Abstract

The interaction of sub-100 fs light pulses (τ p ≲ 75 fs) with single crystals of nominally undoped tin hypothiodiphosphate, Sn2P2S6, is studied in the near-infrared spectral range (590 – 1630 nm). A predominant contribution of the two-photon absorption (TPA) is verified in the measurements of the sample transmission as a function of pulse intensity and of the time delay between pump and probe pulses. Scans over the photon energy show that the two-photon absorption coefficient β increases in a superlinear way for photon energies h̄ω exceeding E g/2; for any quantum energy it is nearly independent of propagation direction and polarization of the incident beam. Such a behavior is qualitatively similar to that predicted by perturbation theory within models with allowed-forbidden transitions. The TPA coefficient saturates at a maximum value of β ≈ 8 cm GW−1 at h̄ω ≈ 1.80 eV. It drops when reaching the bandgap E g. Using pump-probe measurements at 626 nm, a transient absorption is verified that persists for probe pulse delays much longer than the pump pulse duration, up to 2.5 ns. We discuss our results in the framework of the microscopic structure of Sn2P2S6 with emphasis on the optical generation of S small hole polarons.

© 2011 OSA

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  1. G. Dittmar and H. Schäfer, “Crystal structure of Sn2P2S6,” Z. Naturforsch. B 29B, 312–317 (1974).
  2. R. V. Gamernyk, Yu. P. Gnatenko, P. M. Bukivsij, P. A. Skubenko, and V. Yu. Slivka, “Optical and photoelectric spectroscopy of photorefractive Sn2P2S6 crystals,” J. Phys.: Condens. Matter 18, 5323–5331 (2006).
    [CrossRef]
  3. K. Kuepper, B. Schneider, V. Caciuc, M. Neumann, A. V. Postnikov, A. Ruediger, A. A. Grabar, and Yu. M. Vysochanskii, “Electronic structure of Sn2P2S6,” Phys. Rev. B 67, 115101 (2003).
    [CrossRef]
  4. Yu. M. Vysochanskii, K. Glukhov, K. Fedyo, and R. Yevych, “Charge transfer and anharmononicity in Sn2P2S6 ferroelectrics,” Ferroelectrics 414, 30–40 (2011).
    [CrossRef]
  5. S. G. Odoulov, A. N. Shumelyuk, U. Hellwig, R. A. Rupp, A. A. Grabar, and I. M. Stoyka, “Photorefraction in tin hypothiodiphosphate in the near infrared,” J. Opt. Soc. Am. B 13, 2352–2360 (1996).
    [CrossRef]
  6. A. A. Grabar, M. Jazbinsek, 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), pp. 327–362.
    [CrossRef]
  7. R. Mosimann, P. Marty, T. Bach, F. Juvalta, M. M. Jazbinsek, P. Günter, A. A. Grabar, I. M. Stoyka, and M. Vysochanskii, “High-speed photorefraction at telecommunication wavelength 1.55 μm in Sn2P2S6:Te,” Opt. Lett. 32, 2330–2332 (2007).
    [CrossRef]
  8. A. Shumelyuk, A. Hryhorashchuk, and S. Odoulov, “Coherent optical oscillator with periodic zero-π phase modulation,” Phys. Rev. A 72, 023819 (2005).
    [CrossRef]
  9. A. Ruediger, O. Schirmer, S. Odoulov, A. Shumelyuk, and A. Grabar, “Studies of light-induced charge transport in Sn2P2S6 by combined EPR/optical absorption spectroscopy,” Opt. Mater. 18, 123–125 (2001).
    [CrossRef]
  10. A. Shumelyuk, M. Wesner, M. Imlau, and S. Odoulov, “Double-phase conjugate mirror in nominally undoped Sn2P2S6,” Opt. Lett. 34, 734–736 (2009).
    [CrossRef] [PubMed]
  11. A. Shumelyuk and S. Odoulov, “Light pulse manipulation in Sn2P2S6,” J. Opt. 12, 104015 (2010).
    [CrossRef]
  12. G. von Bally, F. Rickermann, S. Odoulov, and A. Shumelyuk, “Near-infrared holographic recording in Sn2P2S6 with nanosecond pulses,” Phys. Status Solidi A 157, 199–204 (1996).
    [CrossRef]
  13. T. Bach, K. Nawata, M. Jazbinsek, T. Omatsu, and P. Günter, “Optical phase conjugation of picosecond pulses at 1.06 μm in Sn2P2S6:Te for wavefront correction in high-power Nd-doped amplifier systems,” Opt. Express 18, 87–95 (2010).
    [CrossRef] [PubMed]
  14. A. A. Grabar, I. V. Kedyk, M. I. Gurzan, I. M. Stoika, A. A. Molnar, and Y. M. Vysochanskii, “Enhanced photorefractive properties of modified Sn2P2S6,” Opt. Commun. 188, 187–194 (2001).
    [CrossRef]
  15. O. Beyer, D. Maxien, K. Buse, B. Sturman, T. H. Hsiech, and D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E 71, 056603 (2005).
    [CrossRef]
  16. M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
    [CrossRef]
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    [CrossRef] [PubMed]
  19. D. C. Hutchings and B. S. Wherrett, “Theory of anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B 49, 2418–2426 (1994).
    [CrossRef]
  20. A. Ruediger, “Light induced charge transfer processes and pyroelectric luminescence in Sn2P2S6,” PhD thesis (University of Osnabrück, 2001).
  21. D. Berben, K. Buse, S. Wevering, P. Herth, M. Imlau, and T. Woike, “Lifetime of small polarons in iron-doped lithium-niobate crystals,” J. Appl. Phys. 87, 1034–1041 (2000).
    [CrossRef]
  22. O. F. Schirmer, “O− bound small polarons in oxide materials,” J. Phys.: Condens. Matter 18, R667–R704 (2006).
    [CrossRef]
  23. P. Herth, T. Granzow, D. Schaniel, Th. Woike, M. Imlau, and E. Krätzig, “Evidence for light-induced hole polarons in LiNbO3,” Phys. Rev. Lett. 95, 067404 (2005).
    [CrossRef] [PubMed]
  24. S. Torbrügge, M. Imlau, B. Schoke, C. Merschjann, O. F. Schirmer, S. Vernay, A. Gross, V. Wesemann, and D. Rytz, “Optically generated small electron and hole polarons in nominally undoped and Fe-doped KNbO3 investigated by transient absorption spectroscopy,” Phys. Rev. B 78, 125112 (2008).
    [CrossRef]
  25. Y. Qiu, K. B. Ucer, and R. T. Williams, “Formation time of a small electron polaron in LiNbO3: measurements and interpretation,” Phys. Status Solidi C 2, 232–235 (2005).
    [CrossRef]

