Abstract

Recently determined complete sets of materials parameters describing the dielectric, elastic, piezoelectric, elasto-optic, and electro-optic properties of BaTiO3 and KNbO3 crystals at room temperature are used to calculate the effective electro-optic coefficients and dielectric constants required for describing photorefractive phenomena. We show a substantial deviation of the new values from the electro-optic coefficients for homogeneously applied electric fields that were used previously in describing the photorefractive effects. We derive angular dependences of the effective electro-optic coefficients and the effective dielectric constants relevant for grating recording in both crystals and verify them experimentally.

© 1995 Optical Society of America

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  1. P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Applications I (Springer-Verlag, Berlin, 1988).
    [CrossRef]
  2. P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
    [CrossRef]
  3. A. A. Izvanov, A. E. Mandel, N. D. Khat’kov, and S. M. Shandarov, “Influence of the piezoelectric effect on hologram writing and reconstruction in photorefractive crystals,” Optoelectronics 2, 80–84 (1986) [Avtometriya 2, 79–84 (1986)].
  4. S. I. Stepanov, S. M. Shandarov, and N. D. Khat’kov, “Photoelastic contribution to the photorefractive effect in cubic crystals,” Sov. Phys. Solid State 29, 1754–1756 (1987).
  5. G. Pauliat, M. Mathey, and G. Roosen, “Influence of piezoelectricity on the photorefractive effect,” J. Opt. Soc. Am. B 8, 1942–1946 (1991).
    [CrossRef]
  6. P. Günter and M. Zgonik, “Clamped–unclamped E-O coefficients dilemma in photorefractive phenomena,” Opt. Lett. 16, 1826–1828 (1991).
    [CrossRef]
  7. M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3crystal,” Phys. Rev. B 50, 5941–5949 (1994).
    [CrossRef]
  8. M. Zgonik, R. Schlesser, I. Biaggio, E. Voit, J. Tscherry, and P. Günter, “Materials constants of KNbO3relevant for electro- and acousto-optics,” J. Appl. Phys. 74, 1287–1297 (1993).
    [CrossRef]
  9. P. Bernasconi, M. Zgonik, and P. Gunter, “Temperature dependence and dispersion of electro-optic and elasto-optic effect in perovskite crystals,” J. Appl. Phys. (to be published).
  10. K. Buse, S. Riehemann, S. Loheide, H. Hesse, F. Mersch, and E. Krätzig, “Refractive indices of single domain BaTiO3for different wavelengths and temperatures,” Phys. Status Solidi (a) 135, K87–K89 (1993).
    [CrossRef]
  11. B. Zysset, I. Biaggio, and P. Günter, “Refractive indices of orthorhombic KNbO3. I: Dispersion and temperature dependence,” J. Opt. Soc. Am. B 9, 380–386 (1992).
    [CrossRef]
  12. J. Sapriel, Acousto-optics (Wiley, Chichester, UK, 1979).
  13. D. F. Nelson and M. Lax, “New symmetry for acousto-optic scattering,” Phys. Rev. Lett. 24, 379–380 (1970).
    [CrossRef]
  14. S. Shandarov, “Influence of piezoelectric effect on photorefractive gratings in electro-optic crystals,” Appl. Phys. A 55, 91–96 (1992).
    [CrossRef]
  15. V. V. Shepelevich, N. N. Egorov, and V. Shepelevich, “Orientation and polarization effects of two-beam coupling in a cubic optically active photorefractive piezoelectric BSO crystal,” J. Opt. Soc. Am. B 11, 1394–1402 (1994).
    [CrossRef]
  16. M. B. Klein and G. C. Valley, “Beam coupling in BaTiO3at 442 nm,” J. Appl. Phys. 57, 4901–4905 (1985).
    [CrossRef]
  17. F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole–electron competition in photorefractive gratings,” Opt. Lett. 11, 312–314 (1986).
    [CrossRef] [PubMed]
  18. C. Medrano, E. Voit, P. Amrhein, and P. Günter, “Optimization of the photorefractive properties of KNbO3crystals,” J. Appl. Phys. 64, 4668–4673 (1988).
    [CrossRef]
  19. M. B. Klein, “Photorefractive properties of BaTiO3,” in Photorefractive Materials and Applications I, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), pp. 195–236.
    [CrossRef]
  20. C. Medrano, M. Zgonik, N. Sonderer, C. Beyeler, S. Krucker, J. Seglins, H. Wüest, and P. Günter, “Photorefractive effect in Cu- and Ni-doped KNbO3in the visible and near infrared,” J. Appl. Phys. 76, 5640–5645 (1994).
    [CrossRef]

