yu. I. Syrotin and M. P. Shaskolskaya, Fundamentals of Crystal Physics (Nauka, 1979).
  19. B. H. Mytsyk, A. S. Andrushchak, Ya. P. Kost', and I. M. Solskii, “Piezooptic effect in LiNbO3:MgO crystals,” J. Phys. Stud. 12, 3702/1-3702/5 (2008).

2008

H. P. Laba, O. V. Yurkevych, I. D. Karbovnyk, M. V. Kaidan, S. S. Dumych, I. M. Solskii, and A. S. Andrushchak, “Spatial anisotropy of electro-, piezo- and acousto-optic effects in crystalline materials of solid electronics. Approbation on example of LiNbO3 and LiNbO3:MgO part II. Completing of elastic and piezoelectric coefficients matrix for LiNbO3 and LiNbO3:MgO crystals,” Herald Lviv Polytechnic National Univ. (Electronics) 619, 172-180 (2008).

B. H. Mytsyk, A. S. Andrushchak, Ya. P. Kost', and I. M. Solskii, “Piezooptic effect in LiNbO3:MgO crystals,” J. Phys. Stud. 12, 3702/1-3702/5 (2008).

2007

B. H. Mytsyk, A. S. Andrushchak, and G. I. Gaskevich, “Comprehensive studies of piezo-optic effect in langasite crystals,” Ukr. J. Phys. Opt. 52, 800-809 (2007).

2005

A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, and B. V. Tybinka, “Spatial analysis of isotropic and anisotropic diffraction of light by transverse acoustic waves in barium beta-borate crystals,” Ukr. J. Phys. 50, 26-33 (2005).

2004

A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, B. V. Tybinka, A. V. Kityk, and W. Schranz, “Spatial anisotropy of photoelastic and acousto-optic properties in ??BaB2O4 crystals,” Opt. Mater. 27, 619-624 (2004).

2003

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

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

2001

F. Brandi, E. Polacco, and G. Ruoso, “Stress-optic modulator,” Meas. Sci. Technol. 12, 1503-1508 (2001).
[CrossRef]

1997

D. Yu. Sugak, A. O. Matkovskii, I. M. Solskii, B. M. Kopko, V. Ya. Oliinyk, I. V. Stefanskii, V. M. Gaba, V. V. Grabowskii, I. M. Zaritskii, and L. G. Rakitina, “Growth and optical properties of LiNbO3:MgO single crystals,” Cryst. Res.?echnol. 32, 805-811 (1997).
[CrossRef]

G. Kloos, “On photoelastic and quadratic electrostrictive effect,” J. Phys. D 30, 1536-1539 (1997).
[CrossRef]

1993

A. S. Andrushchak, B. H. Mytsyk, and B. V. Osyka, “Photoelastic stress transduser,” USSR patent 1,796,936, published in Bulletin No. 7 (1993).

1991

B. H. Mytsyk, Ya. V. Pryriz, and A. S. Andrushchak, “The lithium niobate piezo-optic features,” Cryst. Res. ?echnol. 26, 931-940 (1991).
[CrossRef]

1990

I. M. Silvestrova, A. V. Vinogradov, A. V. Shygorin, T. N. Turskaya, G. S. Belikova, and Ya. V. Pisarevskiy, “Elastic, piezoelectric, acousto-optic and non-linear optical properties of caesium ortosulphobenzoat crystals,” Kristallografiya 35, 906-911 (1990) [in Russian].

1985

J. F. Nye, Physical Properties of Crystals (Clarendon, 1985), p. 329.

1979

D. F. Nelson, Electric, Optic and Acoustic Interactions in Dielectrics (Wiley-Interscience, 1979), p. 539.

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

1973

N. Uchida and N. Niizeki, “Acousto-optic deflection materials and techniques,” Proc. IEEE 61, 1073-1094 (1973).
[CrossRef]

1971

A. S. Sonin and A. S. Vasilevskaya, Electro-Optic Crystals (Atomizdat, 1971), p. 327 [in Russian].

Andrushchak, A. S.

