Abstract

We treat the photorefractive effect in oxide crystals at elevated temperatures where charge compensation occurs in the absence of photoexcitation of the compensating species. These species can be either mobile ions or holes in the valence band. Two models are presented that take into account particularities of ion and hole transport. In the small-modulation approximation, solutions for the steady state and the dynamic evolution of the photorefractive effect are given. The maximum space-charge field Eq that can be reached depends on the effective number of electron traps in the crystal. However, in the steady state, while the component of the space-charge field that is due to electrons and the one that is due to the compensating carriers both approach the value Eq, an almost complete compensation of these two components occurs. The speed of compensation is slower for larger grating spacings than for smaller grating spacings and can be increased by applying an electric field. Applying an external electric field also produces a phase shift between the two gratings, therefore increasing the total space-charge field. Experiments performed in KNbO3 confirm the theoretical predictions and indicate that the ionic model is more appropriate for this crystal. Implications of these compensation effects for quasi-permanent hologram storage are discussed.

© 1993 Optical Society of America

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  1. J. J. Amodei, D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
    [CrossRef]
  2. D. L. Staebler, “Ferroelectric crystals,” in Holographic Recording Materials, H. M. Smith, ed. (Springer-Verlag, Berlin, 1977), pp. 101–132.
    [CrossRef]
  3. L. Arizmendi, “Thermal fixing of holographic gratings in Bi12SiO20,” J. Appl. Phys. 65, 423–427 (1989).
    [CrossRef]
  4. F. Micheron, G. Bismuth, “Electrical control of fixation and erasure of holographic patterns in ferroelectric materials,” Appl. Phys. Lett. 20, 79–81 (1972).
    [CrossRef]
  5. J. B. Thaxter, M. Kestigian, “Unique properties of SBN and their use in a layered optical memory,” Appl. Opt. 13, 913–924 (1974).
    [CrossRef] [PubMed]
  6. S. Redfield, L. Hesselink, “Enhanced nondestructive holographic readout in strontium barium niobate,” Opt. Lett. 13, 880–882 (1988).
    [CrossRef] [PubMed]
  7. D. Von der Linde, A. M. Glass, K. F. Rogers, “Multiphoton photorefractive processes for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
    [CrossRef]
  8. D. Von der Linde, A. M. Glass, K. F. Rogers, “High-sensitivity optical recording in KTN by two photon absorption,” Appl. Phys. Lett. 26, 22–24 (1975).
    [CrossRef]
  9. V. V. Kulikov, S. I. Stepanov, “Mechanisms of holographic recording and thermal fixing in photorefractive LiNbO3:Fe,” Sov. Phys. Solid State 21, 1849–1851 (1979).
  10. W. Meyer, P. Würfel, R. Munser, G. Miller-Vogt, “Kinetics of fixation of phase holograms in LiNbO3,” Phys. Status Solidi A 53171–180 (1979),
    [CrossRef]
  11. P. Hertel, K. H. Ringhofer, R. Sommerfeldt, “Theory of thermal hologram fixing and application to LiNbO3:Cu,” Phys. Status Solidi A 104, 855–862 (1987).
    [CrossRef]
  12. M. Carrascosa, F. Agulló-López, “Theoretical modeling of the fixing and developing of holographic gratings in LiNbO3,” J. Opt. Soc. Am. B 7, 2317–2322 (1990).
    [CrossRef]
  13. H. Vormann, G. Weber, S. Kapphan, M. Wöhlecke, “Hydrogen as origin of themal fixing of LiNbOe:Fe,” Solid State Commun. 57, 543–545 (1981).
    [CrossRef]
  14. G. Montemezzani, M. Ingold, H. Looser, P. Günter, “Multiple photorefractive gratings in Ce-doped LiNbO3and KNbO3crystals,” Ferroelectrics 92, 281–287 (1989).
    [CrossRef]
  15. G. Montemezzani, P. Günter, “Thermal hologram fixing in pure and doped KNbO3crystals,” J. Opt. Soc. Am. B 7, 2323–2328 (1990).
    [CrossRef]
  16. G. S. Trofimov, S. I. Stepanov, “Electrical development of a hologram in a Bi12SiO20crystal,” Sov. Tech. Phys. Lett. 10, 282–283 (1984).