1994 (3)

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3crystal,” Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

V. V. Shepelevich, N. N. Egorov, and V. Shepelevich, “Orientation and polarization effects of two-beam coupling in a cubic optically active photorefractive piezoelectric BSO crystal,” J. Opt. Soc. Am. B 11, 1394–1402 (1994).
[CrossRef]

C. Medrano, M. Zgonik, N. Sonderer, C. Beyeler, S. Krucker, J. Seglins, H. Wüest, and P. Günter, “Photorefractive effect in Cu- and Ni-doped KNbO3in the visible and near infrared,” J. Appl. Phys. 76, 5640–5645 (1994).
[CrossRef]

1993 (2)

M. Zgonik, R. Schlesser, I. Biaggio, E. Voit, J. Tscherry, and P. Günter, “Materials constants of KNbO3relevant for electro- and acousto-optics,” J. Appl. Phys. 74, 1287–1297 (1993).
[CrossRef]

K. Buse, S. Riehemann, S. Loheide, H. Hesse, F. Mersch, and E. Krätzig, “Refractive indices of single domain BaTiO3for different wavelengths and temperatures,” Phys. Status Solidi (a) 135, K87–K89 (1993).
[CrossRef]

1992 (2)

B. Zysset, I. Biaggio, and P. Günter, “Refractive indices of orthorhombic KNbO3. I: Dispersion and temperature dependence,” J. Opt. Soc. Am. B 9, 380–386 (1992).
[CrossRef]

S. Shandarov, “Influence of piezoelectric effect on photorefractive gratings in electro-optic crystals,” Appl. Phys. A 55, 91–96 (1992).
[CrossRef]

1991 (2)

1988 (1)

C. Medrano, E. Voit, P. Amrhein, and P. Günter, “Optimization of the photorefractive properties of KNbO3crystals,” J. Appl. Phys. 64, 4668–4673 (1988).
[CrossRef]

1987 (1)

S. I. Stepanov, S. M. Shandarov, and N. D. Khat’kov, “Photoelastic contribution to the photorefractive effect in cubic crystals,” Sov. Phys. Solid State 29, 1754–1756 (1987).

1986 (2)

F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole–electron competition in photorefractive gratings,” Opt. Lett. 11, 312–314 (1986).
[CrossRef] [PubMed]

A. A. Izvanov, A. E. Mandel, N. D. Khat’kov, and S. M. Shandarov, “Influence of the piezoelectric effect on hologram writing and reconstruction in photorefractive crystals,” Optoelectronics 2, 80–84 (1986) [Avtometriya 2, 79–84 (1986)].

1985 (1)

M. B. Klein and G. C. Valley, “Beam coupling in BaTiO3at 442 nm,” J. Appl. Phys. 57, 4901–4905 (1985).
[CrossRef]

1982 (1)

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
[CrossRef]

1970 (1)

D. F. Nelson and M. Lax, “New symmetry for acousto-optic scattering,” Phys. Rev. Lett. 24, 379–380 (1970).
[CrossRef]

Amrhein, P.

C. Medrano, E. Voit, P. Amrhein, and P. Günter, “Optimization of the photorefractive properties of KNbO3crystals,” J. Appl. Phys. 64, 4668–4673 (1988).
[CrossRef]

Bernasconi, P.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3crystal,” Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

P. Bernasconi, M. Zgonik, and P. Gunter, “Temperature dependence and dispersion of electro-optic and elasto-optic effect in perovskite crystals,” J. Appl. Phys. (to be published).

Beyeler, C.

C. Medrano, M. Zgonik, N. Sonderer, C. Beyeler, S. Krucker, J. Seglins, H. Wüest, and P. Günter, “Photorefractive effect in Cu- and Ni-doped KNbO3in the visible and near infrared,” J. Appl. Phys. 76, 5640–5645 (1994).
[CrossRef]

Biaggio, I.

M. Zgonik, R. Schlesser, I. Biaggio, E. Voit, J. Tscherry, and P. Günter, “Materials constants of KNbO3relevant for electro- and acousto-optics,” J. Appl. Phys. 74, 1287–1297 (1993).
[CrossRef]

B. Zysset, I. Biaggio, and P. Günter, “Refractive indices of orthorhombic KNbO3. I: Dispersion and temperature dependence,” J. Opt. Soc. Am. B 9, 380–386 (1992).
[CrossRef]

Buse, K.