H. P. Laba, O. V. Yurkevych, I. D. Karbovnyk, M. V. Kaidan, S. S. Dumych, I. M. Solskii, and A. S. Andrushchak, “Spatial anisotropy of electro-, piezo- and acousto-optic effects in crystalline materials of solid electronics. Approbation on example of LiNbO3 and LiNbO3:MgO part II. Completing of elastic and piezoelectric coefficients matrix for LiNbO3 and LiNbO3:MgO crystals,” Herald Lviv Polytechnic National Univ. (Electronics) 619, 172-180 (2008).

B. H. Mytsyk, A. S. Andrushchak, Ya. P. Kost', and I. M. Solskii, “Piezooptic effect in LiNbO3:MgO crystals,” J. Phys. Stud. 12, 3702/1-3702/5 (2008).

B. H. Mytsyk, A. S. Andrushchak, and G. I. Gaskevich, “Comprehensive studies of piezo-optic effect in langasite crystals,” Ukr. J. Phys. Opt. 52, 800-809 (2007).

A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, and B. V. Tybinka, “Spatial analysis of isotropic and anisotropic diffraction of light by transverse acoustic waves in barium beta-borate crystals,” Ukr. J. Phys. 50, 26-33 (2005).

A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, B. V. Tybinka, A. V. Kityk, and W. Schranz, “Spatial anisotropy of photoelastic and acousto-optic properties in ??BaB2O4 crystals,” Opt. Mater. 27, 619-624 (2004).

A. S. Andrushchak, B. H. Mytsyk, and B. V. Osyka, “Photoelastic stress transduser,” USSR patent 1,796,936, published in Bulletin No. 7 (1993).

B. H. Mytsyk, Ya. V. Pryriz, and A. S. Andrushchak, “The lithium niobate piezo-optic features,” Cryst. Res. ?echnol. 26, 931-940 (1991).
[CrossRef]

Belikova, G. S.

I. M. Silvestrova, A. V. Vinogradov, A. V. Shygorin, T. N. Turskaya, G. S. Belikova, and Ya. V. Pisarevskiy, “Elastic, piezoelectric, acousto-optic and non-linear optical properties of caesium ortosulphobenzoat crystals,” Kristallografiya 35, 906-911 (1990) [in Russian].

Bobitski, Ya. V.

A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, and B. V. Tybinka, “Spatial analysis of isotropic and anisotropic diffraction of light by transverse acoustic waves in barium beta-borate crystals,” Ukr. J. Phys. 50, 26-33 (2005).

A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, B. V. Tybinka, A. V. Kityk, and W. Schranz, “Spatial anisotropy of photoelastic and acousto-optic properties in ??BaB2O4 crystals,” Opt. Mater. 27, 619-624 (2004).

Brandi, F.

F. Brandi, E. Polacco, and G. Ruoso, “Stress-optic modulator,” Meas. Sci. Technol. 12, 1503-1508 (2001).
[CrossRef]

Dumych, S. S.

H. P. Laba, O. V. Yurkevych, I. D. Karbovnyk, M. V. Kaidan, S. S. Dumych, I. M. Solskii, and A. S. Andrushchak, “Spatial anisotropy of electro-, piezo- and acousto-optic effects in crystalline materials of solid electronics. Approbation on example of LiNbO3 and LiNbO3:MgO part II. Completing of elastic and piezoelectric coefficients matrix for LiNbO3 and LiNbO3:MgO crystals,” Herald Lviv Polytechnic National Univ. (Electronics) 619, 172-180 (2008).

Gaba, V. M.

D. Yu. Sugak, A. O. Matkovskii, I. M. Solskii, B. M. Kopko, V. Ya. Oliinyk, I. V. Stefanskii, V. M. Gaba, V. V. Grabowskii, I. M. Zaritskii, and L. G. Rakitina, “Growth and optical properties of LiNbO3:MgO single crystals,” Cryst. Res.?echnol. 32, 805-811 (1997).
[CrossRef]

Gaskevich, G. I.

