Abstract

We report on the formation and subsequent dark evolution of induced absorption and photorefractive gratings produced by a high-intensity 15-ns pulse in an as-grown sample of BaTiO3 crystal. We show that the experimentally observed multiple time constants for decay of the induced absorption and buildup of the grating in the dark can be explained and successfully simulated by a numerical model of photorefraction incorporating two secondary (hole-trapping) centers in addition to the deep level. The model also takes into account combined electron and hole photoconductivity and high-intensity illumination. We present a full description of the method of numerical solution of the zeroth (homogeneous illumination) and the first-order parameters (inhomogeneous illumination) in this model regime for either steady-state or transient pulse trains and dark-evolution conditions.

© 1998 Optical Society of America

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References

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  1. P. Gunter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications II, Vol. 62 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988).
    [Crossref]
  2. N. V. Kukhtarev, V. M. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. 1. Steady-state,” Ferroelectrics 22, 949 (1979).
    [Crossref]
  3. R. A. Motes and J. J. Kim, “Intensity-dependent absorption coefficient in photorefractive BaTiO3 crystals,” J. Opt. Soc. Am. B 4, 1379 (1987).
    [Crossref]
  4. R. Orlowski and E. Kratzig, “Holographic method for the determination of photoinduced electron and hole transport in electro-optic crystals,” Solid State Commun. 27, 1351 (1978).
    [Crossref]
  5. M. B. Klein and G. C. Valley, “Beam coupling in BaTiO3 at 442 nm,” J. Appl. Phys. 57, 4901 (1985).
    [Crossref]
  6. S. Ducharme and J. Feinberg, “Speed of the photorefractive effect in a BaTiO3 single crystal,” J. Appl. Phys. 56, 839 (1984).
    [Crossref]
  7. R. A. Motes and J. J. Kim, “Beam coupling in photorefractive BaTiO3 crystals,” Opt. Lett. 12, 199 (1987).
    [Crossref] [PubMed]
  8. G. A. Brost, R. A. Motes, and J. R. Rotge, “Intensity-dependent absorption and photorefractive effect in barium titanate,” J. Opt. Soc. Am. B 5, 1879 (1988).
    [Crossref]
  9. P. Tayebati, “Effect of shallow traps on electron–hole com-petition in semi-insulating photorefractive materials,” J. Opt. Soc. Am. B 8, 1053 (1991).
    [Crossref]
  10. N. Barry, L. Duffault, R. Troth, R. Ramos-Garcia, and M. J. Damzen, “Comparison between continuous-wave and pulsed photorefraction in BaTiO3,” J. Opt. Soc. Am. B 11, 1758 (1994).
    [Crossref]
  11. D. Mahgerefteh and J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195 (1990); erratum, 65, 2613 (1990).
    [Crossref] [PubMed]
  12. G. A. Brost and R. A. Motes, “Origin of the sublinear photorefractive response time in BaTiO3,” Opt. Lett. 15, 1194 (1990).
    [Crossref] [PubMed]
  13. M. J. Damzen and N. Barry, “Intensity-dependent hole–electron competition and photorefractive saturation in BaTiO3 when using intense laser pulses,” J. Opt. Soc. Am. B 10, 600 (1993).
    [Crossref]
  14. F. P. Strohkendl, “Light induced dark decays of photorefractive gratings and their observation in Bi12SO20,” J. Appl. Phys. 65, 3773 (1989).
    [Crossref]
  15. P. Tayebati, “The effect of shallow traps on the dark storage of photorefractive gratings in Bi12SO20,” J. Appl. Phys. 70, 4082 (1991).
    [Crossref]
  16. P. Tayebati and D. Mahgerefteh, “Theory of the photorefractive effect for Bi12SiO20 and BaTiO3 with shallow traps,” J. Opt. Soc. Am. B 8, 1053 (1991).
    [Crossref]
  17. A. L. Smirl, K. Bohnert, G. C. Valey, R. A. Mullen, and T. F. Boggess, “Formation, decay, and erasure of photorefractive gratings written in barium titanate by picosecond pulses,” J. Opt. Soc. Am. B 6, 606 (1989).
    [Crossref]
  18. K. Buse, J. Frejlich, G. Kuper, and E. Krätzig, “Dark build-up of holograms in BaTiO3 after recording,” Appl. Phys. A 57, 437 (1993).
    [Crossref]
  19. R. C. Troth, R. Ramos-Garcia, and M. J. Damzen, “Experimental investigation of phase conjugation of a single pulse using self-pumped four-wave mixing in a single BaTiO3 crystal,” Opt. Commun. 116, 435 (1995).
    [Crossref]
  20. A. Motes, G. A. Brost, J. R. Rotge, and J. J. Kim, “Temporal behavior of the intensity-dependent absorption in photorefractive BaTiO3,” Opt. Lett. 13, 509 (1988).
    [Crossref] [PubMed]
  21. K. Buse and E. Krätzig, “Light-induced absorption in BaTiO3 and KNbO3 generated with high intensity laser pulses,” Opt. Mater. 1, 165 (1992).
    [Crossref]
  22. N. Barry, “High intensity effects in BaTiO3,” Ph.D. dissertation (Imperial College of Science, Technology and Medicine, London, 1996).
  23. R. Cudney, R. M. Pierce, G. D. Bacher, and J. Feinberg, “Absorption gratings in photorefractive crystals with multiple levels,” J. Opt. Soc. Am. B 8, 1326 (1991).
    [Crossref]
  24. K. Buse, “Thermal gratings and pyroelectrically produced charge distributions in BaTiO3 and KNbO3,” J. Opt. Soc. Am. B 10, 1266 (1993).
    [Crossref]
  25. F. Jariego and F. Agulló-López, “Holographic writing and erasure in unipolar photorefractive materials with multiple active centers: theoretical analysis,” Appl. Opt. 30, 4615 (1991).
    [Crossref] [PubMed]
  26. G. C. Valley and M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704 (1983).
    [Crossref]
  27. S. H. Wemple, M. Didomenico, and I. Camlibel, “Dielectric and optical properties of melt-grown BaTiO3,” J. Phys. Chem. Solids 29, 1797 (1968).
    [Crossref]
  28. S. Ducharme, J. Feinberg, and R. R. Neurgaonkar, “Electrooptic and piezoelectric measurements in photorefractive barium titanate and strontium barium niobate,” IEEE J. Quantum Electron. QE-23, 2116 (1987).
    [Crossref]
  29. I. Camlibel, M. Didomenico, and S. H. Wemple, “Dielectric properties of single-domain melt-grown BaTiO3,” J. Phys. Chem. Solids 31, 1417 (1970).
    [Crossref]