2011 (1)

Yu. M. Vysochanskii, K. Glukhov, K. Fedyo, and R. Yevych, “Charge transfer and anharmononicity in Sn2P2S6 ferroelectrics,” Ferroelectrics 414, 30–40 (2011).
[CrossRef]

2010 (2)

2009 (1)

2008 (1)

S. Torbrügge, M. Imlau, B. Schoke, C. Merschjann, O. F. Schirmer, S. Vernay, A. Gross, V. Wesemann, and D. Rytz, “Optically generated small electron and hole polarons in nominally undoped and Fe-doped KNbO3 investigated by transient absorption spectroscopy,” Phys. Rev. B 78, 125112 (2008).
[CrossRef]

2007 (1)

2006 (2)

O. F. Schirmer, “O− bound small polarons in oxide materials,” J. Phys.: Condens. Matter 18, R667–R704 (2006).
[CrossRef]

R. V. Gamernyk, Yu. P. Gnatenko, P. M. Bukivsij, P. A. Skubenko, and V. Yu. Slivka, “Optical and photoelectric spectroscopy of photorefractive Sn2P2S6 crystals,” J. Phys.: Condens. Matter 18, 5323–5331 (2006).
[CrossRef]

2005 (4)

A. Shumelyuk, A. Hryhorashchuk, and S. Odoulov, “Coherent optical oscillator with periodic zero-π phase modulation,” Phys. Rev. A 72, 023819 (2005).
[CrossRef]

Y. Qiu, K. B. Ucer, and R. T. Williams, “Formation time of a small electron polaron in LiNbO3: measurements and interpretation,” Phys. Status Solidi C 2, 232–235 (2005).
[CrossRef]

O. Beyer, D. Maxien, K. Buse, B. Sturman, T. H. Hsiech, and D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E 71, 056603 (2005).
[CrossRef]

P. Herth, T. Granzow, D. Schaniel, Th. Woike, M. Imlau, and E. Krätzig, “Evidence for light-induced hole polarons in LiNbO3,” Phys. Rev. Lett. 95, 067404 (2005).
[CrossRef] [PubMed]

2003 (1)

K. Kuepper, B. Schneider, V. Caciuc, M. Neumann, A. V. Postnikov, A. Ruediger, A. A. Grabar, and Yu. M. Vysochanskii, “Electronic structure of Sn2P2S6,” Phys. Rev. B 67, 115101 (2003).
[CrossRef]

2001 (2)

A. Ruediger, O. Schirmer, S. Odoulov, A. Shumelyuk, and A. Grabar, “Studies of light-induced charge transport in Sn2P2S6 by combined EPR/optical absorption spectroscopy,” Opt. Mater. 18, 123–125 (2001).
[CrossRef]

A. A. Grabar, I. V. Kedyk, M. I. Gurzan, I. M. Stoika, A. A. Molnar, and Y. M. Vysochanskii, “Enhanced photorefractive properties of modified Sn2P2S6,” Opt. Commun. 188, 187–194 (2001).
[CrossRef]

2000 (1)

D. Berben, K. Buse, S. Wevering, P. Herth, M. Imlau, and T. Woike, “Lifetime of small polarons in iron-doped lithium-niobate crystals,” J. Appl. Phys. 87, 1034–1041 (2000).
[CrossRef]

1996 (2)

G. von Bally, F. Rickermann, S. Odoulov, and A. Shumelyuk, “Near-infrared holographic recording in Sn2P2S6 with nanosecond pulses,” Phys. Status Solidi A 157, 199–204 (1996).
[CrossRef]

S. G. Odoulov, A. N. Shumelyuk, U. Hellwig, R. A. Rupp, A. A. Grabar, and I. M. Stoyka, “Photorefraction in tin hypothiodiphosphate in the near infrared,” J. Opt. Soc. Am. B 13, 2352–2360 (1996).
[CrossRef]

1994 (1)

D. C. Hutchings and B. S. Wherrett, “Theory of anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B 49, 2418–2426 (1994).
[CrossRef]

1990 (1)

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

1985 (2)

1974 (1)

G. Dittmar and H. Schäfer, “Crystal structure of Sn2P2S6,” Z. Naturforsch. B 29B, 312–317 (1974).

Bach, T.