B. H. Mytsyk, A. S. Andrushchak, and G. I. Gaskevich, “Comprehensive studies of piezo-optic effect in langasite crystals,” Ukr. J. Phys. Opt. 52, 800-809 (2007).

Grabowskii, V. V.

D. Yu. Sugak, A. O. Matkovskii, I. M. Solskii, B. M. Kopko, V. Ya. Oliinyk, I. V. Stefanskii, V. M. Gaba, V. V. Grabowskii, I. M. Zaritskii, and L. G. Rakitina, “Growth and optical properties of LiNbO3:MgO single crystals,” Cryst. Res.?echnol. 32, 805-811 (1997).
[CrossRef]

Kaidan, M. V.

H. P. Laba, O. V. Yurkevych, I. D. Karbovnyk, M. V. Kaidan, S. S. Dumych, I. M. Solskii, and A. S. Andrushchak, “Spatial anisotropy of electro-, piezo- and acousto-optic effects in crystalline materials of solid electronics. Approbation on example of LiNbO3 and LiNbO3:MgO part II. Completing of elastic and piezoelectric coefficients matrix for LiNbO3 and LiNbO3:MgO crystals,” Herald Lviv Polytechnic National Univ. (Electronics) 619, 172-180 (2008).

A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, and B. V. Tybinka, “Spatial analysis of isotropic and anisotropic diffraction of light by transverse acoustic waves in barium beta-borate crystals,” Ukr. J. Phys. 50, 26-33 (2005).

A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, B. V. Tybinka, A. V. Kityk, and W. Schranz, “Spatial anisotropy of photoelastic and acousto-optic properties in ??BaB2O4 crystals,” Opt. Mater. 27, 619-624 (2004).

Karbovnyk, I. D.

H. P. Laba, O. V. Yurkevych, I. D. Karbovnyk, M. V. Kaidan, S. S. Dumych, I. M. Solskii, and A. S. Andrushchak, “Spatial anisotropy of electro-, piezo- and acousto-optic effects in crystalline materials of solid electronics. Approbation on example of LiNbO3 and LiNbO3:MgO part II. Completing of elastic and piezoelectric coefficients matrix for LiNbO3 and LiNbO3:MgO crystals,” Herald Lviv Polytechnic National Univ. (Electronics) 619, 172-180 (2008).

Kityk, A. V.

A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, B. V. Tybinka, A. V. Kityk, and W. Schranz, “Spatial anisotropy of photoelastic and acousto-optic properties in ??BaB2O4 crystals,” Opt. Mater. 27, 619-624 (2004).

Kloos, G.

G. Kloos, “On photoelastic and quadratic electrostrictive effect,” J. Phys. D 30, 1536-1539 (1997).
[CrossRef]

Kopko, B. M.

D. Yu. Sugak, A. O. Matkovskii, I. M. Solskii, B. M. Kopko, V. Ya. Oliinyk, I. V. Stefanskii, V. M. Gaba, V. V. Grabowskii, I. M. Zaritskii, and L. G. Rakitina, “Growth and optical properties of LiNbO3:MgO single crystals,” Cryst. Res.?echnol. 32, 805-811 (1997).
[CrossRef]

Kost', Ya. P.

B. H. Mytsyk, A. S. Andrushchak, Ya. P. Kost', and I. M. Solskii, “Piezooptic effect in LiNbO3:MgO crystals,” J. Phys. Stud. 12, 3702/1-3702/5 (2008).

Laba, H. P.

H. P. Laba, O. V. Yurkevych, I. D. Karbovnyk, M. V. Kaidan, S. S. Dumych, I. M. Solskii, and A. S. Andrushchak, “Spatial anisotropy of electro-, piezo- and acousto-optic effects in crystalline materials of solid electronics. Approbation on example of LiNbO3 and LiNbO3:MgO part II. Completing of elastic and piezoelectric coefficients matrix for LiNbO3 and LiNbO3:MgO crystals,” Herald Lviv Polytechnic National Univ. (Electronics) 619, 172-180 (2008).