  17. J. P. Herriau, J.-P. Huignard, “Hologram fixing process at room temperature in photorefractive Bi12SiO20crystals,” Appl. Phys. Lett. 49, 1140–1142 (1986).
    [CrossRef]
  18. A. Delboulbe, C. Fromont, J. P. Herriau, S. Mallick, J.-P. Huignard, “Quasi-nondestructive readout of holographically stored information in photorefractive Bi12SiO20crystals,” Appl. Phys. Lett. 55, 713–715 (1989).
    [CrossRef]
  19. M. Miteva, L. Nikolova, “Oscillating behaviour of diffracted light on uniform illumination of holograms in photorefractive Bi12TiO20crystals,” Opt. Commun. 67, 192–194 (1988).
    [CrossRef]
  20. M. C. Bashaw, T.-P. Ma, R. C. Barker, S. Mroczkowski, R. R. Dube, “Introduction, revelation, and evolution of complementary gratings in photorefractive bismuth silicon oxide,” Phys. Rev. B 42, 5641–5648 (1990).
    [CrossRef]
  21. D. Kirillov, J. Feinberg, “Fixable complementary gratings in photorefractive BaTiO3,” Opt. Lett. 16, 1520–1522 (1991).
    [CrossRef] [PubMed]
  22. N. K. Kukhtarev, “Kinetics of hologram recording and erasure in electrooptic crystals,” Sov. Tech. Phys. Lett. 2, 438–440 (1976).
  23. N. K. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I: Steady state,” Ferroelectrics 22, 949–960 (1979).
    [CrossRef]
  24. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. II: Beam coupling, light amplification,” Ferroelectrics 22, 961–964 (1990).
    [CrossRef]
  25. I. Biaggio, M. Zgonik, P. Günter, “Build-up and dark decay of transient photorefractive gratings in reduced KNbO3,” Opt. Commun. 77, 312–317 (1990).
    [CrossRef]
  26. J. Mort, D. M. Pai, eds., Photoconductivity and Related Phenomena (Elsevier, Amsterdam, 1976).
  27. E. I. Bondarenko, V. A. Zagorulko, Yu. S. Kuz’minov, A. N. Pavlov, E. M. Panchenko, O. I. Prokopalo, “Model of the electret state in oxygen-octahedral materials,” Sov. Phys. Solid State 27, 629–630 (1985).
  28. N. V. Kukhtarev, G. E. Dogvalenko, V. N. Markov, “Influence of the optical activity on hologram formation in photorefractive crystals,” Appl. Phys. A 33, 227–230 (1984).
    [CrossRef]
  29. G. C. Valley, “Simultaneous electron/hole transport in photorefractive materials,” J. Appl. Phys. 59, 3363–3366 (1986).
    [CrossRef]
  30. M. C. Bashaw, T.-P. Ma, R. C. Barker, S. Mroczkowski, R. R. Dube, “Theory of complementary holograms arising from electron-hole transport in photorefractive media,” J. Opt. Soc. Am. B 7, 2329–2338 (1990).
    [CrossRef]
  31. S. Zhivkova, M. Miteva, “Holographic recording in photorefractive crystals with simultaneous electron-hole transport and two active centers,” J. Appl. Phys. 68, 3099–3103 (1990).
    [CrossRef]
  32. D. Fluck, P. Amrhein, P. Günter, “Photorefractive effect in crystals with a nonlinear recombination of charge carriers: theory and observation in KNbO3,” J. Opt. Soc. Am. B 8, 2196–2203 (1991).
    [CrossRef]
  33. E. V. Bursian, Ya. G. Girshberg, A. V. Ruzhnikov, “The correlation between optical absorption spectra, carrier mobility, and phase transition temperature in some ferroelectrics,” Phys. Status Solidi B 74, 689–693 (1976).
    [CrossRef]
  34. I. Biaggio, M. Zgonik, P. Günter, “Photorefractive effects induced by picosecond light pulses in reduced KNbO3,” J. Opt. Soc. Am. B 9, 1480–1487 (1992).
    [CrossRef]
  35. F. P. Strohkendl, “Light-induced dark decays of photorefractive gratings and their observation in Bi12SiO20,” J. Appl. Phys. 65, 3773–3780 (1989).
    [CrossRef]
  36. J. P. Partanen, P. Nouchi, J. M. C. Jonathan, R. W. Hellwarth, “Comparison between holographic and transient-photocurrent measurements of electron mobility in photorefractive Bi12SiO20,” Phys. Rev. B 44, 1487–1491 (1991).
    [CrossRef]

1992 (1)

1991 (3)

1990 (7)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. II: Beam coupling, light amplification,” Ferroelectrics 22, 961–964 (1990).
[CrossRef]

I. Biaggio, M. Zgonik, P. Günter, “Build-up and dark decay of transient photorefractive gratings in reduced KNbO3,” Opt. Commun. 77, 312–317 (1990).
[CrossRef]

