Abstract

The purpose of this paper is to find the polarizations and spatial orientations of the two interacting counterpropagating coherent light waves which ensure the largest beam coupling in monoclinic photorefractive crystal. The results of calculations are presented that are verified experimentally with Sn2P2S6.

© 2014 Optical Society of America

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References

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  1. A. A. Grabar, M. Jazbinšek, A. N. Shumelyuk, Yu. M. Vysochanskii, G. Montemezzani, and P. Günter, “Photorefractive effects in Sn2P2S6,” in Photorefractive Materials and Their Applications II, P. Günter and J.-P. Huignard, eds. (Springer Verlag, 2007).
  2. Y. Petit, S. Joly, P. Segonds, and B. Boulanger, “Recent advances in monoclinic crystal optics,” Laser Photon. Rev. 7(6), 920–937 (2013).
    [Crossref]
  3. A. Shumelyuk, S. Odoulov, G. Cook, and D. R. Evans, “Coupling of counterpropagating light beams in low symmetry photorefractive crystals,” Opt. Lett. 34(14), 2126–2128 (2009).
    [Crossref] [PubMed]
  4. A. Shumelyuk, A. Volkov, S. Odoulov, G. Cook, and D. R. Evans, “Coupling of counterpropagating light waves in low-symmetry photorefractive crystals,” Appl. Phys. B 100(1), 101–108 (2010).
    [Crossref]
  5. X. Yue, F. Mersch, R. Rupp, U. Hellwig, and M. Simon, “Holographic recording and beam coupling in ferroelectric Bi4Ti3O12,” Phys. Rev. B 53, 8967–8970 (1996).
    [Crossref]
  6. X. Yue, J. Xu, F. Mersch, R. A. Rupp, and E. Krätzig, “Photorefractive properties of Bi4Ti3O12,” Phys. Rev. B 53, 9495–9502 (1997).
    [Crossref]
  7. G. Montemezzani, J. Fousek, P. Günter, and J. Stankowska, “Phase gratings in Fe3+-doped triglycine sulphate single crystals recorded in the ultraviolet spectral region,” Appl. Phys. Lett. 56, 2367–2369 (1990).
    [Crossref]
  8. G. Montemezzani and M. Zgonik, “Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries,” Phys. Rev. E 55(1), 1035–1047 (1997).
    [Crossref]
  9. Y. M. Vysochanskii and V. Y. Slivka, “Ferroelectrics of the Sn2P2S6 family. Properties in Vicinity of Lifshitz Point” (Oriana-Nova, 1994) (in Russian).
  10. V. M. Kedyulich, A. G. Slivka, E. I. Gerzanich, P. P. Guranich, V. S. Shusta, and P. M. Lucach, “The influence of the temperature and uniform pressure on the anisotropy of dielectric properties of the Sn2P2S6 crystal,” Uzhgorod Univ. Bull. Phys. Ser. 5, 30–32 (1999).
  11. A. Shumelyuk, D. Barilov, S. Odoulov, and E. Krätzig, “Anisotropy of the dielectric permittivity of Sn2P2S6 measured with light-induced grating techniques,” Appl. Phys. B 76(4), 417–421 (2003).
    [Crossref]
  12. D. Haertle, A. Guarino, J. Hajfler, G. Montemezzani, and P. Günter, “Refractive indices of Sn2P2S6 at visible and infrared wavelengths,” Opt. Express 13(6), 2046–2057 (2005).
  13. C. Traum, P. L. Inácio, C. Félix, P. Segonds, A. Peña, J. Debray, B. Boulanger, Y. Petit, D. Rytz, G. Montemezzani, P. Goldner, and A. Ferrie, “Direct measurement of the dielectric frame rotation of monoclinic crystals as a function of the wavelength,” Opt. Mater. Express 4, 57–62 (2014).
    [Crossref]
  14. D. Haertle, G. Caimi, A. Haldi, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Yu. M. Vysochanskii, “Electro-optical properties of Sn2P2S6,” Opt. Commun. 215(4), 333–343 (2003).
    [Crossref]
  15. A. Volkov, A. Shumelyuk, S. Odoulov, D. R. Evans, and G. Cook, “Anisotropic diffraction from photorefractive gratings and Pockels tensor of Sn2P2S6,” Opt. Express 16(21), 16923–16934 (2008).
    [Crossref] [PubMed]
  16. G. Montemezzani, M. Aillerie, X. Zheng, H. Remmach, and A. Grabar, “Third column electro-optical coefficients of monoclinic Sn2P2S6,” Opt. Mater. Express 2(7), 920–928 (2012).
    [Crossref]
  17. A. Volkov, “Evaluation of non-diagonal components of Pockels tensor for photorefractive Sn2P2S6 crystal,” Ukr. J. Phys. 58(4), 335–340 (2013).
  18. A. Grabar, “Energy spectra and photoinduced phenomena in ferroelectrc-semiconductor of Sn2P2S6 family,” Dr of Science Thesis, Uzhgorod National University, Ukraine, Uzhgorod (2004).
  19. D. Haertle, “Photorefractive and nonlinear properties of Sn2P2S6,” PhD Thesis, ETH No. 16107, Zürich (2005).
  20. G. Dittmar and H. Schäfer, “Die Stuktur des Di-Zinn-Hexathiohypodiphoshatus Sn2P2S6,” Z. Naturforsch. 29B(5–6), 312–317 (1974).
  21. ANSI/IEEE, Std 176 - IEEE Standard on Piezoelectricity, (IEEE, 1987), p. 242.
  22. C. D. Carpentier and R. Nitsche, “Ferroelectricity in Sn2P2S6,” Mater. Res. Bull. 9(8), 1097–1100 (1974).
    [Crossref]
  23. M. M. Major, Yu. M. Vysochanskii, I. P. Prits, Sh. B. Molnar, V. Yu. Slivka, E. D. Rogach, F. I. Savenko, and A. P. Kudinov, “Piezoeffect in Sn2P2S6 single crystals,” Bull. USSR Acad. Sci., Inorg. Mater. 27(3), 604–606 (1991).
  24. T. Bach, M. Jazbinšek, G. Montemezzani, P. Günter, A. Grabar, and Yu. Vysochanskii, “Tailoring of infrared photorefractive properties of Sn2P2S6 crystals by Te and Sb doping,” J. Opt. Soc. Am. B 24(7), 1535–1541 (2007).
    [Crossref]
  25. A. Shumelyuk, A. Volkov, A. Selinger, M. Imlau, and S. Odoulov, “Frequency-degenerate nonlinear light scattering in low-symmetry crystals,” Opt. Lett. 33(2), 150–152 (2008).
    [Crossref] [PubMed]