Matkovskii, A. O.

D. Yu. Sugak, A. O. Matkovskii, I. M. Solskii, B. M. Kopko, V. Ya. Oliinyk, I. V. Stefanskii, V. M. Gaba, V. V. Grabowskii, I. M. Zaritskii, and L. G. Rakitina, “Growth and optical properties of LiNbO3:MgO single crystals,” Cryst. Res.?echnol. 32, 805-811 (1997).
[CrossRef]

Mytsyk, B.

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

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

Mytsyk, B. H.

B. H. Mytsyk, A. S. Andrushchak, Ya. P. Kost', and I. M. Solskii, “Piezooptic effect in LiNbO3:MgO crystals,” J. Phys. Stud. 12, 3702/1-3702/5 (2008).

B. H. Mytsyk, A. S. Andrushchak, and G. I. Gaskevich, “Comprehensive studies of piezo-optic effect in langasite crystals,” Ukr. J. Phys. Opt. 52, 800-809 (2007).

A. S. Andrushchak, B. H. Mytsyk, and B. V. Osyka, “Photoelastic stress transduser,” USSR patent 1,796,936, published in Bulletin No. 7 (1993).

B. H. Mytsyk, Ya. V. Pryriz, and A. S. Andrushchak, “The lithium niobate piezo-optic features,” Cryst. Res. ?echnol. 26, 931-940 (1991).
[CrossRef]

Nelson, D. F.

D. F. Nelson, Electric, Optic and Acoustic Interactions in Dielectrics (Wiley-Interscience, 1979), p. 539.

Niizeki, N.

N. Uchida and N. Niizeki, “Acousto-optic deflection materials and techniques,” Proc. IEEE 61, 1073-1094 (1973).
[CrossRef]

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Clarendon, 1985), p. 329.

Oliinyk, V. Ya.

D. Yu. Sugak, A. O. Matkovskii, I. M. Solskii, B. M. Kopko, V. Ya. Oliinyk, I. V. Stefanskii, V. M. Gaba, V. V. Grabowskii, I. M. Zaritskii, and L. G. Rakitina, “Growth and optical properties of LiNbO3:MgO single crystals,” Cryst. Res.?echnol. 32, 805-811 (1997).
[CrossRef]

Osyka, B. V.

A. S. Andrushchak, B. H. Mytsyk, and B. V. Osyka, “Photoelastic stress transduser,” USSR patent 1,796,936, published in Bulletin No. 7 (1993).

Pisarevskiy, Ya. V.

I. M. Silvestrova, A. V. Vinogradov, A. V. Shygorin, T. N. Turskaya, G. S. Belikova, and Ya. V. Pisarevskiy, “Elastic, piezoelectric, acousto-optic and non-linear optical properties of caesium ortosulphobenzoat crystals,” Kristallografiya 35, 906-911 (1990) [in Russian].

Polacco, E.

F. Brandi, E. Polacco, and G. Ruoso, “Stress-optic modulator,” Meas. Sci. Technol. 12, 1503-1508 (2001).
[CrossRef]

Pryriz, Ya. V.

B. H. Mytsyk, Ya. V. Pryriz, and A. S. Andrushchak, “The lithium niobate piezo-optic features,” Cryst. Res. ?echnol. 26, 931-940 (1991).
[CrossRef]

Rakitina, L. G.

D. Yu. Sugak, A. O. Matkovskii, I. M. Solskii, B. M. Kopko, V. Ya. Oliinyk, I. V. Stefanskii, V. M. Gaba, V. V. Grabowskii, I. M. Zaritskii, and L. G. Rakitina, “Growth and optical properties of LiNbO3:MgO single crystals,” Cryst. Res.?echnol. 32, 805-811 (1997).
[CrossRef]

Ruoso, G.

F. Brandi, E. Polacco, and G. Ruoso, “Stress-optic modulator,” Meas. Sci. Technol. 12, 1503-1508 (2001).
[CrossRef]

Schranz, W.