Berben, D.

D. Berben, K. Buse, S. Wevering, P. Herth, M. Imlau, and T. Woike, “Lifetime of small polarons in iron-doped lithium-niobate crystals,” J. Appl. Phys. 87, 1034–1041 (2000).
[CrossRef]

Beyer, O.

O. Beyer, D. Maxien, K. Buse, B. Sturman, T. H. Hsiech, and D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E 71, 056603 (2005).
[CrossRef]

Bukivsij, P. M.

R. V. Gamernyk, Yu. P. Gnatenko, P. M. Bukivsij, P. A. Skubenko, and V. Yu. Slivka, “Optical and photoelectric spectroscopy of photorefractive Sn2P2S6 crystals,” J. Phys.: Condens. Matter 18, 5323–5331 (2006).
[CrossRef]

Buse, K.

O. Beyer, D. Maxien, K. Buse, B. Sturman, T. H. Hsiech, and D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E 71, 056603 (2005).
[CrossRef]

D. Berben, K. Buse, S. Wevering, P. Herth, M. Imlau, and T. Woike, “Lifetime of small polarons in iron-doped lithium-niobate crystals,” J. Appl. Phys. 87, 1034–1041 (2000).
[CrossRef]

Caciuc, V.

K. Kuepper, B. Schneider, V. Caciuc, M. Neumann, A. V. Postnikov, A. Ruediger, A. A. Grabar, and Yu. M. Vysochanskii, “Electronic structure of Sn2P2S6,” Phys. Rev. B 67, 115101 (2003).
[CrossRef]

Dittmar, G.

G. Dittmar and H. Schäfer, “Crystal structure of Sn2P2S6,” Z. Naturforsch. B 29B, 312–317 (1974).

Fedyo, K.

Yu. M. Vysochanskii, K. Glukhov, K. Fedyo, and R. Yevych, “Charge transfer and anharmononicity in Sn2P2S6 ferroelectrics,” Ferroelectrics 414, 30–40 (2011).
[CrossRef]

Gamernyk, R. V.

R. V. Gamernyk, Yu. P. Gnatenko, P. M. Bukivsij, P. A. Skubenko, and V. Yu. Slivka, “Optical and photoelectric spectroscopy of photorefractive Sn2P2S6 crystals,” J. Phys.: Condens. Matter 18, 5323–5331 (2006).
[CrossRef]

Glukhov, K.

Yu. M. Vysochanskii, K. Glukhov, K. Fedyo, and R. Yevych, “Charge transfer and anharmononicity in Sn2P2S6 ferroelectrics,” Ferroelectrics 414, 30–40 (2011).
[CrossRef]

Gnatenko, Yu. P.

R. V. Gamernyk, Yu. P. Gnatenko, P. M. Bukivsij, P. A. Skubenko, and V. Yu. Slivka, “Optical and photoelectric spectroscopy of photorefractive Sn2P2S6 crystals,” J. Phys.: Condens. Matter 18, 5323–5331 (2006).
[CrossRef]

Grabar, A.

A. Ruediger, O. Schirmer, S. Odoulov, A. Shumelyuk, and A. Grabar, “Studies of light-induced charge transport in Sn2P2S6 by combined EPR/optical absorption spectroscopy,” Opt. Mater. 18, 123–125 (2001).
[CrossRef]

Grabar, A. A.

R. Mosimann, P. Marty, T. Bach, F. Juvalta, M. M. Jazbinsek, P. Günter, A. A. Grabar, I. M. Stoyka, and M. Vysochanskii, “High-speed photorefraction at telecommunication wavelength 1.55 μm in Sn2P2S6:Te,” Opt. Lett. 32, 2330–2332 (2007).
[CrossRef]

K. Kuepper, B. Schneider, V. Caciuc, M. Neumann, A. V. Postnikov, A. Ruediger, A. A. Grabar, and Yu. M. Vysochanskii, “Electronic structure of Sn2P2S6,” Phys. Rev. B 67, 115101 (2003).
[CrossRef]

A. A. Grabar, I. V. Kedyk, M. I. Gurzan, I. M. Stoika, A. A. Molnar, and Y. M. Vysochanskii, “Enhanced photorefractive properties of modified Sn2P2S6,” Opt. Commun. 188, 187–194 (2001).
[CrossRef]

S. G. Odoulov, A. N. Shumelyuk, U. Hellwig, R. A. Rupp, A. A. Grabar, and I. M. Stoyka, “Photorefraction in tin hypothiodiphosphate in the near infrared,” J. Opt. Soc. Am. B 13, 2352–2360 (1996).
[CrossRef]

A. A. Grabar, M. Jazbinsek, 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), pp. 327–362.
[CrossRef]

Granzow, T.