2014 (1)

2013 (2)

A. Volkov, “Evaluation of non-diagonal components of Pockels tensor for photorefractive Sn2P2S6 crystal,” Ukr. J. Phys. 58(4), 335–340 (2013).

Y. Petit, S. Joly, P. Segonds, and B. Boulanger, “Recent advances in monoclinic crystal optics,” Laser Photon. Rev. 7(6), 920–937 (2013).
[Crossref]

2012 (1)

2010 (1)

A. Shumelyuk, A. Volkov, S. Odoulov, G. Cook, and D. R. Evans, “Coupling of counterpropagating light waves in low-symmetry photorefractive crystals,” Appl. Phys. B 100(1), 101–108 (2010).
[Crossref]

2009 (1)

2008 (2)

2007 (1)

2005 (1)

D. Haertle, A. Guarino, J. Hajfler, G. Montemezzani, and P. Günter, “Refractive indices of Sn2P2S6 at visible and infrared wavelengths,” Opt. Express 13(6), 2046–2057 (2005).

2003 (2)

A. Shumelyuk, D. Barilov, S. Odoulov, and E. Krätzig, “Anisotropy of the dielectric permittivity of Sn2P2S6 measured with light-induced grating techniques,” Appl. Phys. B 76(4), 417–421 (2003).
[Crossref]

D. Haertle, G. Caimi, A. Haldi, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Yu. M. Vysochanskii, “Electro-optical properties of Sn2P2S6,” Opt. Commun. 215(4), 333–343 (2003).
[Crossref]

1999 (1)

V. M. Kedyulich, A. G. Slivka, E. I. Gerzanich, P. P. Guranich, V. S. Shusta, and P. M. Lucach, “The influence of the temperature and uniform pressure on the anisotropy of dielectric properties of the Sn2P2S6 crystal,” Uzhgorod Univ. Bull. Phys. Ser. 5, 30–32 (1999).

1997 (2)

G. Montemezzani and M. Zgonik, “Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries,” Phys. Rev. E 55(1), 1035–1047 (1997).
[Crossref]

X. Yue, J. Xu, F. Mersch, R. A. Rupp, and E. Krätzig, “Photorefractive properties of Bi4Ti3O12,” Phys. Rev. B 53, 9495–9502 (1997).
[Crossref]

1996 (1)

X. Yue, F. Mersch, R. Rupp, U. Hellwig, and M. Simon, “Holographic recording and beam coupling in ferroelectric Bi4Ti3O12,” Phys. Rev. B 53, 8967–8970 (1996).
[Crossref]

1991 (1)

M. M. Major, Yu. M. Vysochanskii, I. P. Prits, Sh. B. Molnar, V. Yu. Slivka, E. D. Rogach, F. I. Savenko, and A. P. Kudinov, “Piezoeffect in Sn2P2S6 single crystals,” Bull. USSR Acad. Sci., Inorg. Mater. 27(3), 604–606 (1991).

1990 (1)

G. Montemezzani, J. Fousek, P. Günter, and J. Stankowska, “Phase gratings in Fe3+-doped triglycine sulphate single crystals recorded in the ultraviolet spectral region,” Appl. Phys. Lett. 56, 2367–2369 (1990).
[Crossref]

1974 (2)

G. Dittmar and H. Schäfer, “Die Stuktur des Di-Zinn-Hexathiohypodiphoshatus Sn2P2S6,” Z. Naturforsch. 29B(5–6), 312–317 (1974).