M. C. Bashaw, T.-P. Ma, R. C. Barker, S. Mroczkowski, R. R. Dube, “Introduction, revelation, and evolution of complementary gratings in photorefractive bismuth silicon oxide,” Phys. Rev. B 42, 5641–5648 (1990).
[CrossRef]

M. C. Bashaw, T.-P. Ma, R. C. Barker, S. Mroczkowski, R. R. Dube, “Theory of complementary holograms arising from electron-hole transport in photorefractive media,” J. Opt. Soc. Am. B 7, 2329–2338 (1990).
[CrossRef]

S. Zhivkova, M. Miteva, “Holographic recording in photorefractive crystals with simultaneous electron-hole transport and two active centers,” J. Appl. Phys. 68, 3099–3103 (1990).
[CrossRef]

M. Carrascosa, F. Agulló-López, “Theoretical modeling of the fixing and developing of holographic gratings in LiNbO3,” J. Opt. Soc. Am. B 7, 2317–2322 (1990).
[CrossRef]

G. Montemezzani, P. Günter, “Thermal hologram fixing in pure and doped KNbO3crystals,” J. Opt. Soc. Am. B 7, 2323–2328 (1990).
[CrossRef]

1989 (4)

G. Montemezzani, M. Ingold, H. Looser, P. Günter, “Multiple photorefractive gratings in Ce-doped LiNbO3and KNbO3crystals,” Ferroelectrics 92, 281–287 (1989).
[CrossRef]

L. Arizmendi, “Thermal fixing of holographic gratings in Bi12SiO20,” J. Appl. Phys. 65, 423–427 (1989).
[CrossRef]

F. P. Strohkendl, “Light-induced dark decays of photorefractive gratings and their observation in Bi12SiO20,” J. Appl. Phys. 65, 3773–3780 (1989).
[CrossRef]

A. Delboulbe, C. Fromont, J. P. Herriau, S. Mallick, J.-P. Huignard, “Quasi-nondestructive readout of holographically stored information in photorefractive Bi12SiO20crystals,” Appl. Phys. Lett. 55, 713–715 (1989).
[CrossRef]

1988 (2)

M. Miteva, L. Nikolova, “Oscillating behaviour of diffracted light on uniform illumination of holograms in photorefractive Bi12TiO20crystals,” Opt. Commun. 67, 192–194 (1988).
[CrossRef]

S. Redfield, L. Hesselink, “Enhanced nondestructive holographic readout in strontium barium niobate,” Opt. Lett. 13, 880–882 (1988).
[CrossRef] [PubMed]

1987 (1)

P. Hertel, K. H. Ringhofer, R. Sommerfeldt, “Theory of thermal hologram fixing and application to LiNbO3:Cu,” Phys. Status Solidi A 104, 855–862 (1987).
[CrossRef]

1986 (2)

J. P. Herriau, J.-P. Huignard, “Hologram fixing process at room temperature in photorefractive Bi12SiO20crystals,” Appl. Phys. Lett. 49, 1140–1142 (1986).
[CrossRef]

G. C. Valley, “Simultaneous electron/hole transport in photorefractive materials,” J. Appl. Phys. 59, 3363–3366 (1986).
[CrossRef]

1985 (1)

E. I. Bondarenko, V. A. Zagorulko, Yu. S. Kuz’minov, A. N. Pavlov, E. M. Panchenko, O. I. Prokopalo, “Model of the electret state in oxygen-octahedral materials,” Sov. Phys. Solid State 27, 629–630 (1985).

1984 (2)

N. V. Kukhtarev, G. E. Dogvalenko, V. N. Markov, “Influence of the optical activity on hologram formation in photorefractive crystals,” Appl. Phys. A 33, 227–230 (1984).
[CrossRef]

G. S. Trofimov, S. I. Stepanov, “Electrical development of a hologram in a Bi12SiO20crystal,” Sov. Tech. Phys. Lett. 10, 282–283 (1984).

1981 (1)

H. Vormann, G. Weber, S. Kapphan, M. Wöhlecke, “Hydrogen as origin of themal fixing of LiNbOe:Fe,” Solid State Commun. 57, 543–545 (1981).
[CrossRef]

1979 (3)

V. V. Kulikov, S. I. Stepanov, “Mechanisms of holographic recording and thermal fixing in photorefractive LiNbO3:Fe,” Sov. Phys. Solid State 21, 1849–1851 (1979).