P. Herth, T. Granzow, D. Schaniel, Th. Woike, M. Imlau, and E. Krätzig, “Evidence for light-induced hole polarons in LiNbO3,” Phys. Rev. Lett. 95, 067404 (2005).
[CrossRef] [PubMed]

Gross, A.

S. Torbrügge, M. Imlau, B. Schoke, C. Merschjann, O. F. Schirmer, S. Vernay, A. Gross, V. Wesemann, and D. Rytz, “Optically generated small electron and hole polarons in nominally undoped and Fe-doped KNbO3 investigated by transient absorption spectroscopy,” Phys. Rev. B 78, 125112 (2008).
[CrossRef]

Guenter, A. H.

Günter, P.

Gurzan, M. I.

A. A. Grabar, I. V. Kedyk, M. I. Gurzan, I. M. Stoika, A. A. Molnar, and Y. M. Vysochanskii, “Enhanced photorefractive properties of modified Sn2P2S6,” Opt. Commun. 188, 187–194 (2001).
[CrossRef]

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Hellwig, U.

Herth, P.

P. Herth, T. Granzow, D. Schaniel, Th. Woike, M. Imlau, and E. Krätzig, “Evidence for light-induced hole polarons in LiNbO3,” Phys. Rev. Lett. 95, 067404 (2005).
[CrossRef] [PubMed]

D. Berben, K. Buse, S. Wevering, P. Herth, M. Imlau, and T. Woike, “Lifetime of small polarons in iron-doped lithium-niobate crystals,” J. Appl. Phys. 87, 1034–1041 (2000).
[CrossRef]

Hryhorashchuk, A.

A. Shumelyuk, A. Hryhorashchuk, and S. Odoulov, “Coherent optical oscillator with periodic zero-π phase modulation,” Phys. Rev. A 72, 023819 (2005).
[CrossRef]

Hsiech, T. H.

O. Beyer, D. Maxien, K. Buse, B. Sturman, T. H. Hsiech, and D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E 71, 056603 (2005).
[CrossRef]

Hutchings, D. C.

D. C. Hutchings and B. S. Wherrett, “Theory of anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B 49, 2418–2426 (1994).
[CrossRef]

Imlau, M.

A. Shumelyuk, M. Wesner, M. Imlau, and S. Odoulov, “Double-phase conjugate mirror in nominally undoped Sn2P2S6,” Opt. Lett. 34, 734–736 (2009).
[CrossRef] [PubMed]

S. Torbrügge, M. Imlau, B. Schoke, C. Merschjann, O. F. Schirmer, S. Vernay, A. Gross, V. Wesemann, and D. Rytz, “Optically generated small electron and hole polarons in nominally undoped and Fe-doped KNbO3 investigated by transient absorption spectroscopy,” Phys. Rev. B 78, 125112 (2008).
[CrossRef]

P. Herth, T. Granzow, D. Schaniel, Th. Woike, M. Imlau, and E. Krätzig, “Evidence for light-induced hole polarons in LiNbO3,” Phys. Rev. Lett. 95, 067404 (2005).
[CrossRef] [PubMed]

D. Berben, K. Buse, S. Wevering, P. Herth, M. Imlau, and T. Woike, “Lifetime of small polarons in iron-doped lithium-niobate crystals,” J. Appl. Phys. 87, 1034–1041 (2000).
[CrossRef]

Jazbinsek, M.

T. Bach, K. Nawata, M. Jazbinsek, T. Omatsu, and P. Günter, “Optical phase conjugation of picosecond pulses at 1.06 μm in Sn2P2S6:Te for wavefront correction in high-power Nd-doped amplifier systems,” Opt. Express 18, 87–95 (2010).
[CrossRef] [PubMed]

A. A. Grabar, M. Jazbinsek, 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), pp. 327–362.
[CrossRef]

Jazbinsek, M. M.

Juvalta, F.

Kedyk, I. V.

A. A. Grabar, I. V. Kedyk, M. I. Gurzan, I. M. Stoika, A. A. Molnar, and Y. M. Vysochanskii, “Enhanced photorefractive properties of modified Sn2P2S6,” Opt. Commun. 188, 187–194 (2001).
[CrossRef]

Krätzig, E.

P. Herth, T. Granzow, D. Schaniel, Th. Woike, M. Imlau, and E. Krätzig, “Evidence for light-induced hole polarons in LiNbO3,” Phys. Rev. Lett. 95, 067404 (2005).
[CrossRef] [PubMed]

Kuepper, K.

K. Kuepper, B. Schneider, V. Caciuc, M. Neumann, A. V. Postnikov, A. Ruediger, A. A. Grabar, and Yu. M. Vysochanskii, “Electronic structure of Sn2P2S6,” Phys. Rev. B 67, 115101 (2003).
[CrossRef]

Marty, P.

Maxien, D.

O. Beyer, D. Maxien, K. Buse, B. Sturman, T. H. Hsiech, and D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E 71, 056603 (2005).
[CrossRef]

Merschjann, C.