1995 (1)

R. C. Troth, R. Ramos-Garcia, and M. J. Damzen, “Experimental investigation of phase conjugation of a single pulse using self-pumped four-wave mixing in a single BaTiO3 crystal,” Opt. Commun. 116, 435 (1995).
[Crossref]

1994 (1)

1993 (3)

1992 (1)

K. Buse and E. Krätzig, “Light-induced absorption in BaTiO3 and KNbO3 generated with high intensity laser pulses,” Opt. Mater. 1, 165 (1992).
[Crossref]

1991 (5)

1990 (2)

D. Mahgerefteh and J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195 (1990); erratum, 65, 2613 (1990).
[Crossref] [PubMed]

G. A. Brost and R. A. Motes, “Origin of the sublinear photorefractive response time in BaTiO3,” Opt. Lett. 15, 1194 (1990).
[Crossref] [PubMed]

1989 (2)

1988 (2)

1987 (3)

R. A. Motes and J. J. Kim, “Beam coupling in photorefractive BaTiO3 crystals,” Opt. Lett. 12, 199 (1987).
[Crossref] [PubMed]

R. A. Motes and J. J. Kim, “Intensity-dependent absorption coefficient in photorefractive BaTiO3 crystals,” J. Opt. Soc. Am. B 4, 1379 (1987).
[Crossref]

S. Ducharme, J. Feinberg, and R. R. Neurgaonkar, “Electrooptic and piezoelectric measurements in photorefractive barium titanate and strontium barium niobate,” IEEE J. Quantum Electron. QE-23, 2116 (1987).
[Crossref]

1985 (1)

M. B. Klein and G. C. Valley, “Beam coupling in BaTiO3 at 442 nm,” J. Appl. Phys. 57, 4901 (1985).
[Crossref]

1984 (1)

S. Ducharme and J. Feinberg, “Speed of the photorefractive effect in a BaTiO3 single crystal,” J. Appl. Phys. 56, 839 (1984).
[Crossref]

1983 (1)

G. C. Valley and M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704 (1983).
[Crossref]

1979 (1)