C. D. Carpentier and R. Nitsche, “Ferroelectricity in Sn2P2S6,” Mater. Res. Bull. 9(8), 1097–1100 (1974).
[Crossref]

Aillerie, M.

Bach, T.

Barilov, D.

A. Shumelyuk, D. Barilov, S. Odoulov, and E. Krätzig, “Anisotropy of the dielectric permittivity of Sn2P2S6 measured with light-induced grating techniques,” Appl. Phys. B 76(4), 417–421 (2003).
[Crossref]

Boulanger, B.

Caimi, G.

D. Haertle, G. Caimi, A. Haldi, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Yu. M. Vysochanskii, “Electro-optical properties of Sn2P2S6,” Opt. Commun. 215(4), 333–343 (2003).
[Crossref]

Carpentier, C. D.

C. D. Carpentier and R. Nitsche, “Ferroelectricity in Sn2P2S6,” Mater. Res. Bull. 9(8), 1097–1100 (1974).
[Crossref]

Cook, G.

Debray, J.

Dittmar, G.

G. Dittmar and H. Schäfer, “Die Stuktur des Di-Zinn-Hexathiohypodiphoshatus Sn2P2S6,” Z. Naturforsch. 29B(5–6), 312–317 (1974).

Evans, D. R.

Félix, C.

Ferrie, A.

Fousek, J.

G. Montemezzani, J. Fousek, P. Günter, and J. Stankowska, “Phase gratings in Fe3+-doped triglycine sulphate single crystals recorded in the ultraviolet spectral region,” Appl. Phys. Lett. 56, 2367–2369 (1990).
[Crossref]

Gerzanich, E. I.

V. M. Kedyulich, A. G. Slivka, E. I. Gerzanich, P. P. Guranich, V. S. Shusta, and P. M. Lucach, “The influence of the temperature and uniform pressure on the anisotropy of dielectric properties of the Sn2P2S6 crystal,” Uzhgorod Univ. Bull. Phys. Ser. 5, 30–32 (1999).

Goldner, P.

Grabar, A.

Grabar, A. A.

D. Haertle, G. Caimi, A. Haldi, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Yu. M. Vysochanskii, “Electro-optical properties of Sn2P2S6,” Opt. Commun. 215(4), 333–343 (2003).
[Crossref]

A. A. Grabar, M. Jazbinšek, A. N. Shumelyuk, Yu. M. Vysochanskii, G. Montemezzani, and P. Günter, “Photorefractive effects in Sn2P2S6,” in Photorefractive Materials and Their Applications II, P. Günter and J.-P. Huignard, eds. (Springer Verlag, 2007).

Guarino, A.

D. Haertle, A. Guarino, J. Hajfler, G. Montemezzani, and P. Günter, “Refractive indices of Sn2P2S6 at visible and infrared wavelengths,” Opt. Express 13(6), 2046–2057 (2005).

Günter, P.

T. Bach, M. Jazbinšek, G. Montemezzani, P. Günter, A. Grabar, and Yu. Vysochanskii, “Tailoring of infrared photorefractive properties of Sn2P2S6 crystals by Te and Sb doping,” J. Opt. Soc. Am. B 24(7), 1535–1541 (2007).
[Crossref]

D. Haertle, A. Guarino, J. Hajfler, G. Montemezzani, and P. Günter, “Refractive indices of Sn2P2S6 at visible and infrared wavelengths,” Opt. Express 13(6), 2046–2057 (2005).

D. Haertle, G. Caimi, A. Haldi, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Yu. M. Vysochanskii, “Electro-optical properties of Sn2P2S6,” Opt. Commun. 215(4), 333–343 (2003).
[Crossref]

G. Montemezzani, J. Fousek, P. Günter, and J. Stankowska, “Phase gratings in Fe3+-doped triglycine sulphate single crystals recorded in the ultraviolet spectral region,” Appl. Phys. Lett. 56, 2367–2369 (1990).
[Crossref]

A. A. Grabar, M. Jazbinšek, A. N. Shumelyuk, Yu. M. Vysochanskii, G. Montemezzani, and P. Günter, “Photorefractive effects in Sn2P2S6,” in Photorefractive Materials and Their Applications II, P. Günter and J.-P. Huignard, eds. (Springer Verlag, 2007).

Guranich, P. P.

V. M. Kedyulich, A. G. Slivka, E. I. Gerzanich, P. P. Guranich, V. S. Shusta, and P. M. Lucach, “The influence of the temperature and uniform pressure on the anisotropy of dielectric properties of the Sn2P2S6 crystal,” Uzhgorod Univ. Bull. Phys. Ser. 5, 30–32 (1999).

Haertle, D.

D. Haertle, A. Guarino, J. Hajfler, G. Montemezzani, and P. Günter, “Refractive indices of Sn2P2S6 at visible and infrared wavelengths,” Opt. Express 13(6), 2046–2057 (2005).