S. Torbrügge, M. Imlau, B. Schoke, C. Merschjann, O. F. Schirmer, S. Vernay, A. Gross, V. Wesemann, and D. Rytz, “Optically generated small electron and hole polarons in nominally undoped and Fe-doped KNbO3 investigated by transient absorption spectroscopy,” Phys. Rev. B 78, 125112 (2008).
[CrossRef]

Mitra, S. S.

Molnar, A. A.

A. A. Grabar, I. V. Kedyk, M. I. Gurzan, I. M. Stoika, A. A. Molnar, and Y. M. Vysochanskii, “Enhanced photorefractive properties of modified Sn2P2S6,” Opt. Commun. 188, 187–194 (2001).
[CrossRef]

Montemezzani, G.

A. A. Grabar, M. Jazbinsek, 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), pp. 327–362.
[CrossRef]

Mosimann, R.

Nathan, V.

Nawata, K.

Neumann, M.

K. Kuepper, B. Schneider, V. Caciuc, M. Neumann, A. V. Postnikov, A. Ruediger, A. A. Grabar, and Yu. M. Vysochanskii, “Electronic structure of Sn2P2S6,” Phys. Rev. B 67, 115101 (2003).
[CrossRef]

Odoulov, S.

A. Shumelyuk and S. Odoulov, “Light pulse manipulation in Sn2P2S6,” J. Opt. 12, 104015 (2010).
[CrossRef]

A. Shumelyuk, M. Wesner, M. Imlau, and S. Odoulov, “Double-phase conjugate mirror in nominally undoped Sn2P2S6,” Opt. Lett. 34, 734–736 (2009).
[CrossRef] [PubMed]

A. Shumelyuk, A. Hryhorashchuk, and S. Odoulov, “Coherent optical oscillator with periodic zero-π phase modulation,” Phys. Rev. A 72, 023819 (2005).
[CrossRef]

A. Ruediger, O. Schirmer, S. Odoulov, A. Shumelyuk, and A. Grabar, “Studies of light-induced charge transport in Sn2P2S6 by combined EPR/optical absorption spectroscopy,” Opt. Mater. 18, 123–125 (2001).
[CrossRef]

G. von Bally, F. Rickermann, S. Odoulov, and A. Shumelyuk, “Near-infrared holographic recording in Sn2P2S6 with nanosecond pulses,” Phys. Status Solidi A 157, 199–204 (1996).
[CrossRef]

Odoulov, S. G.

Omatsu, T.

Postnikov, A. V.

K. Kuepper, B. Schneider, V. Caciuc, M. Neumann, A. V. Postnikov, A. Ruediger, A. A. Grabar, and Yu. M. Vysochanskii, “Electronic structure of Sn2P2S6,” Phys. Rev. B 67, 115101 (2003).
[CrossRef]

Psaltis, D.

O. Beyer, D. Maxien, K. Buse, B. Sturman, T. H. Hsiech, and D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E 71, 056603 (2005).
[CrossRef]

Qiu, Y.

Y. Qiu, K. B. Ucer, and R. T. Williams, “Formation time of a small electron polaron in LiNbO3: measurements and interpretation,” Phys. Status Solidi C 2, 232–235 (2005).
[CrossRef]

Rickermann, F.

G. von Bally, F. Rickermann, S. Odoulov, and A. Shumelyuk, “Near-infrared holographic recording in Sn2P2S6 with nanosecond pulses,” Phys. Status Solidi A 157, 199–204 (1996).
[CrossRef]

Ruediger, A.

K. Kuepper, B. Schneider, V. Caciuc, M. Neumann, A. V. Postnikov, A. Ruediger, A. A. Grabar, and Yu. M. Vysochanskii, “Electronic structure of Sn2P2S6,” Phys. Rev. B 67, 115101 (2003).
[CrossRef]

A. Ruediger, O. Schirmer, S. Odoulov, A. Shumelyuk, and A. Grabar, “Studies of light-induced charge transport in Sn2P2S6 by combined EPR/optical absorption spectroscopy,” Opt. Mater. 18, 123–125 (2001).
[CrossRef]

Rupp, R. A.

Rytz, D.

S. Torbrügge, M. Imlau, B. Schoke, C. Merschjann, O. F. Schirmer, S. Vernay, A. Gross, V. Wesemann, and D. Rytz, “Optically generated small electron and hole polarons in nominally undoped and Fe-doped KNbO3 investigated by transient absorption spectroscopy,” Phys. Rev. B 78, 125112 (2008).
[CrossRef]

Said, A. A.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Schäfer, H.

G. Dittmar and H. Schäfer, “Crystal structure of Sn2P2S6,” Z. Naturforsch. B 29B, 312–317 (1974).

Schaniel, D.

P. Herth, T. Granzow, D. Schaniel, Th. Woike, M. Imlau, and E. Krätzig, “Evidence for light-induced hole polarons in LiNbO3,” Phys. Rev. Lett. 95, 067404 (2005).
[CrossRef] [PubMed]

Schirmer, O.