N. V. Kukhtarev, V. M. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. 1. Steady-state,” Ferroelectrics 22, 949 (1979).
[Crossref]

1978 (1)

R. Orlowski and E. Kratzig, “Holographic method for the determination of photoinduced electron and hole transport in electro-optic crystals,” Solid State Commun. 27, 1351 (1978).
[Crossref]

1970 (1)

I. Camlibel, M. Didomenico, and S. H. Wemple, “Dielectric properties of single-domain melt-grown BaTiO3,” J. Phys. Chem. Solids 31, 1417 (1970).
[Crossref]

1968 (1)

S. H. Wemple, M. Didomenico, and I. Camlibel, “Dielectric and optical properties of melt-grown BaTiO3,” J. Phys. Chem. Solids 29, 1797 (1968).
[Crossref]

Agulló-López, F.

Bacher, G. D.

Barry, N.

Boggess, T. F.

Bohnert, K.

Brost, G. A.

Buse, K.

K. Buse, “Thermal gratings and pyroelectrically produced charge distributions in BaTiO3 and KNbO3,” J. Opt. Soc. Am. B 10, 1266 (1993).
[Crossref]

K. Buse, J. Frejlich, G. Kuper, and E. Krätzig, “Dark build-up of holograms in BaTiO3 after recording,” Appl. Phys. A 57, 437 (1993).
[Crossref]

K. Buse and E. Krätzig, “Light-induced absorption in BaTiO3 and KNbO3 generated with high intensity laser pulses,” Opt. Mater. 1, 165 (1992).
[Crossref]

Camlibel, I.

I. Camlibel, M. Didomenico, and S. H. Wemple, “Dielectric properties of single-domain melt-grown BaTiO3,” J. Phys. Chem. Solids 31, 1417 (1970).
[Crossref]

S. H. Wemple, M. Didomenico, and I. Camlibel, “Dielectric and optical properties of melt-grown BaTiO3,” J. Phys. Chem. Solids 29, 1797 (1968).
[Crossref]

Cudney, R.

Damzen, M. J.

Didomenico, M.

I. Camlibel, M. Didomenico, and S. H. Wemple, “Dielectric properties of single-domain melt-grown BaTiO3,” J. Phys. Chem. Solids 31, 1417 (1970).
[Crossref]

S. H. Wemple, M. Didomenico, and I. Camlibel, “Dielectric and optical properties of melt-grown BaTiO3,” J. Phys. Chem. Solids 29, 1797 (1968).
[Crossref]

Ducharme, S.

S. Ducharme, J. Feinberg, and R. R. Neurgaonkar, “Electrooptic and piezoelectric measurements in photorefractive barium titanate and strontium barium niobate,” IEEE J. Quantum Electron. QE-23, 2116 (1987).
[Crossref]

S. Ducharme and J. Feinberg, “Speed of the photorefractive effect in a BaTiO3 single crystal,” J. Appl. Phys. 56, 839 (1984).
[Crossref]

Duffault, L.

Feinberg, J.

R. Cudney, R. M. Pierce, G. D. Bacher, and J. Feinberg, “Absorption gratings in photorefractive crystals with multiple levels,” J. Opt. Soc. Am. B 8, 1326 (1991).
[Crossref]

D. Mahgerefteh and J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195 (1990); erratum, 65, 2613 (1990).
[Crossref] [PubMed]

S. Ducharme, J. Feinberg, and R. R. Neurgaonkar, “Electrooptic and piezoelectric measurements in photorefractive barium titanate and strontium barium niobate,” IEEE J. Quantum Electron. QE-23, 2116 (1987).
[Crossref]

S. Ducharme and J. Feinberg, “Speed of the photorefractive effect in a BaTiO3 single crystal,” J. Appl. Phys. 56, 839 (1984).
[Crossref]

Frejlich, J.

K. Buse, J. Frejlich, G. Kuper, and E. Krätzig, “Dark build-up of holograms in BaTiO3 after recording,” Appl. Phys. A 57, 437 (1993).
[Crossref]

Jariego, F.

Kim, J. J.

Klein, M. B.

M. B. Klein and G. C. Valley, “Beam coupling in BaTiO3 at 442 nm,” J. Appl. Phys. 57, 4901 (1985).
[Crossref]

G. C. Valley and M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704 (1983).
[Crossref]

Kratzig, E.