D. Haertle, G. Caimi, A. Haldi, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Yu. M. Vysochanskii, “Electro-optical properties of Sn2P2S6,” Opt. Commun. 215(4), 333–343 (2003).
[Crossref]

D. Haertle, “Photorefractive and nonlinear properties of Sn2P2S6,” PhD Thesis, ETH No. 16107, Zürich (2005).

Hajfler, J.

D. Haertle, A. Guarino, J. Hajfler, G. Montemezzani, and P. Günter, “Refractive indices of Sn2P2S6 at visible and infrared wavelengths,” Opt. Express 13(6), 2046–2057 (2005).

Haldi, A.

D. Haertle, G. Caimi, A. Haldi, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Yu. M. Vysochanskii, “Electro-optical properties of Sn2P2S6,” Opt. Commun. 215(4), 333–343 (2003).
[Crossref]

Hellwig, U.

X. Yue, F. Mersch, R. Rupp, U. Hellwig, and M. Simon, “Holographic recording and beam coupling in ferroelectric Bi4Ti3O12,” Phys. Rev. B 53, 8967–8970 (1996).
[Crossref]

Imlau, M.

Inácio, P. L.

Jazbinšek, M.

T. Bach, M. Jazbinšek, G. Montemezzani, P. Günter, A. Grabar, and Yu. Vysochanskii, “Tailoring of infrared photorefractive properties of Sn2P2S6 crystals by Te and Sb doping,” J. Opt. Soc. Am. B 24(7), 1535–1541 (2007).
[Crossref]

A. A. Grabar, M. Jazbinšek, A. N. Shumelyuk, Yu. M. Vysochanskii, G. Montemezzani, and P. Günter, “Photorefractive effects in Sn2P2S6,” in Photorefractive Materials and Their Applications II, P. Günter and J.-P. Huignard, eds. (Springer Verlag, 2007).

Joly, S.

Y. Petit, S. Joly, P. Segonds, and B. Boulanger, “Recent advances in monoclinic crystal optics,” Laser Photon. Rev. 7(6), 920–937 (2013).
[Crossref]

Kedyulich, V. M.

V. M. Kedyulich, A. G. Slivka, E. I. Gerzanich, P. P. Guranich, V. S. Shusta, and P. M. Lucach, “The influence of the temperature and uniform pressure on the anisotropy of dielectric properties of the Sn2P2S6 crystal,” Uzhgorod Univ. Bull. Phys. Ser. 5, 30–32 (1999).

Krätzig, E.

A. Shumelyuk, D. Barilov, S. Odoulov, and E. Krätzig, “Anisotropy of the dielectric permittivity of Sn2P2S6 measured with light-induced grating techniques,” Appl. Phys. B 76(4), 417–421 (2003).
[Crossref]

X. Yue, J. Xu, F. Mersch, R. A. Rupp, and E. Krätzig, “Photorefractive properties of Bi4Ti3O12,” Phys. Rev. B 53, 9495–9502 (1997).
[Crossref]

Kudinov, A. P.

M. M. Major, Yu. M. Vysochanskii, I. P. Prits, Sh. B. Molnar, V. Yu. Slivka, E. D. Rogach, F. I. Savenko, and A. P. Kudinov, “Piezoeffect in Sn2P2S6 single crystals,” Bull. USSR Acad. Sci., Inorg. Mater. 27(3), 604–606 (1991).

Lucach, P. M.

V. M. Kedyulich, A. G. Slivka, E. I. Gerzanich, P. P. Guranich, V. S. Shusta, and P. M. Lucach, “The influence of the temperature and uniform pressure on the anisotropy of dielectric properties of the Sn2P2S6 crystal,” Uzhgorod Univ. Bull. Phys. Ser. 5, 30–32 (1999).

Major, M. M.

M. M. Major, Yu. M. Vysochanskii, I. P. Prits, Sh. B. Molnar, V. Yu. Slivka, E. D. Rogach, F. I. Savenko, and A. P. Kudinov, “Piezoeffect in Sn2P2S6 single crystals,” Bull. USSR Acad. Sci., Inorg. Mater. 27(3), 604–606 (1991).

Mersch, F.

X. Yue, J. Xu, F. Mersch, R. A. Rupp, and E. Krätzig, “Photorefractive properties of Bi4Ti3O12,” Phys. Rev. B 53, 9495–9502 (1997).
[Crossref]

X. Yue, F. Mersch, R. Rupp, U. Hellwig, and M. Simon, “Holographic recording and beam coupling in ferroelectric Bi4Ti3O12,” Phys. Rev. B 53, 8967–8970 (1996).
[Crossref]

Molnar, Sh. B.

M. M. Major, Yu. M. Vysochanskii, I. P. Prits, Sh. B. Molnar, V. Yu. Slivka, E. D. Rogach, F. I. Savenko, and A. P. Kudinov, “Piezoeffect in Sn2P2S6 single crystals,” Bull. USSR Acad. Sci., Inorg. Mater. 27(3), 604–606 (1991).

Montemezzani, G.