K. Buse, S. Riehemann, S. Loheide, H. Hesse, F. Mersch, and E. Krätzig, “Refractive indices of single domain BaTiO3for different wavelengths and temperatures,” Phys. Status Solidi (a) 135, K87–K89 (1993).
[CrossRef]

Duelli, M.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3crystal,” Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

Egorov, N. N.

Garrett, M. H.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3crystal,” Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

Gunter, P.

P. Bernasconi, M. Zgonik, and P. Gunter, “Temperature dependence and dispersion of electro-optic and elasto-optic effect in perovskite crystals,” J. Appl. Phys. (to be published).

Günter, P.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3crystal,” Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

C. Medrano, M. Zgonik, N. Sonderer, C. Beyeler, S. Krucker, J. Seglins, H. Wüest, and P. Günter, “Photorefractive effect in Cu- and Ni-doped KNbO3in the visible and near infrared,” J. Appl. Phys. 76, 5640–5645 (1994).
[CrossRef]

M. Zgonik, R. Schlesser, I. Biaggio, E. Voit, J. Tscherry, and P. Günter, “Materials constants of KNbO3relevant for electro- and acousto-optics,” J. Appl. Phys. 74, 1287–1297 (1993).
[CrossRef]

B. Zysset, I. Biaggio, and P. Günter, “Refractive indices of orthorhombic KNbO3. I: Dispersion and temperature dependence,” J. Opt. Soc. Am. B 9, 380–386 (1992).
[CrossRef]

P. Günter and M. Zgonik, “Clamped–unclamped E-O coefficients dilemma in photorefractive phenomena,” Opt. Lett. 16, 1826–1828 (1991).
[CrossRef]

C. Medrano, E. Voit, P. Amrhein, and P. Günter, “Optimization of the photorefractive properties of KNbO3crystals,” J. Appl. Phys. 64, 4668–4673 (1988).
[CrossRef]

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
[CrossRef]

Hellwarth, R. W.

Hesse, H.

K. Buse, S. Riehemann, S. Loheide, H. Hesse, F. Mersch, and E. Krätzig, “Refractive indices of single domain BaTiO3for different wavelengths and temperatures,” Phys. Status Solidi (a) 135, K87–K89 (1993).
[CrossRef]

Izvanov, A. A.

A. A. Izvanov, A. E. Mandel, N. D. Khat’kov, and S. M. Shandarov, “Influence of the piezoelectric effect on hologram writing and reconstruction in photorefractive crystals,” Optoelectronics 2, 80–84 (1986) [Avtometriya 2, 79–84 (1986)].

Jonathan, J. M. C.

Khat’kov, N. D.

S. I. Stepanov, S. M. Shandarov, and N. D. Khat’kov, “Photoelastic contribution to the photorefractive effect in cubic crystals,” Sov. Phys. Solid State 29, 1754–1756 (1987).

A. A. Izvanov, A. E. Mandel, N. D. Khat’kov, and S. M. Shandarov, “Influence of the piezoelectric effect on hologram writing and reconstruction in photorefractive crystals,” Optoelectronics 2, 80–84 (1986) [Avtometriya 2, 79–84 (1986)].

Klein, M. B.

M. B. Klein and G. C. Valley, “Beam coupling in BaTiO3at 442 nm,” J. Appl. Phys. 57, 4901–4905 (1985).
[CrossRef]

M. B. Klein, “Photorefractive properties of BaTiO3,” in Photorefractive Materials and Applications I, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), pp. 195–236.
[CrossRef]

Krätzig, E.

K. Buse, S. Riehemann, S. Loheide, H. Hesse, F. Mersch, and E. Krätzig, “Refractive indices of single domain BaTiO3for different wavelengths and temperatures,” Phys. Status Solidi (a) 135, K87–K89 (1993).
[CrossRef]

Krucker, S.

C. Medrano, M. Zgonik, N. Sonderer, C. Beyeler, S. Krucker, J. Seglins, H. Wüest, and P. Günter, “Photorefractive effect in Cu- and Ni-doped KNbO3in the visible and near infrared,” J. Appl. Phys. 76, 5640–5645 (1994).
[CrossRef]

Lax, M.