A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, B. V. Tybinka, A. V. Kityk, and W. Schranz, “Spatial anisotropy of photoelastic and acousto-optic properties in ??BaB2O4 crystals,” Opt. Mater. 27, 619-624 (2004).

Shaskolskaya, M. P.

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

Shygorin, A. V.

I. M. Silvestrova, A. V. Vinogradov, A. V. Shygorin, T. N. Turskaya, G. S. Belikova, and Ya. V. Pisarevskiy, “Elastic, piezoelectric, acousto-optic and non-linear optical properties of caesium ortosulphobenzoat crystals,” Kristallografiya 35, 906-911 (1990) [in Russian].

Silvestrova, I. M.

I. M. Silvestrova, A. V. Vinogradov, A. V. Shygorin, T. N. Turskaya, G. S. Belikova, and Ya. V. Pisarevskiy, “Elastic, piezoelectric, acousto-optic and non-linear optical properties of caesium ortosulphobenzoat crystals,” Kristallografiya 35, 906-911 (1990) [in Russian].

Solskii, I. M.

B. H. Mytsyk, A. S. Andrushchak, Ya. P. Kost', and I. M. Solskii, “Piezooptic effect in LiNbO3:MgO crystals,” J. Phys. Stud. 12, 3702/1-3702/5 (2008).

H. P. Laba, O. V. Yurkevych, I. D. Karbovnyk, M. V. Kaidan, S. S. Dumych, I. M. Solskii, and A. S. Andrushchak, “Spatial anisotropy of electro-, piezo- and acousto-optic effects in crystalline materials of solid electronics. Approbation on example of LiNbO3 and LiNbO3:MgO part II. Completing of elastic and piezoelectric coefficients matrix for LiNbO3 and LiNbO3:MgO crystals,” Herald Lviv Polytechnic National Univ. (Electronics) 619, 172-180 (2008).

D. Yu. Sugak, A. O. Matkovskii, I. M. Solskii, B. M. Kopko, V. Ya. Oliinyk, I. V. Stefanskii, V. M. Gaba, V. V. Grabowskii, I. M. Zaritskii, and L. G. Rakitina, “Growth and optical properties of LiNbO3:MgO single crystals,” Cryst. Res.?echnol. 32, 805-811 (1997).
[CrossRef]

Sonin, A. S.

A. S. Sonin and A. S. Vasilevskaya, Electro-Optic Crystals (Atomizdat, 1971), p. 327 [in Russian].

Stefanskii, I. V.

D. Yu. Sugak, A. O. Matkovskii, I. M. Solskii, B. M. Kopko, V. Ya. Oliinyk, I. V. Stefanskii, V. M. Gaba, V. V. Grabowskii, I. M. Zaritskii, and L. G. Rakitina, “Growth and optical properties of LiNbO3:MgO single crystals,” Cryst. Res.?echnol. 32, 805-811 (1997).
[CrossRef]

Sugak, D. Yu.

D. Yu. Sugak, A. O. Matkovskii, I. M. Solskii, B. M. Kopko, V. Ya. Oliinyk, I. V. Stefanskii, V. M. Gaba, V. V. Grabowskii, I. M. Zaritskii, and L. G. Rakitina, “Growth and optical properties of LiNbO3:MgO single crystals,” Cryst. Res.?echnol. 32, 805-811 (1997).
[CrossRef]

Syrotin, Yu. I.

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

Trainer, M. N.

M. N. Trainer, “Photoelastic measuring transducer and accelerometer based thereon,” U.S. patent 4,648,274 (3 October 1997).

Turskaya, T. N.

I. M. Silvestrova, A. V. Vinogradov, A. V. Shygorin, T. N. Turskaya, G. S. Belikova, and Ya. V. Pisarevskiy, “Elastic, piezoelectric, acousto-optic and non-linear optical properties of caesium ortosulphobenzoat crystals,” Kristallografiya 35, 906-911 (1990) [in Russian].