A. Ruediger, O. Schirmer, S. Odoulov, A. Shumelyuk, and A. Grabar, “Studies of light-induced charge transport in Sn2P2S6 by combined EPR/optical absorption spectroscopy,” Opt. Mater. 18, 123–125 (2001).
[CrossRef]

Schirmer, O. F.

S. Torbrügge, M. Imlau, B. Schoke, C. Merschjann, O. F. Schirmer, S. Vernay, A. Gross, V. Wesemann, and D. Rytz, “Optically generated small electron and hole polarons in nominally undoped and Fe-doped KNbO3 investigated by transient absorption spectroscopy,” Phys. Rev. B 78, 125112 (2008).
[CrossRef]

O. F. Schirmer, “O− bound small polarons in oxide materials,” J. Phys.: Condens. Matter 18, R667–R704 (2006).
[CrossRef]

Schneider, B.

K. Kuepper, B. Schneider, V. Caciuc, M. Neumann, A. V. Postnikov, A. Ruediger, A. A. Grabar, and Yu. M. Vysochanskii, “Electronic structure of Sn2P2S6,” Phys. Rev. B 67, 115101 (2003).
[CrossRef]

Schoke, B.

S. Torbrügge, M. Imlau, B. Schoke, C. Merschjann, O. F. Schirmer, S. Vernay, A. Gross, V. Wesemann, and D. Rytz, “Optically generated small electron and hole polarons in nominally undoped and Fe-doped KNbO3 investigated by transient absorption spectroscopy,” Phys. Rev. B 78, 125112 (2008).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Shumelyuk, A.

A. Shumelyuk and S. Odoulov, “Light pulse manipulation in Sn2P2S6,” J. Opt. 12, 104015 (2010).
[CrossRef]

A. Shumelyuk, M. Wesner, M. Imlau, and S. Odoulov, “Double-phase conjugate mirror in nominally undoped Sn2P2S6,” Opt. Lett. 34, 734–736 (2009).
[CrossRef] [PubMed]

A. Shumelyuk, A. Hryhorashchuk, and S. Odoulov, “Coherent optical oscillator with periodic zero-π phase modulation,” Phys. Rev. A 72, 023819 (2005).
[CrossRef]

A. Ruediger, O. Schirmer, S. Odoulov, A. Shumelyuk, and A. Grabar, “Studies of light-induced charge transport in Sn2P2S6 by combined EPR/optical absorption spectroscopy,” Opt. Mater. 18, 123–125 (2001).
[CrossRef]

G. von Bally, F. Rickermann, S. Odoulov, and A. Shumelyuk, “Near-infrared holographic recording in Sn2P2S6 with nanosecond pulses,” Phys. Status Solidi A 157, 199–204 (1996).
[CrossRef]

Shumelyuk, A. N.

S. G. Odoulov, A. N. Shumelyuk, U. Hellwig, R. A. Rupp, A. A. Grabar, and I. M. Stoyka, “Photorefraction in tin hypothiodiphosphate in the near infrared,” J. Opt. Soc. Am. B 13, 2352–2360 (1996).
[CrossRef]

A. A. Grabar, M. Jazbinsek, 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), pp. 327–362.
[CrossRef]

Skubenko, P. A.

R. V. Gamernyk, Yu. P. Gnatenko, P. M. Bukivsij, P. A. Skubenko, and V. Yu. Slivka, “Optical and photoelectric spectroscopy of photorefractive Sn2P2S6 crystals,” J. Phys.: Condens. Matter 18, 5323–5331 (2006).
[CrossRef]

Slivka, V. Yu.

R. V. Gamernyk, Yu. P. Gnatenko, P. M. Bukivsij, P. A. Skubenko, and V. Yu. Slivka, “Optical and photoelectric spectroscopy of photorefractive Sn2P2S6 crystals,” J. Phys.: Condens. Matter 18, 5323–5331 (2006).
[CrossRef]

Soileau, M. J.

Stoika, I. M.

A. A. Grabar, I. V. Kedyk, M. I. Gurzan, I. M. Stoika, A. A. Molnar, and Y. M. Vysochanskii, “Enhanced photorefractive properties of modified Sn2P2S6,” Opt. Commun. 188, 187–194 (2001).
[CrossRef]

Stoyka, I. M.

Sturman, B.

O. Beyer, D. Maxien, K. Buse, B. Sturman, T. H. Hsiech, and D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E 71, 056603 (2005).
[CrossRef]

Torbrügge, S.

S. Torbrügge, M. Imlau, B. Schoke, C. Merschjann, O. F. Schirmer, S. Vernay, A. Gross, V. Wesemann, and D. Rytz, “Optically generated small electron and hole polarons in nominally undoped and Fe-doped KNbO3 investigated by transient absorption spectroscopy,” Phys. Rev. B 78, 125112 (2008).
[CrossRef]

Ucer, K. B.

Y. Qiu, K. B. Ucer, and R. T. Williams, “Formation time of a small electron polaron in LiNbO3: measurements and interpretation,” Phys. Status Solidi C 2, 232–235 (2005).
[CrossRef]

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

E. W. Van Stryland, M. A. Woodall, H. Vanherzeele, and M. J. Soileau, “Energy band-gap dependence of two-photon absorption,” Opt. Lett. 10, 490–492 (1985).
[CrossRef] [PubMed]

Vanherzeele, H.