D. F. Nelson and M. Lax, “New symmetry for acousto-optic scattering,” Phys. Rev. Lett. 24, 379–380 (1970).
[CrossRef]

Loheide, S.

K. Buse, S. Riehemann, S. Loheide, H. Hesse, F. Mersch, and E. Krätzig, “Refractive indices of single domain BaTiO3for different wavelengths and temperatures,” Phys. Status Solidi (a) 135, K87–K89 (1993).
[CrossRef]

Mandel, A. E.

A. A. Izvanov, A. E. Mandel, N. D. Khat’kov, and S. M. Shandarov, “Influence of the piezoelectric effect on hologram writing and reconstruction in photorefractive crystals,” Optoelectronics 2, 80–84 (1986) [Avtometriya 2, 79–84 (1986)].

Mathey, M.

Medrano, C.

C. Medrano, M. Zgonik, N. Sonderer, C. Beyeler, S. Krucker, J. Seglins, H. Wüest, and P. Günter, “Photorefractive effect in Cu- and Ni-doped KNbO3in the visible and near infrared,” J. Appl. Phys. 76, 5640–5645 (1994).
[CrossRef]

C. Medrano, E. Voit, P. Amrhein, and P. Günter, “Optimization of the photorefractive properties of KNbO3crystals,” J. Appl. Phys. 64, 4668–4673 (1988).
[CrossRef]

Mersch, F.

K. Buse, S. Riehemann, S. Loheide, H. Hesse, F. Mersch, and E. Krätzig, “Refractive indices of single domain BaTiO3for different wavelengths and temperatures,” Phys. Status Solidi (a) 135, K87–K89 (1993).
[CrossRef]

Nelson, D. F.

D. F. Nelson and M. Lax, “New symmetry for acousto-optic scattering,” Phys. Rev. Lett. 24, 379–380 (1970).
[CrossRef]

Pauliat, G.

Riehemann, S.

K. Buse, S. Riehemann, S. Loheide, H. Hesse, F. Mersch, and E. Krätzig, “Refractive indices of single domain BaTiO3for different wavelengths and temperatures,” Phys. Status Solidi (a) 135, K87–K89 (1993).
[CrossRef]

Roosen, G.

Rytz, D.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3crystal,” Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

Sapriel, J.

J. Sapriel, Acousto-optics (Wiley, Chichester, UK, 1979).

Schlesser, R.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3crystal,” Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

M. Zgonik, R. Schlesser, I. Biaggio, E. Voit, J. Tscherry, and P. Günter, “Materials constants of KNbO3relevant for electro- and acousto-optics,” J. Appl. Phys. 74, 1287–1297 (1993).
[CrossRef]

Seglins, J.

C. Medrano, M. Zgonik, N. Sonderer, C. Beyeler, S. Krucker, J. Seglins, H. Wüest, and P. Günter, “Photorefractive effect in Cu- and Ni-doped KNbO3in the visible and near infrared,” J. Appl. Phys. 76, 5640–5645 (1994).
[CrossRef]

Shandarov, S.

S. Shandarov, “Influence of piezoelectric effect on photorefractive gratings in electro-optic crystals,” Appl. Phys. A 55, 91–96 (1992).
[CrossRef]

Shandarov, S. M.

S. I. Stepanov, S. M. Shandarov, and N. D. Khat’kov, “Photoelastic contribution to the photorefractive effect in cubic crystals,” Sov. Phys. Solid State 29, 1754–1756 (1987).

A. A. Izvanov, A. E. Mandel, N. D. Khat’kov, and S. M. Shandarov, “Influence of the piezoelectric effect on hologram writing and reconstruction in photorefractive crystals,” Optoelectronics 2, 80–84 (1986) [Avtometriya 2, 79–84 (1986)].

Shepelevich, V.

Shepelevich, V. V.

Sonderer, N.

C. Medrano, M. Zgonik, N. Sonderer, C. Beyeler, S. Krucker, J. Seglins, H. Wüest, and P. Günter, “Photorefractive effect in Cu- and Ni-doped KNbO3in the visible and near infrared,” J. Appl. Phys. 76, 5640–5645 (1994).
[CrossRef]

Stepanov, S. I.

S. I. Stepanov, S. M. Shandarov, and N. D. Khat’kov, “Photoelastic contribution to the photorefractive effect in cubic crystals,” Sov. Phys. Solid State 29, 1754–1756 (1987).