Tybinka, B. V.

A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, and B. V. Tybinka, “Spatial analysis of isotropic and anisotropic diffraction of light by transverse acoustic waves in barium beta-borate crystals,” Ukr. J. Phys. 50, 26-33 (2005).

A. S. Andrushchak, Ya. V. Bobitski, M. V. Kaidan, B. V. Tybinka, A. V. Kityk, and W. Schranz, “Spatial anisotropy of photoelastic and acousto-optic properties in ??BaB2O4 crystals,” Opt. Mater. 27, 619-624 (2004).

Uchida, N.

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[CrossRef]

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A. S. Sonin and A. S. Vasilevskaya, Electro-Optic Crystals (Atomizdat, 1971), p. 327 [in Russian].

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I. M. Silvestrova, A. V. Vinogradov, A. V. Shygorin, T. N. Turskaya, G. S. Belikova, and Ya. V. Pisarevskiy, “Elastic, piezoelectric, acousto-optic and non-linear optical properties of caesium ortosulphobenzoat crystals,” Kristallografiya 35, 906-911 (1990) [in Russian].

Yurkevych, O. V.

H. P. Laba, O. V. Yurkevych, I. D. Karbovnyk, M. V. Kaidan, S. S. Dumych, I. M. Solskii, and A. S. Andrushchak, “Spatial anisotropy of electro-, piezo- and acousto-optic effects in crystalline materials of solid electronics. Approbation on example of LiNbO3 and LiNbO3:MgO part II. Completing of elastic and piezoelectric coefficients matrix for LiNbO3 and LiNbO3:MgO crystals,” Herald Lviv Polytechnic National Univ. (Electronics) 619, 172-180 (2008).

Zaritskii, I. M.

D. Yu. Sugak, A. O. Matkovskii, I. M. Solskii, B. M. Kopko, V. Ya. Oliinyk, I. V. Stefanskii, V. M. Gaba, V. V. Grabowskii, I. M. Zaritskii, and L. G. Rakitina, “Growth and optical properties of LiNbO3:MgO single crystals,” Cryst. Res.?echnol. 32, 805-811 (1997).
[CrossRef]

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[CrossRef]

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[CrossRef]

Herald Lviv Polytechnic National Univ.

H. P. Laba, O. V. Yurkevych, I. D. Karbovnyk, M. V. Kaidan, S. S. Dumych, I. M. Solskii, and A. S. Andrushchak, “Spatial anisotropy of electro-, piezo- and acousto-optic effects in crystalline materials of solid electronics. Approbation on example of LiNbO3 and LiNbO3:MgO part II. Completing of elastic and piezoelectric coefficients matrix for LiNbO3 and LiNbO3:MgO crystals,” Herald Lviv Polytechnic National Univ. (Electronics) 619, 172-180 (2008).

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Nonparallelism of the sample leads to an error ( δ * d k ) in the determination of the piezo-optic coefficients: 1 and 2 are the laser beam positions at F m = 0 and F m 0 , respectively. (а) Normal sample orientation and (b) inverted sample orientation (turned by 180 ° around the laser beam). By combining the normal and inverted sample orientations the error due to sample nonparallelism can be eliminated.

Fig. 2
Fig. 2

Sample orientation required for the determination of POCs π 14 , π 41 , and π 44 .

Tables (3)

Tables Icon

Table 1 Results of Piezo-Optic Measurements of Li Nb O 3 :MgO Crystals in Different Sample Geometries a

Tables Icon

Table 2 POCs π im of Li Nb O 3 :MgO and Li Nb O 3 Crystals a

Tables Icon

Table 3 Effective POCs π km * of Li Nb O 3 :MgO and Li Nb O 3 Crystals a

Equations (22)