W. Meyer, P. Würfel, R. Munser, G. Miller-Vogt, “Kinetics of fixation of phase holograms in LiNbO3,” Phys. Status Solidi A 53171–180 (1979),
[CrossRef]

N. K. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I: Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

1976 (2)

E. V. Bursian, Ya. G. Girshberg, A. V. Ruzhnikov, “The correlation between optical absorption spectra, carrier mobility, and phase transition temperature in some ferroelectrics,” Phys. Status Solidi B 74, 689–693 (1976).
[CrossRef]

N. K. Kukhtarev, “Kinetics of hologram recording and erasure in electrooptic crystals,” Sov. Tech. Phys. Lett. 2, 438–440 (1976).

1975 (1)

D. Von der Linde, A. M. Glass, K. F. Rogers, “High-sensitivity optical recording in KTN by two photon absorption,” Appl. Phys. Lett. 26, 22–24 (1975).
[CrossRef]

1974 (2)

D. Von der Linde, A. M. Glass, K. F. Rogers, “Multiphoton photorefractive processes for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
[CrossRef]

J. B. Thaxter, M. Kestigian, “Unique properties of SBN and their use in a layered optical memory,” Appl. Opt. 13, 913–924 (1974).
[CrossRef] [PubMed]

1972 (1)

F. Micheron, G. Bismuth, “Electrical control of fixation and erasure of holographic patterns in ferroelectric materials,” Appl. Phys. Lett. 20, 79–81 (1972).
[CrossRef]

1971 (1)

J. J. Amodei, D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
[CrossRef]

Agulló-López, F.

Amodei, J. J.

J. J. Amodei, D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
[CrossRef]

Amrhein, P.

Arizmendi, L.

L. Arizmendi, “Thermal fixing of holographic gratings in Bi12SiO20,” J. Appl. Phys. 65, 423–427 (1989).
[CrossRef]

Barker, R. C.

M. C. Bashaw, T.-P. Ma, R. C. Barker, S. Mroczkowski, R. R. Dube, “Introduction, revelation, and evolution of complementary gratings in photorefractive bismuth silicon oxide,” Phys. Rev. B 42, 5641–5648 (1990).
[CrossRef]

M. C. Bashaw, T.-P. Ma, R. C. Barker, S. Mroczkowski, R. R. Dube, “Theory of complementary holograms arising from electron-hole transport in photorefractive media,” J. Opt. Soc. Am. B 7, 2329–2338 (1990).
[CrossRef]

Bashaw, M. C.

M. C. Bashaw, T.-P. Ma, R. C. Barker, S. Mroczkowski, R. R. Dube, “Theory of complementary holograms arising from electron-hole transport in photorefractive media,” J. Opt. Soc. Am. B 7, 2329–2338 (1990).
[CrossRef]

M. C. Bashaw, T.-P. Ma, R. C. Barker, S. Mroczkowski, R. R. Dube, “Introduction, revelation, and evolution of complementary gratings in photorefractive bismuth silicon oxide,” Phys. Rev. B 42, 5641–5648 (1990).
[CrossRef]

Biaggio, I.

I. Biaggio, M. Zgonik, P. Günter, “Photorefractive effects induced by picosecond light pulses in reduced KNbO3,” J. Opt. Soc. Am. B 9, 1480–1487 (1992).
[CrossRef]

I. Biaggio, M. Zgonik, P. Günter, “Build-up and dark decay of transient photorefractive gratings in reduced KNbO3,” Opt. Commun. 77, 312–317 (1990).
[CrossRef]

Bismuth, G.

F. Micheron, G. Bismuth, “Electrical control of fixation and erasure of holographic patterns in ferroelectric materials,” Appl. Phys. Lett. 20, 79–81 (1972).
[CrossRef]

Bondarenko, E. I.

E. I. Bondarenko, V. A. Zagorulko, Yu. S. Kuz’minov, A. N. Pavlov, E. M. Panchenko, O. I. Prokopalo, “Model of the electret state in oxygen-octahedral materials,” Sov. Phys. Solid State 27, 629–630 (1985).

Bursian, E. V.

E. V. Bursian, Ya. G. Girshberg, A. V. Ruzhnikov, “The correlation between optical absorption spectra, carrier mobility, and phase transition temperature in some ferroelectrics,” Phys. Status Solidi B 74, 689–693 (1976).
[CrossRef]

Carrascosa, M.

Delboulbe, A.

A. Delboulbe, C. Fromont, J. P. Herriau, S. Mallick, J.-P. Huignard, “Quasi-nondestructive readout of holographically stored information in photorefractive Bi12SiO20crystals,” Appl. Phys. Lett. 55, 713–715 (1989).
[CrossRef]

Dogvalenko, G. E.