Strohkendl, F. P.

Tscherry, J.

M. Zgonik, R. Schlesser, I. Biaggio, E. Voit, J. Tscherry, and P. Günter, “Materials constants of KNbO3relevant for electro- and acousto-optics,” J. Appl. Phys. 74, 1287–1297 (1993).
[CrossRef]

Valley, G. C.

M. B. Klein and G. C. Valley, “Beam coupling in BaTiO3at 442 nm,” J. Appl. Phys. 57, 4901–4905 (1985).
[CrossRef]

Voit, E.

M. Zgonik, R. Schlesser, I. Biaggio, E. Voit, J. Tscherry, and P. Günter, “Materials constants of KNbO3relevant for electro- and acousto-optics,” J. Appl. Phys. 74, 1287–1297 (1993).
[CrossRef]

C. Medrano, E. Voit, P. Amrhein, and P. Günter, “Optimization of the photorefractive properties of KNbO3crystals,” J. Appl. Phys. 64, 4668–4673 (1988).
[CrossRef]

Wu, X.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3crystal,” Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

Wüest, H.

C. Medrano, M. Zgonik, N. Sonderer, C. Beyeler, S. Krucker, J. Seglins, H. Wüest, and P. Günter, “Photorefractive effect in Cu- and Ni-doped KNbO3in the visible and near infrared,” J. Appl. Phys. 76, 5640–5645 (1994).
[CrossRef]

Zgonik, M.

C. Medrano, M. Zgonik, N. Sonderer, C. Beyeler, S. Krucker, J. Seglins, H. Wüest, and P. Günter, “Photorefractive effect in Cu- and Ni-doped KNbO3in the visible and near infrared,” J. Appl. Phys. 76, 5640–5645 (1994).
[CrossRef]

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3crystal,” Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

M. Zgonik, R. Schlesser, I. Biaggio, E. Voit, J. Tscherry, and P. Günter, “Materials constants of KNbO3relevant for electro- and acousto-optics,” J. Appl. Phys. 74, 1287–1297 (1993).
[CrossRef]

P. Günter and M. Zgonik, “Clamped–unclamped E-O coefficients dilemma in photorefractive phenomena,” Opt. Lett. 16, 1826–1828 (1991).
[CrossRef]

P. Bernasconi, M. Zgonik, and P. Gunter, “Temperature dependence and dispersion of electro-optic and elasto-optic effect in perovskite crystals,” J. Appl. Phys. (to be published).

Zhu, Y.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3crystal,” Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

Zysset, B.

Appl. Phys. A (1)

S. Shandarov, “Influence of piezoelectric effect on photorefractive gratings in electro-optic crystals,” Appl. Phys. A 55, 91–96 (1992).
[CrossRef]

J. Appl. Phys. (4)

M. B. Klein and G. C. Valley, “Beam coupling in BaTiO3at 442 nm,” J. Appl. Phys. 57, 4901–4905 (1985).
[CrossRef]

M. Zgonik, R. Schlesser, I. Biaggio, E. Voit, J. Tscherry, and P. Günter, “Materials constants of KNbO3relevant for electro- and acousto-optics,” J. Appl. Phys. 74, 1287–1297 (1993).
[CrossRef]

C. Medrano, E. Voit, P. Amrhein, and P. Günter, “Optimization of the photorefractive properties of KNbO3crystals,” J. Appl. Phys. 64, 4668–4673 (1988).
[CrossRef]

C. Medrano, M. Zgonik, N. Sonderer, C. Beyeler, S. Krucker, J. Seglins, H. Wüest, and P. Günter, “Photorefractive effect in Cu- and Ni-doped KNbO3in the visible and near infrared,” J. Appl. Phys. 76, 5640–5645 (1994).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Lett. (2)

Optoelectronics (1)

A. A. Izvanov, A. E. Mandel, N. D. Khat’kov, and S. M. Shandarov, “Influence of the piezoelectric effect on hologram writing and reconstruction in photorefractive crystals,” Optoelectronics 2, 80–84 (1986) [Avtometriya 2, 79–84 (1986)].