C. Traum, P. L. Inácio, C. Félix, P. Segonds, A. Peña, J. Debray, B. Boulanger, Y. Petit, D. Rytz, G. Montemezzani, P. Goldner, and A. Ferrie, “Direct measurement of the dielectric frame rotation of monoclinic crystals as a function of the wavelength,” Opt. Mater. Express 4, 57–62 (2014).
[Crossref]

G. Montemezzani, M. Aillerie, X. Zheng, H. Remmach, and A. Grabar, “Third column electro-optical coefficients of monoclinic Sn2P2S6,” Opt. Mater. Express 2(7), 920–928 (2012).
[Crossref]

T. Bach, M. Jazbinšek, G. Montemezzani, P. Günter, A. Grabar, and Yu. Vysochanskii, “Tailoring of infrared photorefractive properties of Sn2P2S6 crystals by Te and Sb doping,” J. Opt. Soc. Am. B 24(7), 1535–1541 (2007).
[Crossref]

D. Haertle, A. Guarino, J. Hajfler, G. Montemezzani, and P. Günter, “Refractive indices of Sn2P2S6 at visible and infrared wavelengths,” Opt. Express 13(6), 2046–2057 (2005).

D. Haertle, G. Caimi, A. Haldi, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Yu. M. Vysochanskii, “Electro-optical properties of Sn2P2S6,” Opt. Commun. 215(4), 333–343 (2003).
[Crossref]

G. Montemezzani and M. Zgonik, “Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries,” Phys. Rev. E 55(1), 1035–1047 (1997).
[Crossref]

G. Montemezzani, J. Fousek, P. Günter, and J. Stankowska, “Phase gratings in Fe3+-doped triglycine sulphate single crystals recorded in the ultraviolet spectral region,” Appl. Phys. Lett. 56, 2367–2369 (1990).
[Crossref]

A. A. Grabar, M. Jazbinšek, A. N. Shumelyuk, Yu. M. Vysochanskii, G. Montemezzani, and P. Günter, “Photorefractive effects in Sn2P2S6,” in Photorefractive Materials and Their Applications II, P. Günter and J.-P. Huignard, eds. (Springer Verlag, 2007).

Nitsche, R.

C. D. Carpentier and R. Nitsche, “Ferroelectricity in Sn2P2S6,” Mater. Res. Bull. 9(8), 1097–1100 (1974).
[Crossref]

Odoulov, S.

Peña, A.

Petit, Y.

Prits, I. P.

M. M. Major, Yu. M. Vysochanskii, I. P. Prits, Sh. B. Molnar, V. Yu. Slivka, E. D. Rogach, F. I. Savenko, and A. P. Kudinov, “Piezoeffect in Sn2P2S6 single crystals,” Bull. USSR Acad. Sci., Inorg. Mater. 27(3), 604–606 (1991).

Remmach, H.

Rogach, E. D.

M. M. Major, Yu. M. Vysochanskii, I. P. Prits, Sh. B. Molnar, V. Yu. Slivka, E. D. Rogach, F. I. Savenko, and A. P. Kudinov, “Piezoeffect in Sn2P2S6 single crystals,” Bull. USSR Acad. Sci., Inorg. Mater. 27(3), 604–606 (1991).

Rupp, R.

X. Yue, F. Mersch, R. Rupp, U. Hellwig, and M. Simon, “Holographic recording and beam coupling in ferroelectric Bi4Ti3O12,” Phys. Rev. B 53, 8967–8970 (1996).
[Crossref]

Rupp, R. A.

X. Yue, J. Xu, F. Mersch, R. A. Rupp, and E. Krätzig, “Photorefractive properties of Bi4Ti3O12,” Phys. Rev. B 53, 9495–9502 (1997).
[Crossref]

Rytz, D.

Savenko, F. I.

M. M. Major, Yu. M. Vysochanskii, I. P. Prits, Sh. B. Molnar, V. Yu. Slivka, E. D. Rogach, F. I. Savenko, and A. P. Kudinov, “Piezoeffect in Sn2P2S6 single crystals,” Bull. USSR Acad. Sci., Inorg. Mater. 27(3), 604–606 (1991).

Schäfer, H.

G. Dittmar and H. Schäfer, “Die Stuktur des Di-Zinn-Hexathiohypodiphoshatus Sn2P2S6,” Z. Naturforsch. 29B(5–6), 312–317 (1974).

Segonds, P.

Selinger, A.

Shumelyuk, A.

Shumelyuk, A. N.

A. A. Grabar, M. Jazbinšek, A. N. Shumelyuk, Yu. M. Vysochanskii, G. Montemezzani, and P. Günter, “Photorefractive effects in Sn2P2S6,” in Photorefractive Materials and Their Applications II, P. Günter and J.-P. Huignard, eds. (Springer Verlag, 2007).

Shusta, V. S.

V. M. Kedyulich, A. G. Slivka, E. I. Gerzanich, P. P. Guranich, V. S. Shusta, and P. M. Lucach, “The influence of the temperature and uniform pressure on the anisotropy of dielectric properties of the Sn2P2S6 crystal,” Uzhgorod Univ. Bull. Phys. Ser. 5, 30–32 (1999).

Simon, M.