R. Orlowski and E. Kratzig, “Holographic method for the determination of photoinduced electron and hole transport in electro-optic crystals,” Solid State Commun. 27, 1351 (1978).
[Crossref]

Krätzig, E.

K. Buse, J. Frejlich, G. Kuper, and E. Krätzig, “Dark build-up of holograms in BaTiO3 after recording,” Appl. Phys. A 57, 437 (1993).
[Crossref]

K. Buse and E. Krätzig, “Light-induced absorption in BaTiO3 and KNbO3 generated with high intensity laser pulses,” Opt. Mater. 1, 165 (1992).
[Crossref]

Kukhtarev, N. V.

N. V. Kukhtarev, V. M. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. 1. Steady-state,” Ferroelectrics 22, 949 (1979).
[Crossref]

Kuper, G.

K. Buse, J. Frejlich, G. Kuper, and E. Krätzig, “Dark build-up of holograms in BaTiO3 after recording,” Appl. Phys. A 57, 437 (1993).
[Crossref]

Mahgerefteh, D.

P. Tayebati and D. Mahgerefteh, “Theory of the photorefractive effect for Bi12SiO20 and BaTiO3 with shallow traps,” J. Opt. Soc. Am. B 8, 1053 (1991).
[Crossref]

D. Mahgerefteh and J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195 (1990); erratum, 65, 2613 (1990).
[Crossref] [PubMed]

Markov, V. M.

N. V. Kukhtarev, V. M. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. 1. Steady-state,” Ferroelectrics 22, 949 (1979).
[Crossref]

Motes, A.

Motes, R. A.

Mullen, R. A.

Neurgaonkar, R. R.

S. Ducharme, J. Feinberg, and R. R. Neurgaonkar, “Electrooptic and piezoelectric measurements in photorefractive barium titanate and strontium barium niobate,” IEEE J. Quantum Electron. QE-23, 2116 (1987).
[Crossref]

Odulov, S. G.

N. V. Kukhtarev, V. M. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. 1. Steady-state,” Ferroelectrics 22, 949 (1979).
[Crossref]

Orlowski, R.

R. Orlowski and E. Kratzig, “Holographic method for the determination of photoinduced electron and hole transport in electro-optic crystals,” Solid State Commun. 27, 1351 (1978).
[Crossref]

Pierce, R. M.

Ramos-Garcia, R.

R. C. Troth, R. Ramos-Garcia, and M. J. Damzen, “Experimental investigation of phase conjugation of a single pulse using self-pumped four-wave mixing in a single BaTiO3 crystal,” Opt. Commun. 116, 435 (1995).
[Crossref]

N. Barry, L. Duffault, R. Troth, R. Ramos-Garcia, and M. J. Damzen, “Comparison between continuous-wave and pulsed photorefraction in BaTiO3,” J. Opt. Soc. Am. B 11, 1758 (1994).
[Crossref]

Rotge, J. R.

Smirl, A. L.

Soskin, M. S.

N. V. Kukhtarev, V. M. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. 1. Steady-state,” Ferroelectrics 22, 949 (1979).
[Crossref]

Strohkendl, F. P.

F. P. Strohkendl, “Light induced dark decays of photorefractive gratings and their observation in Bi12SO20,” J. Appl. Phys. 65, 3773 (1989).
[Crossref]

Tayebati, P.

Troth, R.

Troth, R. C.

R. C. Troth, R. Ramos-Garcia, and M. J. Damzen, “Experimental investigation of phase conjugation of a single pulse using self-pumped four-wave mixing in a single BaTiO3 crystal,” Opt. Commun. 116, 435 (1995).
[Crossref]

Valey, G. C.

Valley, G. C.

M. B. Klein and G. C. Valley, “Beam coupling in BaTiO3 at 442 nm,” J. Appl. Phys. 57, 4901 (1985).
[Crossref]

G. C. Valley and M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704 (1983).
[Crossref]

Vinetskii, V. L.

N. V. Kukhtarev, V. M. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. 1. Steady-state,” Ferroelectrics 22, 949 (1979).
[Crossref]

Wemple, S. H.