Vernay, S.

S. Torbrügge, M. Imlau, B. Schoke, C. Merschjann, O. F. Schirmer, S. Vernay, A. Gross, V. Wesemann, and D. Rytz, “Optically generated small electron and hole polarons in nominally undoped and Fe-doped KNbO3 investigated by transient absorption spectroscopy,” Phys. Rev. B 78, 125112 (2008).
[CrossRef]

von Bally, G.

G. von Bally, F. Rickermann, S. Odoulov, and A. Shumelyuk, “Near-infrared holographic recording in Sn2P2S6 with nanosecond pulses,” Phys. Status Solidi A 157, 199–204 (1996).
[CrossRef]

Vysochanskii, M.

Vysochanskii, Y. M.

A. A. Grabar, I. V. Kedyk, M. I. Gurzan, I. M. Stoika, A. A. Molnar, and Y. M. Vysochanskii, “Enhanced photorefractive properties of modified Sn2P2S6,” Opt. Commun. 188, 187–194 (2001).
[CrossRef]

Vysochanskii, Yu. M.

Yu. M. Vysochanskii, K. Glukhov, K. Fedyo, and R. Yevych, “Charge transfer and anharmononicity in Sn2P2S6 ferroelectrics,” Ferroelectrics 414, 30–40 (2011).
[CrossRef]

K. Kuepper, B. Schneider, V. Caciuc, M. Neumann, A. V. Postnikov, A. Ruediger, A. A. Grabar, and Yu. M. Vysochanskii, “Electronic structure of Sn2P2S6,” Phys. Rev. B 67, 115101 (2003).
[CrossRef]

A. A. Grabar, M. Jazbinsek, 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), pp. 327–362.
[CrossRef]

Wei, T.-H.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Wesemann, V.

S. Torbrügge, M. Imlau, B. Schoke, C. Merschjann, O. F. Schirmer, S. Vernay, A. Gross, V. Wesemann, and D. Rytz, “Optically generated small electron and hole polarons in nominally undoped and Fe-doped KNbO3 investigated by transient absorption spectroscopy,” Phys. Rev. B 78, 125112 (2008).
[CrossRef]

Wesner, M.

Wevering, S.

D. Berben, K. Buse, S. Wevering, P. Herth, M. Imlau, and T. Woike, “Lifetime of small polarons in iron-doped lithium-niobate crystals,” J. Appl. Phys. 87, 1034–1041 (2000).
[CrossRef]

Wherrett, B. S.

D. C. Hutchings and B. S. Wherrett, “Theory of anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B 49, 2418–2426 (1994).
[CrossRef]

Williams, R. T.

Y. Qiu, K. B. Ucer, and R. T. Williams, “Formation time of a small electron polaron in LiNbO3: measurements and interpretation,” Phys. Status Solidi C 2, 232–235 (2005).
[CrossRef]

Woike, T.

D. Berben, K. Buse, S. Wevering, P. Herth, M. Imlau, and T. Woike, “Lifetime of small polarons in iron-doped lithium-niobate crystals,” J. Appl. Phys. 87, 1034–1041 (2000).
[CrossRef]

Woike, Th.

P. Herth, T. Granzow, D. Schaniel, Th. Woike, M. Imlau, and E. Krätzig, “Evidence for light-induced hole polarons in LiNbO3,” Phys. Rev. Lett. 95, 067404 (2005).
[CrossRef] [PubMed]

Woodall, M. A.

Yevych, R.

Yu. M. Vysochanskii, K. Glukhov, K. Fedyo, and R. Yevych, “Charge transfer and anharmononicity in Sn2P2S6 ferroelectrics,” Ferroelectrics 414, 30–40 (2011).
[CrossRef]

Ferroelectrics (1)

Yu. M. Vysochanskii, K. Glukhov, K. Fedyo, and R. Yevych, “Charge transfer and anharmononicity in Sn2P2S6 ferroelectrics,” Ferroelectrics 414, 30–40 (2011).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

J. Appl. Phys. (1)

D. Berben, K. Buse, S. Wevering, P. Herth, M. Imlau, and T. Woike, “Lifetime of small polarons in iron-doped lithium-niobate crystals,” J. Appl. Phys. 87, 1034–1041 (2000).
[CrossRef]

J. Opt. (1)

A. Shumelyuk and S. Odoulov, “Light pulse manipulation in Sn2P2S6,” J. Opt. 12, 104015 (2010).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys.: Condens. Matter (2)

O. F. Schirmer, “O− bound small polarons in oxide materials,” J. Phys.: Condens. Matter 18, R667–R704 (2006).
[CrossRef]

R. V. Gamernyk, Yu. P. Gnatenko, P. M. Bukivsij, P. A. Skubenko, and V. Yu. Slivka, “Optical and photoelectric spectroscopy of photorefractive Sn2P2S6 crystals,” J. Phys.: Condens. Matter 18, 5323–5331 (2006).
[CrossRef]

Opt. Commun. (1)

A. A. Grabar, I. V. Kedyk, M. I. Gurzan, I. M. Stoika, A. A. Molnar, and Y. M. Vysochanskii, “Enhanced photorefractive properties of modified Sn2P2S6,” Opt. Commun. 188, 187–194 (2001).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Opt. Mater. (1)