X. Yue, F. Mersch, R. Rupp, U. Hellwig, and M. Simon, “Holographic recording and beam coupling in ferroelectric Bi4Ti3O12,” Phys. Rev. B 53, 8967–8970 (1996).
[Crossref]

Slivka, A. G.

V. M. Kedyulich, A. G. Slivka, E. I. Gerzanich, P. P. Guranich, V. S. Shusta, and P. M. Lucach, “The influence of the temperature and uniform pressure on the anisotropy of dielectric properties of the Sn2P2S6 crystal,” Uzhgorod Univ. Bull. Phys. Ser. 5, 30–32 (1999).

Slivka, V. Y.

Y. M. Vysochanskii and V. Y. Slivka, “Ferroelectrics of the Sn2P2S6 family. Properties in Vicinity of Lifshitz Point” (Oriana-Nova, 1994) (in Russian).

Slivka, V. Yu.

M. M. Major, Yu. M. Vysochanskii, I. P. Prits, Sh. B. Molnar, V. Yu. Slivka, E. D. Rogach, F. I. Savenko, and A. P. Kudinov, “Piezoeffect in Sn2P2S6 single crystals,” Bull. USSR Acad. Sci., Inorg. Mater. 27(3), 604–606 (1991).

Stankowska, J.

G. Montemezzani, J. Fousek, P. Günter, and J. Stankowska, “Phase gratings in Fe3+-doped triglycine sulphate single crystals recorded in the ultraviolet spectral region,” Appl. Phys. Lett. 56, 2367–2369 (1990).
[Crossref]

Stoika, I. M.

D. Haertle, G. Caimi, A. Haldi, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Yu. M. Vysochanskii, “Electro-optical properties of Sn2P2S6,” Opt. Commun. 215(4), 333–343 (2003).
[Crossref]

Traum, C.

Volkov, A.

A. Volkov, “Evaluation of non-diagonal components of Pockels tensor for photorefractive Sn2P2S6 crystal,” Ukr. J. Phys. 58(4), 335–340 (2013).

A. Shumelyuk, A. Volkov, S. Odoulov, G. Cook, and D. R. Evans, “Coupling of counterpropagating light waves in low-symmetry photorefractive crystals,” Appl. Phys. B 100(1), 101–108 (2010).
[Crossref]

A. Shumelyuk, A. Volkov, A. Selinger, M. Imlau, and S. Odoulov, “Frequency-degenerate nonlinear light scattering in low-symmetry crystals,” Opt. Lett. 33(2), 150–152 (2008).
[Crossref] [PubMed]

A. Volkov, A. Shumelyuk, S. Odoulov, D. R. Evans, and G. Cook, “Anisotropic diffraction from photorefractive gratings and Pockels tensor of Sn2P2S6,” Opt. Express 16(21), 16923–16934 (2008).
[Crossref] [PubMed]

Vysochanskii, Y. M.

Y. M. Vysochanskii and V. Y. Slivka, “Ferroelectrics of the Sn2P2S6 family. Properties in Vicinity of Lifshitz Point” (Oriana-Nova, 1994) (in Russian).

Vysochanskii, Yu.

Vysochanskii, Yu. M.

D. Haertle, G. Caimi, A. Haldi, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Yu. M. Vysochanskii, “Electro-optical properties of Sn2P2S6,” Opt. Commun. 215(4), 333–343 (2003).
[Crossref]

M. M. Major, Yu. M. Vysochanskii, I. P. Prits, Sh. B. Molnar, V. Yu. Slivka, E. D. Rogach, F. I. Savenko, and A. P. Kudinov, “Piezoeffect in Sn2P2S6 single crystals,” Bull. USSR Acad. Sci., Inorg. Mater. 27(3), 604–606 (1991).

A. A. Grabar, M. Jazbinšek, A. N. Shumelyuk, Yu. M. Vysochanskii, G. Montemezzani, and P. Günter, “Photorefractive effects in Sn2P2S6,” in Photorefractive Materials and Their Applications II, P. Günter and J.-P. Huignard, eds. (Springer Verlag, 2007).

Xu, J.

X. Yue, J. Xu, F. Mersch, R. A. Rupp, and E. Krätzig, “Photorefractive properties of Bi4Ti3O12,” Phys. Rev. B 53, 9495–9502 (1997).
[Crossref]

Yue, X.

X. Yue, J. Xu, F. Mersch, R. A. Rupp, and E. Krätzig, “Photorefractive properties of Bi4Ti3O12,” Phys. Rev. B 53, 9495–9502 (1997).
[Crossref]

X. Yue, F. Mersch, R. Rupp, U. Hellwig, and M. Simon, “Holographic recording and beam coupling in ferroelectric Bi4Ti3O12,” Phys. Rev. B 53, 8967–8970 (1996).
[Crossref]

Zgonik, M.

G. Montemezzani and M. Zgonik, “Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries,” Phys. Rev. E 55(1), 1035–1047 (1997).
[Crossref]

Zheng, X.