I. Camlibel, M. Didomenico, and S. H. Wemple, “Dielectric properties of single-domain melt-grown BaTiO3,” J. Phys. Chem. Solids 31, 1417 (1970).
[Crossref]

S. H. Wemple, M. Didomenico, and I. Camlibel, “Dielectric and optical properties of melt-grown BaTiO3,” J. Phys. Chem. Solids 29, 1797 (1968).
[Crossref]

Appl. Opt. (1)

Appl. Phys. A (1)

K. Buse, J. Frejlich, G. Kuper, and E. Krätzig, “Dark build-up of holograms in BaTiO3 after recording,” Appl. Phys. A 57, 437 (1993).
[Crossref]

Ferroelectrics (1)

N. V. Kukhtarev, V. M. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals. 1. Steady-state,” Ferroelectrics 22, 949 (1979).
[Crossref]

IEEE J. Quantum Electron. (1)

S. Ducharme, J. Feinberg, and R. R. Neurgaonkar, “Electrooptic and piezoelectric measurements in photorefractive barium titanate and strontium barium niobate,” IEEE J. Quantum Electron. QE-23, 2116 (1987).
[Crossref]

J. Appl. Phys. (4)

M. B. Klein and G. C. Valley, “Beam coupling in BaTiO3 at 442 nm,” J. Appl. Phys. 57, 4901 (1985).
[Crossref]

S. Ducharme and J. Feinberg, “Speed of the photorefractive effect in a BaTiO3 single crystal,” J. Appl. Phys. 56, 839 (1984).
[Crossref]

F. P. Strohkendl, “Light induced dark decays of photorefractive gratings and their observation in Bi12SO20,” J. Appl. Phys. 65, 3773 (1989).
[Crossref]

P. Tayebati, “The effect of shallow traps on the dark storage of photorefractive gratings in Bi12SO20,” J. Appl. Phys. 70, 4082 (1991).
[Crossref]

J. Opt. Soc. Am. B (9)

P. Tayebati and D. Mahgerefteh, “Theory of the photorefractive effect for Bi12SiO20 and BaTiO3 with shallow traps,” J. Opt. Soc. Am. B 8, 1053 (1991).
[Crossref]

A. L. Smirl, K. Bohnert, G. C. Valey, R. A. Mullen, and T. F. Boggess, “Formation, decay, and erasure of photorefractive gratings written in barium titanate by picosecond pulses,” J. Opt. Soc. Am. B 6, 606 (1989).
[Crossref]

R. A. Motes and J. J. Kim, “Intensity-dependent absorption coefficient in photorefractive BaTiO3 crystals,” J. Opt. Soc. Am. B 4, 1379 (1987).
[Crossref]

G. A. Brost, R. A. Motes, and J. R. Rotge, “Intensity-dependent absorption and photorefractive effect in barium titanate,” J. Opt. Soc. Am. B 5, 1879 (1988).
[Crossref]

P. Tayebati, “Effect of shallow traps on electron–hole com-petition in semi-insulating photorefractive materials,” J. Opt. Soc. Am. B 8, 1053 (1991).
[Crossref]

N. Barry, L. Duffault, R. Troth, R. Ramos-Garcia, and M. J. Damzen, “Comparison between continuous-wave and pulsed photorefraction in BaTiO3,” J. Opt. Soc. Am. B 11, 1758 (1994).
[Crossref]

M. J. Damzen and N. Barry, “Intensity-dependent hole–electron competition and photorefractive saturation in BaTiO3 when using intense laser pulses,” J. Opt. Soc. Am. B 10, 600 (1993).
[Crossref]

R. Cudney, R. M. Pierce, G. D. Bacher, and J. Feinberg, “Absorption gratings in photorefractive crystals with multiple levels,” J. Opt. Soc. Am. B 8, 1326 (1991).
[Crossref]

K. Buse, “Thermal gratings and pyroelectrically produced charge distributions in BaTiO3 and KNbO3,” J. Opt. Soc. Am. B 10, 1266 (1993).
[Crossref]

J. Phys. Chem. Solids (2)

S. H. Wemple, M. Didomenico, and I. Camlibel, “Dielectric and optical properties of melt-grown BaTiO3,” J. Phys. Chem. Solids 29, 1797 (1968).
[Crossref]

I. Camlibel, M. Didomenico, and S. H. Wemple, “Dielectric properties of single-domain melt-grown BaTiO3,” J. Phys. Chem. Solids 31, 1417 (1970).
[Crossref]

Opt. Commun. (1)

R. C. Troth, R. Ramos-Garcia, and M. J. Damzen, “Experimental investigation of phase conjugation of a single pulse using self-pumped four-wave mixing in a single BaTiO3 crystal,” Opt. Commun. 116, 435 (1995).
[Crossref]