A. Ruediger, O. Schirmer, S. Odoulov, A. Shumelyuk, and A. Grabar, “Studies of light-induced charge transport in Sn2P2S6 by combined EPR/optical absorption spectroscopy,” Opt. Mater. 18, 123–125 (2001).
[CrossRef]

Phys. Rev. A (1)

A. Shumelyuk, A. Hryhorashchuk, and S. Odoulov, “Coherent optical oscillator with periodic zero-π phase modulation,” Phys. Rev. A 72, 023819 (2005).
[CrossRef]

Phys. Rev. B (3)

K. Kuepper, B. Schneider, V. Caciuc, M. Neumann, A. V. Postnikov, A. Ruediger, A. A. Grabar, and Yu. M. Vysochanskii, “Electronic structure of Sn2P2S6,” Phys. Rev. B 67, 115101 (2003).
[CrossRef]

D. C. Hutchings and B. S. Wherrett, “Theory of anisotropy of two-photon absorption in zinc-blende semiconductors,” Phys. Rev. B 49, 2418–2426 (1994).
[CrossRef]

S. Torbrügge, M. Imlau, B. Schoke, C. Merschjann, O. F. Schirmer, S. Vernay, A. Gross, V. Wesemann, and D. Rytz, “Optically generated small electron and hole polarons in nominally undoped and Fe-doped KNbO3 investigated by transient absorption spectroscopy,” Phys. Rev. B 78, 125112 (2008).
[CrossRef]

Phys. Rev. E (1)

O. Beyer, D. Maxien, K. Buse, B. Sturman, T. H. Hsiech, and D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E 71, 056603 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

P. Herth, T. Granzow, D. Schaniel, Th. Woike, M. Imlau, and E. Krätzig, “Evidence for light-induced hole polarons in LiNbO3,” Phys. Rev. Lett. 95, 067404 (2005).
[CrossRef] [PubMed]

Phys. Status Solidi A (1)

G. von Bally, F. Rickermann, S. Odoulov, and A. Shumelyuk, “Near-infrared holographic recording in Sn2P2S6 with nanosecond pulses,” Phys. Status Solidi A 157, 199–204 (1996).
[CrossRef]

Phys. Status Solidi C (1)

Y. Qiu, K. B. Ucer, and R. T. Williams, “Formation time of a small electron polaron in LiNbO3: measurements and interpretation,” Phys. Status Solidi C 2, 232–235 (2005).
[CrossRef]

Z. Naturforsch. B (1)

G. Dittmar and H. Schäfer, “Crystal structure of Sn2P2S6,” Z. Naturforsch. B 29B, 312–317 (1974).

Other (2)

A. A. Grabar, M. Jazbinsek, 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), pp. 327–362.
[CrossRef]

A. Ruediger, “Light induced charge transfer processes and pyroelectric luminescence in Sn2P2S6,” PhD thesis (University of Osnabrück, 2001).

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Figures (4)

Fig. 1
Fig. 1

Schematic representation of the experimental set-ups. a) Single beam set-up for determination of the nonlinear absorption. The beam is attenuated by ND-filters and slightly focused by lens L1 to the sample. b) Pump-probe setup: both beams, attenuated by ND-filters, are focused to the sample by concave mirrors KM1, KM2. The pump beam is delayed in the time domain by the delay line DL.

Fig. 2
Fig. 2

Reciprocal transmittance of the 3.5 mm thick SPS sample versus maximum peak on-axis intensity I p 0 of the 73 fs pulse on the input face (left frame), and sample transmission versus dimensionless parameter q = β I p 0 (right frame). The light beam propagates along the z-axis and is polarized along the x-axis. Circles, squares, diamonds, and triangles mark the wavelengths of the incident pulse as indicated in the legend. The solid lines in the left frame serve to guide the eye, while in the right frame it represents the dependence calculated for solely two-photon absorption (see Eq. (2)).

Fig. 3
Fig. 3

Photon energy E = h̄ω dependence of the TPA coefficient β of nominally undoped SPS. The light beam propagates along the z-axis and is polarized along the x-axis. The red solid line shows the result of the fit of Eq. (4) to the experimental data in the range of E g/2 to 1.6 eV. The dashed part (from 1.6 to 1.8 eV) is a continuation of the function using the parameters obtained from the fitting procedure.

Fig. 4
Fig. 4

Beam attenuation of the SPS sample K16 as a function of the time delay between pump and probe pulses. Wavelength: λ = 626 nm, light polarization parallel y-axis, and beam propagation along z-direction. The red line marks the saturation value of the transmission of T ≈ (94 ± 2)% for Δt ≫ 5 ps.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

I p ( x = 0 ) = I p 0 exp [ ( t / t p ) 2 ( r / r p ) 2 ] .
T ( q ) = 2 q π 0 ln [ 1 + q exp ( s 2 ) ] d s .
χ T 2 ( β ) = i [ T exp ( q i ) T ( q i ) ] 2 T ( q i ) ,
β [ ( 2 h ¯ ω E g ) 1 ] 3 / 2 .

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