Phys. Rep. (1)

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
[CrossRef]

Phys. Rev. B (1)

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3crystal,” Phys. Rev. B 50, 5941–5949 (1994).
[CrossRef]

Phys. Rev. Lett. (1)

D. F. Nelson and M. Lax, “New symmetry for acousto-optic scattering,” Phys. Rev. Lett. 24, 379–380 (1970).
[CrossRef]

Phys. Status Solidi (a) (1)

K. Buse, S. Riehemann, S. Loheide, H. Hesse, F. Mersch, and E. Krätzig, “Refractive indices of single domain BaTiO3for different wavelengths and temperatures,” Phys. Status Solidi (a) 135, K87–K89 (1993).
[CrossRef]

Sov. Phys. Solid State (1)

S. I. Stepanov, S. M. Shandarov, and N. D. Khat’kov, “Photoelastic contribution to the photorefractive effect in cubic crystals,” Sov. Phys. Solid State 29, 1754–1756 (1987).

Other (4)

P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Applications I (Springer-Verlag, Berlin, 1988).
[CrossRef]

P. Bernasconi, M. Zgonik, and P. Gunter, “Temperature dependence and dispersion of electro-optic and elasto-optic effect in perovskite crystals,” J. Appl. Phys. (to be published).

J. Sapriel, Acousto-optics (Wiley, Chichester, UK, 1979).

M. B. Klein, “Photorefractive properties of BaTiO3,” in Photorefractive Materials and Applications I, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), pp. 195–236.
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Figures (7)

Fig. 1
Fig. 1

Effective dielectric constant eff PR of BaTiO3 to be used in a photorefractive experiment (solid curve) when the grating vector lies in the zx plane at an angle α from the z axis. For comparison the effective dielectric constant eff S = i i S n i n i (dashed curve) and eff T = i i T n i n i (dotted curve) for clamped and unclamped crystals subjected to a uniform electric field are shown.

Fig. 2
Fig. 2

Effective EO coefficients r i j eff ( 515 nm ) of BaTiO3 for a periodic electric field in the zx plane. The upper graph shows r 33 eff (solid curve), r 11 eff (dashed curve), r 22 eff (dotted curve), and for comparison r 33 eff in clamped (dotted–dashed curve) and unclamped (double-dotted–dashed curve) crystals under the influence of a uniform field. The lower graph shows r 23 eff = r 32 eff (solid curve) and for comparison r 23 eff in clamped (dotted–double-dashed curve) and unclamped (double-dotted–dashed) crystals.

Fig. 3
Fig. 3

Charge-diffusion limited two-beam coupling experiment in BaTiO3 and KNbO3 platelets with edges parallel to the crystallographic axes. The sample is adjusted symmetrically to the beams and rotated about the axis perpendicular to the large surface. An Ar+-ion laser at a wavelength of 515 nm is used at intensities of approximately 1 W cm−2, and the intensity ratio between the pump and the probe beams is 10. The polarizations of the two interacting beams are the same and are selected to correspond to an eigenpolarization direction. The rotation angle of the sample determines the direction of the grating vector inside the sample. The polarizations are rotated by the same angle to preserve the eigenpolarization of the beams inside the sample. A small angle between the beams, 2θ, is used to ensure that ESC is determined by the diffusion-limited field only and that the polarizations of the beams are practically parallel to the crystallographic axes. PR, photorefractive.

Fig. 4
Fig. 4

Exponential two-beam coupling coefficient Γ is a nominally undoped BaTiO3 crystal for both polarizations of the beams as a function of the grating vector orientation in the zx plane. The angle between the beams in air is 2θ = 1.74°. Filled circles show the measured values for polarization parallel to the z axis, and open circles show them parallel to the x axis. The solid and dotted curves are calculated from the single charge (holes) carrier model. Charge competition reduces Γ by ~35%, as shown by the dashed curves.

Fig. 5
Fig. 5

Exponential two-beam coupling coefficient Γ in a Fe:KNbO3 crystal as a function of the grating vector orientation in the zx plane. The measurements at three different angles between the beams in air, 2θ = 2.8° (●), 1.9° (×), and 0.9° (○), are shown, together with theoretical curves—calculated from a single charge carrier model—shown as solid, dashed, and dotted curves, respectively. The upper part shows Γ for z polarization, and the lower part shows Γ for x polarization.

Fig. 6
Fig. 6

Two components of the effective EO tensor of Fe:KNbO3 as determined from the two-beam coupling measurements with the grating vector in the zx plane. The circles show the values for r 33 eff and r 11 eff, as determined from the measurements presented in Fig. 5 with σ ¯ = 0.95. Solid and dashed curves are calculated r 33 eff and r 11 eff, respectively.