Opt. Eng. (1)

G. C. Valley and M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704 (1983).
[Crossref]

Opt. Lett. (3)

Opt. Mater. (1)

K. Buse and E. Krätzig, “Light-induced absorption in BaTiO3 and KNbO3 generated with high intensity laser pulses,” Opt. Mater. 1, 165 (1992).
[Crossref]

Phys. Rev. Lett. (1)

D. Mahgerefteh and J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195 (1990); erratum, 65, 2613 (1990).
[Crossref] [PubMed]

Solid State Commun. (1)

R. Orlowski and E. Kratzig, “Holographic method for the determination of photoinduced electron and hole transport in electro-optic crystals,” Solid State Commun. 27, 1351 (1978).
[Crossref]

Other (2)

N. Barry, “High intensity effects in BaTiO3,” Ph.D. dissertation (Imperial College of Science, Technology and Medicine, London, 1996).

P. Gunter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications II, Vol. 62 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1

Experimental setup for (a) induced absorption and (b) grating recording by short-pulsed illumination. When the pump–writing beams are switched off the dark evolution is studied. PMT, photomultiplier tube; BS’s, beam splitters.

Fig. 2
Fig. 2

Typical dark decay of the induced absorption at I=13 MW/cm2. The dashed curve is a theory fit as described in text. Two time constants (τ1=40 ms and τ22 s) are clearly observed.

Fig. 3
Fig. 3

Typical dark buildup of photorefractive gratings written with a pair of short pulses of 15 ns and writing intensity I0=5 MW/cm2. Inset, grating buildup during the first 500 ms.

Fig. 4
Fig. 4

Dark buildup of the space-charge field for several intensities. Inset, damped oscillation.

Fig. 5
Fig. 5

Energy-diagram model with two hole shallow traps and electron–hole competition. p and n are the hole and the electron number densities in the valence and the conduction bands, respectively.

Fig. 6
Fig. 6

Dark buildup of the space-charge field after grating writing with a one-shallow-trap model with a large number of retrappings.

Fig. 7
Fig. 7

Dark buildup of the space-charge field with single-pulse recording and two hole shallow traps.

Tables (2)

Tables Icon

Table 1 Crystal Parameters Used in the Numerical Simulations

Tables Icon

Table 2 Parameters for Shallow Traps

Equations (63)