Appl. Phys. B (2)

A. Shumelyuk, A. Volkov, S. Odoulov, G. Cook, and D. R. Evans, “Coupling of counterpropagating light waves in low-symmetry photorefractive crystals,” Appl. Phys. B 100(1), 101–108 (2010).
[Crossref]

A. Shumelyuk, D. Barilov, S. Odoulov, and E. Krätzig, “Anisotropy of the dielectric permittivity of Sn2P2S6 measured with light-induced grating techniques,” Appl. Phys. B 76(4), 417–421 (2003).
[Crossref]

Appl. Phys. Lett. (1)

G. Montemezzani, J. Fousek, P. Günter, and J. Stankowska, “Phase gratings in Fe3+-doped triglycine sulphate single crystals recorded in the ultraviolet spectral region,” Appl. Phys. Lett. 56, 2367–2369 (1990).
[Crossref]

Bull. USSR Acad. Sci., Inorg. Mater. (1)

M. M. Major, Yu. M. Vysochanskii, I. P. Prits, Sh. B. Molnar, V. Yu. Slivka, E. D. Rogach, F. I. Savenko, and A. P. Kudinov, “Piezoeffect in Sn2P2S6 single crystals,” Bull. USSR Acad. Sci., Inorg. Mater. 27(3), 604–606 (1991).

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

Laser Photon. Rev. (1)

Y. Petit, S. Joly, P. Segonds, and B. Boulanger, “Recent advances in monoclinic crystal optics,” Laser Photon. Rev. 7(6), 920–937 (2013).
[Crossref]

Mater. Res. Bull. (1)

C. D. Carpentier and R. Nitsche, “Ferroelectricity in Sn2P2S6,” Mater. Res. Bull. 9(8), 1097–1100 (1974).
[Crossref]

Opt. Commun. (1)

D. Haertle, G. Caimi, A. Haldi, G. Montemezzani, P. Günter, A. A. Grabar, I. M. Stoika, and Yu. M. Vysochanskii, “Electro-optical properties of Sn2P2S6,” Opt. Commun. 215(4), 333–343 (2003).
[Crossref]

Opt. Express (2)

A. Volkov, A. Shumelyuk, S. Odoulov, D. R. Evans, and G. Cook, “Anisotropic diffraction from photorefractive gratings and Pockels tensor of Sn2P2S6,” Opt. Express 16(21), 16923–16934 (2008).
[Crossref] [PubMed]

D. Haertle, A. Guarino, J. Hajfler, G. Montemezzani, and P. Günter, “Refractive indices of Sn2P2S6 at visible and infrared wavelengths,” Opt. Express 13(6), 2046–2057 (2005).

Opt. Lett. (2)

Opt. Mater. Express (2)

Phys. Rev. B (2)

X. Yue, F. Mersch, R. Rupp, U. Hellwig, and M. Simon, “Holographic recording and beam coupling in ferroelectric Bi4Ti3O12,” Phys. Rev. B 53, 8967–8970 (1996).
[Crossref]

X. Yue, J. Xu, F. Mersch, R. A. Rupp, and E. Krätzig, “Photorefractive properties of Bi4Ti3O12,” Phys. Rev. B 53, 9495–9502 (1997).
[Crossref]

Phys. Rev. E (1)

G. Montemezzani and M. Zgonik, “Light diffraction at mixed phase and absorption gratings in anisotropic media for arbitrary geometries,” Phys. Rev. E 55(1), 1035–1047 (1997).
[Crossref]

Ukr. J. Phys. (1)

A. Volkov, “Evaluation of non-diagonal components of Pockels tensor for photorefractive Sn2P2S6 crystal,” Ukr. J. Phys. 58(4), 335–340 (2013).

Uzhgorod Univ. Bull. Phys. Ser. (1)

V. M. Kedyulich, A. G. Slivka, E. I. Gerzanich, P. P. Guranich, V. S. Shusta, and P. M. Lucach, “The influence of the temperature and uniform pressure on the anisotropy of dielectric properties of the Sn2P2S6 crystal,” Uzhgorod Univ. Bull. Phys. Ser. 5, 30–32 (1999).

Z. Naturforsch. (1)

G. Dittmar and H. Schäfer, “Die Stuktur des Di-Zinn-Hexathiohypodiphoshatus Sn2P2S6,” Z. Naturforsch. 29B(5–6), 312–317 (1974).

Other (5)

ANSI/IEEE, Std 176 - IEEE Standard on Piezoelectricity, (IEEE, 1987), p. 242.

A. Grabar, “Energy spectra and photoinduced phenomena in ferroelectrc-semiconductor of Sn2P2S6 family,” Dr of Science Thesis, Uzhgorod National University, Ukraine, Uzhgorod (2004).

D. Haertle, “Photorefractive and nonlinear properties of Sn2P2S6,” PhD Thesis, ETH No. 16107, Zürich (2005).

A. A. Grabar, M. Jazbinšek, A. N. Shumelyuk, Yu. M. Vysochanskii, G. Montemezzani, and P. Günter, “Photorefractive effects in Sn2P2S6,” in Photorefractive Materials and Their Applications II, P. Günter and J.-P. Huignard, eds. (Springer Verlag, 2007).