Fig. 7
Fig. 7

Two components of the effective EO tensor of doped KNbO3 crystals as determined from the two-beam coupling measurements with the grating vector in the zy plane are shown as points, Fe-doped (●), Cu-doped (×), and Rh-doped (○) samples were used for the measurements. Various degrees of electron–hole competition in these samples are described by σ ¯ = 0.8 for Fe- and Rh-doped and by σ ¯ = 0.6 for Cu-doped samples. Solid and dashed curves are calculated r 33 eff and r 22 eff, respectively.

Equations (15)

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ρ 0 K g 0 = ( i j S n i n j + 0 - 1 e i j k e m n l n i n j n m n n A k l - 1 ) E SC = eff PR E SC .
A k l = C k p l q E n p n q .
B i = e p i q n p n q ,
r i j eff = r i j k S n k + p i j k l E n l A k m - 1 B m .
eff PR = 1937 - 2066 cos 2 α + 321 cos 4 α - 69 cos 6 α - 40 cos 8 α , r 11 eff ( 633 nm ) = ( 34.5 cos α - 0.5 cos 3 α - 15 cos 5 α - 1.5 cos 7 α + 1.5 cos 9 α )             pm V - 1 , r 22 eff ( 633 nm ) = ( 31.5 cos α - 18.5 cos 3 α + 4 cos 5 α + 2.5 cos 7 α )             pm V - 1 , r 33 eff ( 633 nm ) = ( 121 cos α - 87 cos 3 α + 32 cos 5 α + 12 cos 7 α )             pm V - 1 , r 13 eff ( 633 nm ) = ( 1133 sin α - 113 sin 3 α + 69 sin 5 α + 19 sin 7 α )             pm V - 1 , r 11 eff ( 515 nm ) = ( 40 cos α - 0 cos 3 α - 18 cos 5 α - 2 cos 7 α + 1.5 cos 9 α )             pm V - 1 , r 22 eff ( 515 nm ) = ( 36.5 cos α - 21.5 cos 3 α + 4.5 cos 5 α + 2.5 cos 7 α )             pm V - 1 , r 33 eff ( 515 nm ) = ( 141 cos α - 102 cos 3 α + 37 cos 5 α + 14 cos 7 α )             pm V - 1 , r 13 eff ( 515 nm ) = ( 1160 sin α - 115 sin 3 α + 70 sin 5 α + 19 sin 7 α )             pm V - 1 .
eff PR = 73 - 46 cos 2 α + 19 cos 4 α - 12 cos 6 α + 3 cos 8 α - 2 cos 10 α , r 11 eff = ( 42 cos α - 12 cos 3 α + 10 cos 5 α - 2 cos 7 α + 2 cos 9 α )             pm V - 1 , r 22 eff = ( 11.5 cos α - 3.5 cos 3 α + 3.5 cos 5 α )             pm V - 1 , r 33 eff = ( 74 cos α - 17 cos 3 α + 5 cos 5 α - 3 cos 7 α )             pm V - 1 , r 13 eff = ( 91 sin α - 18 sin 3 α + 20 sin 5 α - 3 sin 7 α + 4 sin 9 α )             pm V - 1 .
eff PR = 486 - 470 cos 2 β + 27 cos 4 β - 6 cos 6 β , r 11 eff = ( 50 cos β - 17 cos 3 β + 5 cos 5 β + 1 cos 7 β )             pm V - 1 , r 22 eff = ( 15 cos β - 2.5 cos 3 β - 1 cos 5 β )             pm V - 1 , r 33 eff = ( 76 cos β - 24 cos 3 β + 6.5 cos 5 β + 1.5 cos 7 β )             pm V - 1 , r 23 eff = ( 434 sin β - 18 sin 3 β + 9 sin 5 β + 1.5 sin 7 β )             pm V - 1 .
r eff = d ^ pmp · r eff · d ^ sig ,
Γ = 2 π λ 0 ( n pmp n sig ) 3 / 2 r eff E SC m o ,
m = 2 I pmp I sig I pmp + I sig + I inc ( e ^ pmp · e ^ sig ) .
E SC = m E q E D E q + E D
E q = e N eff eff PR 0 K g ,
E D = k B T K g e ,
Γ = 2 π λ 0 n i 3 r i i eff k B T K g e m m o ,
σ ¯ = μ h p - μ e n μ h p + μ e n ,

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