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

nt-1e je=(seI+βe)N-γenN+,
pt+1ejh=(shI+βh)N+-γhpN+(sfI+βf)Nf+-γfpNf+(ssI+βs)Ns+-γspNs,
je=eμenE+kBTμen+κeseNI,
jh=eμhpE-kBTμhp+κhshN+I,
t (n-p-N+-Nf+-Ns+)
=1e (jh+je),
E=-eε0εr (n+NA-p-N+-Nf+-Ns+),
Nf+t=-(sfI+βf)Nf+γfpNf,
Ns+t=-(ssI+βs)Ns++γspNs,
N+N+=ND,
Nf+Nf+=NTf,
Ns+Ns+=NTs.
I=I0(1+m cos kgz),
q(t)=q0(t)+q1(t)exp(ikgz),
Nf0+t=-β*Nf0+,
β*(t)=βf1+NR(t),
NR(t)=γs[NTf-Nf0+(t)]γh[ND-NA+Nf0+(t)].
α(I0)hcλ (shNA+sfNf0++ssNs0+),
sfNf0+2.4×1017 cm-1 J-1,
ssNs0+1.9×1017 cm-1 J-1.
n0p0=(seI0+βe)(shI0+βh)γeγhψ2;
n0=ψ2/p0,
N0+=NA+n0-p0-N0f+-N0s+,
N0=ND-NA-n0+p0+N0f++N0s+.
a5p05+a4p04+a3p03+a2p02+a1p0+a0=0,
a5=γhγfγs,
a4=γhγfγs(ND-NA+NTf+NTs)+γfγs(shI0+βh)+γhγs(sfI0+βf)+γhγf(ssI0+βs),
a3=-γhγfγsψ2+γhγs[(sfI0+βf)(ND-NA)+(sfI0+βf)NTs]+γhγf[(ssI0+βs)(ND-NA)+(ssI0+βs)NTf]+γfγs[-(shI0+βh)NA+(shI0+βh)NTf+(shI0+βh)NTs]+γh(sfI0+βf)(ssI0+βs)+γf(shI0+βh)×(ssI0+βs)+γs(shI0+βh)(sfI0+βf),
a2=(shI0+βh)(sfI0+βf)(ssI0+βs)-γhγf(ssI0+βs)ψ2-γhγs(sfI0+βf)ψ2-γfγs(shI0+βh)ψ2+γh(ND-NA)(sfI0+βf)(ssI0+βs)-γsNA(shI0+βh)(ssI0+βs)-γsNA(shI0+βh)×(sfI0+βf)+γfNTf(shI0+βh)×(ssI0+βs)+γsNTs(shI0+βh)(sfI0+βf),
a1=-NA(shI0+βh)(sfI0+βf)(ssI0+βs)-γh(sfI0+βf)(ssI0+βs)ψ2-γf(shI0+βh)×(ssI0+βs)ψ2-γs(shI0+βh)(sfI0+βf)ψ2,
a0=-(shI0+βh)(sfI0+βf)(ssI0+βs)ψ2.
Ax=y,
x=n1p1N1+Nf1+Ns1+,
y=semI0(ND-NA-n0+p0+Nf0++Ns0+)shmI0(NA+n0-p0-Nf0+-Ns0+)0sfmI0Nf0+ssmI0Ns0+.
A11=ΓDe+ΓRe+ΓDie-γe(Nf0++Ns0+)-ΓDih-ΓDie-ΓDih-ΓDe00,
A12=-ΓDieΓDh+ΓRh+ΓDih+γh(Nf0++Ns0+)ΓDie+ΓDih+ΓDh-γf(NTf-Nf0+)-γs(NTs-Ns0+),
A13=ΓIe-ΓDie-ΓIh+ΓDihΓDie+ΓDih00,A14=-ΓDieΓDihΓDie+ΓDihΓIf0,
A15=-ΓDieΓDihΓDie+ΓDih0ΓIs,
ΓDie=eμen0/(εrε0)(dielectricrelaxationrate),
ΓIe=seI0+βe+γen0(sumofproductionand
ionrecombinationrates),
ΓRe=γe(NA+n0-p0)(electronrecombinationrate),
ΓDe=kg2kBTμe/e(diffusionrate).
ΓDih=eμhn0/(εrε0),
ΓIh=shI0+βh+γhp0,
ΓRh=γh(ND-NA-n0+p0),
ΓDh=kg2kBTμh/e,
ΓIf=sfI0+βf+γfp0,
ΓIs=ssI0+βs+γsp0.
E1=-ekεrε0 (n1-p1-N1+-Nf1+-Ns1+).
I0(t)=I0 exp[-2(t/τp)2],
I0(t)=n=0npI0 exp[-2(t/τp)2]δ(t-n/f )
dn0dt=[seI0(t)+βe]N0-γen0N0+,
dp0dt=[shI0(t)+βh]N0+-γhp0N0+[sfI0(t)+βf]Nf0+-γfp0(NTf-Nf0+)+[ssI0(t)+βs]Ns0+-γsp0(NTs-Ns0+),
dNf0+dt=-[sfI0(t)+βf]Nf0++γfp0(NTf-Nf0+),
dNs0+dt=-[ssI0(t)+βs]Ns0++γsp0(NTs-Ns0+),
N0+=NA+n0-p0-Nf0+-Ns0+,
N0=ND-NA-n0+p0+Nf0++Ns0+.
dn1dt=-[ΓDe+ΓRe+ΓDie-γe(Nf0++Ns0+)]n1+(ΓDie)p1+(ΓDie-ΓIe)N1++(ΓDie)Nf1++(ΓDie)Ns1++mI0seN0,
dp1dt=(ΓDih)n1-[ΓDh+ΓRh+ΓDih+γh(Nf0++Ns0+)+γfNTf+γsNTs]p1+(ΓIh-ΓDih)N1++(ΓIs-ΓDih)Nf1++(ΓIp-ΓDih)Ns1++mI0(shN0++ssNf0++ssNs0+),
dN1+dt=-[ΓRe-γe(Nf0++Ns0+)]n1-[ΓRh-γh(Nf0++Ns0+)]p1-(ΓIe+ΓIh)N1++mI0(seN0-shN0+),
dNf1+dt=[γf(NTf-Nf0+)]p1-(ΓIf)Nf1+-mI0sfNf0+,
dNs1+dt=[γs(NTs-Ns0+)]p1-(ΓIs)Ns1+-mI0ssNs0+

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