Y. M. Vysochanskii and V. Y. Slivka, “Ferroelectrics of the Sn2P2S6 family. Properties in Vicinity of Lifshitz Point” (Oriana-Nova, 1994) (in Russian).

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Figures (9)

Fig. 1
Fig. 1 The orientation of the crystallographic axes a and c, the spontaneous polarization vector Ps, the major (n3) and middle (n1) axes of the optical indicatrix (dashed lines) of Sn2P2S6 crystal in the crystallophysic coordinates. The angular dependence of the effective dielectric permittivity εeff is shown as a solid line. The quadrants are enumerated as I, II, III, and IV as it is shown in the corners of the gray area.
Fig. 2
Fig. 2 Left drawing introduces spherical coordinates for orientation dependences of the gain factor. Right drawing shows the numeration of quadrants I, II, III and IV in the crystal mirror plane xz.
Fig. 3
Fig. 3 Pseudocolor 2D maps that represent normalized two-beam coupling gain factor versus orientation of a pair of interacting counterpropagating crystal eigenwaves that belong to the inner and outer shells of the normal surface (upper and lower panels, respectively.) This calculation is done for light waves with 633 nm wavelength and Sn2P2S6 crystal at ambient temperature. Red lines mark the crystal mirror plane xz while bright spots indicate signal wave orientation for which the largest gain factor can be achieved.
Fig. 4
Fig. 4 The Sn2P2S6 samples used in the experiment, #1 and #2, left and right, respectively. The arrows show the crystallophysic axes and the dashed line frames indicate the input faces.
Fig. 5
Fig. 5 Gain factor Γ versus tilt angle θ of grating vector K with respect to the y-axis in the xy-plane for azimuth angle φ = 0 (sample #1). Solid lines show the best fit with calculated dependences (see text). Red and blue colors mark the interaction of waves that belong to the inner and outer shells of the normal surface, respectively.
Fig. 6
Fig. 6 A fragment of the 2D plot of gain factor angular dependence (Fig. 3) that represents actual positive gain aria. The red lines show how the grating vector direction changes in sample #1 when it is rotated above the z-axis (vertical lines), and above the axis tilted to 20° with respect to the x-axis in the xy-plane (arcs). The solid lines mark the angular windows inside the crystal that are accessible with sample #1, while the asterisk indicates the normal incidence to the input/output faces of the sample #2.
Fig. 7
Fig. 7 Angular dependence of gain factor Γ measured with sample #1 (circles) and with sample #2 at normal incidence to the input face (squares). Solid lines show the best fit with calculated dependences (see text). Red and blue colors mark the interaction of waves that belong to the inner and outer shells of the normal surface, respectively.
Fig. 8
Fig. 8 Conical scattering pattern from a y-cut Sn2P2S6 sample. The incident beam corresponds to the eigenwave of inner shell of the normal surface, while the light scattered into the bright arc on the left corresponds to the eigenwave of outer shell of the normal surface. The Polaroid sheet was placed behind the sample to filter out the transmitted light of the incident wave and reduce beam fanning.
Fig. 9
Fig. 9 Gain factor for coupling of two co-propagating waves versus orientation angle of the grating vector in the xz-plane. Circles and squares show the results of measurements for two different grating spacings, 7 μm and 1.5 μm, respectively. Both recording waves are polarized identically and belong to the outer shell (upper panel) and inner shell (lower panel) of the normal surface (index of refraction n1 and n3, respectively). The solid lines show fitting with Eq. (7) provided 2πℓsX =1.5 μm and ε13 is positive. The dashed line represents the calculation for hypothetic case, when the largest dielectric permittivity appears in the quadrant IV (i.e., when ε13 is negative.) The quadrants are numbered on top of the upper panel.

Equations (7)

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Γ = ( e s e p ) 2 π n s n p 2 r eff E D λ cos α 1 1 + s 2 K 2 .
Γ = N eff e 2 ε 0 ( n 2 r eff ε eff ) .
r ^ r 11 = ( 1 0 0.19 0.53 0 0.08 0.87 0 0.11 0 5 10 3 0 0.12 0 0.2 0 0.03 0 ) ,
ε ^ ε 11 = ( 1 0 0.2 0 0.1 0 0.2 0 0.25 ) .
B ^ = ( n 1 2 sin 2 φ 0 + n 3 2 cos 2 φ 0 0 1 2 ( n 3 2 n 1 2 ) sin 2 φ 0 0 n 2 2 0 1 2 ( n 3 2 n 1 2 ) sin 2 φ 0 0 n 1 2 cos 2 φ 0 + n 3 2 sin 2 φ 0 ) ,
Γ = ( 1 / ) ln ( I s / I s 0 ) ,
Γ ~ ( r 11 + r 31 ± 2 r 51 ) cos β + ( r 13 + r 33 ± 2 r 53 ) sin β 1 + ( 2 π s X / Λ ) 2 ( ε 11 cos 2 β + ε 33 sin 2 β + ε 13 sin 2 β ) / ε 11 ,

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