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δ Δ k = 1 2 π i m σ m n i 3 d k + S k m σ m d k ( n i 1 ) ,
π im = λ σ im n i 3 d k + 2 S km n i 3 ( n i 1 ) ,
π im = λ 2 n i 3 d k ( 1 σ im + 1 σ im ) + 2 S km n i 3 ( n i 1 ) ,
π 14 + π 12 + π 13 = λ n 1 3 ( 1 d 4 ¯ σ 14 + 1 d 4 ¯ σ 14 ) + n 1 1 n 1 3 ( S 11 + S 33 S 44 + 2 S 13 ) ,
π 14 + π 12 + π 13 = λ n 1 3 ( 1 d 4 σ 1 4 ¯ + 1 d 4 σ 1 4 ¯ ) + n 1 1 n 1 3 ( S 11 + S 33 S 44 + 2 S 13 ) .
π 14 = λ 2 n 1 3 ( 1 σ 14 0 + 1 σ 14 0 1 σ 1 4 ¯ 0 - 1 σ 1 4 ¯ 0 ) ,
π 41 = λ 4 n 4 3 ( 1 σ 41 0 + 1 σ 41 0 1 σ 4 ¯ 1 0 1 σ 4 ¯ 1 0 ) S 14 n 4 1 n 4 3 .
π 44 + 1 2 ( π 11 + π 13 + π 31 + π 33 ) = λ 2 n 4 3 · ( 1 σ 44 0 + 1 σ 44 0 + 1 σ 44 ¯ 0 + 1 σ 44 ¯ 0 ) + ( S 11 + S 33 S 44 + 2 S 13 ) · n 4 1 n 4 3 .
π 11 = λ 2 n 1 3 d 2 ( 1 σ 11 + 1 σ 11 ) + 2 S 21 ( n 1 1 ) n 1 3 .
π 11 = λ 2 n 1 3 d 4 ( 1 σ 11 ( k = 4 ) + 1 σ 11 ( k = 4 ) ) + ( S 12 + S 13 + S 14 ) n 1 - 1 n 1 3 .
π 11 = λ 2 n 1 3 d 4 ¯ ( 1 σ 11 ( k = 4 ¯ ) + 1 σ 11 ( k = 4 ¯ ) ) + ( S 12 + S 13 S 14 ) n 1 1 n 1 3 .
π 12 + π 13 = λ 2 n 1 3 ( 1 d 4 ¯ σ 14 + 1 d 4 ¯ σ 14 + 1 d 4 σ 1 4 ¯ + 1 d 4 σ 1 4 ¯ ) + ( S 11 + S 33 S 44 + 2 S 13 ) n 1 1 n 1 3 .
π 12 + π 31 = λ 2 n 4 3 ( 1 d 4 ¯ σ 41 + 1 d 4 ¯ σ 41 + 1 d 4 σ 4 ¯ 1 + 1 d 4 σ 4 ¯ 1 ) + 2 ( S 12 + S 13 ) n 4 1 n 4 3 ,
π 41 + 1 2 π 14 = λ 2 n 4 3 ( 1 d 4 ¯ σ 44 + 1 d 4 ¯ σ 44 1 d 4 σ 4 ¯ 4 ¯ 1 d 4 σ 4 ¯ 4 ¯ ) .
n 4 = 2 n 1 · n 3 / n 1 2 + n 3 2 = 2.236.
π km * = 2 δ ( Δ n k ) σ m = 2 σ m ( δ n i δ n j ) ,
δ n i = 1 2 π im σ m n i 3 .
π km * = π im n i 3 π j m n j 3 ,
π 4 4 ¯ * = 2 σ 4 ¯ ( δ n 4 ¯ δ n 1 ) ,
δ n 4 ¯ = 1 8 ( π 11 + π 13 + π 14 + π 31 + π 33 + 2 π 41 + 2 π 44 ) σ 4 ¯ n 4 3 ,
δ n 1 = 1 4 ( π 11 + π 13 + π 14 ) σ 4 ¯ n 1 3 .
π 4 4 ¯ * = 1 4 ( π 11 + π 13 + π 14 + π 31 + π 33 + 2 π 41 + 2 π 44 ) × n 4 3 1 2 ( π 12 + π 13 + π 14 ) n 1 3 .

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