N. V. Kukhtarev, G. E. Dogvalenko, V. N. Markov, “Influence of the optical activity on hologram formation in photorefractive crystals,” Appl. Phys. A 33, 227–230 (1984).
[CrossRef]

Dube, R. R.

M. C. Bashaw, T.-P. Ma, R. C. Barker, S. Mroczkowski, R. R. Dube, “Theory of complementary holograms arising from electron-hole transport in photorefractive media,” J. Opt. Soc. Am. B 7, 2329–2338 (1990).
[CrossRef]

M. C. Bashaw, T.-P. Ma, R. C. Barker, S. Mroczkowski, R. R. Dube, “Introduction, revelation, and evolution of complementary gratings in photorefractive bismuth silicon oxide,” Phys. Rev. B 42, 5641–5648 (1990).
[CrossRef]

Feinberg, J.

Fluck, D.

Fromont, C.

A. Delboulbe, C. Fromont, J. P. Herriau, S. Mallick, J.-P. Huignard, “Quasi-nondestructive readout of holographically stored information in photorefractive Bi12SiO20crystals,” Appl. Phys. Lett. 55, 713–715 (1989).
[CrossRef]

Girshberg, Ya. G.

E. V. Bursian, Ya. G. Girshberg, A. V. Ruzhnikov, “The correlation between optical absorption spectra, carrier mobility, and phase transition temperature in some ferroelectrics,” Phys. Status Solidi B 74, 689–693 (1976).
[CrossRef]

Glass, A. M.

D. Von der Linde, A. M. Glass, K. F. Rogers, “High-sensitivity optical recording in KTN by two photon absorption,” Appl. Phys. Lett. 26, 22–24 (1975).
[CrossRef]

D. Von der Linde, A. M. Glass, K. F. Rogers, “Multiphoton photorefractive processes for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
[CrossRef]

Günter, P.

Hellwarth, R. W.

J. P. Partanen, P. Nouchi, J. M. C. Jonathan, R. W. Hellwarth, “Comparison between holographic and transient-photocurrent measurements of electron mobility in photorefractive Bi12SiO20,” Phys. Rev. B 44, 1487–1491 (1991).
[CrossRef]

Herriau, J. P.

A. Delboulbe, C. Fromont, J. P. Herriau, S. Mallick, J.-P. Huignard, “Quasi-nondestructive readout of holographically stored information in photorefractive Bi12SiO20crystals,” Appl. Phys. Lett. 55, 713–715 (1989).
[CrossRef]

J. P. Herriau, J.-P. Huignard, “Hologram fixing process at room temperature in photorefractive Bi12SiO20crystals,” Appl. Phys. Lett. 49, 1140–1142 (1986).
[CrossRef]

Hertel, P.

P. Hertel, K. H. Ringhofer, R. Sommerfeldt, “Theory of thermal hologram fixing and application to LiNbO3:Cu,” Phys. Status Solidi A 104, 855–862 (1987).
[CrossRef]

Hesselink, L.

Huignard, J.-P.

A. Delboulbe, C. Fromont, J. P. Herriau, S. Mallick, J.-P. Huignard, “Quasi-nondestructive readout of holographically stored information in photorefractive Bi12SiO20crystals,” Appl. Phys. Lett. 55, 713–715 (1989).
[CrossRef]

J. P. Herriau, J.-P. Huignard, “Hologram fixing process at room temperature in photorefractive Bi12SiO20crystals,” Appl. Phys. Lett. 49, 1140–1142 (1986).
[CrossRef]

Ingold, M.

G. Montemezzani, M. Ingold, H. Looser, P. Günter, “Multiple photorefractive gratings in Ce-doped LiNbO3and KNbO3crystals,” Ferroelectrics 92, 281–287 (1989).
[CrossRef]

Jonathan, J. M. C.

J. P. Partanen, P. Nouchi, J. M. C. Jonathan, R. W. Hellwarth, “Comparison between holographic and transient-photocurrent measurements of electron mobility in photorefractive Bi12SiO20,” Phys. Rev. B 44, 1487–1491 (1991).
[CrossRef]

Kapphan, S.

H. Vormann, G. Weber, S. Kapphan, M. Wöhlecke, “Hydrogen as origin of themal fixing of LiNbOe:Fe,” Solid State Commun. 57, 543–545 (1981).
[CrossRef]

Kestigian, M.

Kirillov, D.

Kukhtarev, N. K.

N. K. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I: Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

N. K. Kukhtarev, “Kinetics of hologram recording and erasure in electrooptic crystals,” Sov. Tech. Phys. Lett. 2, 438–440 (1976).

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. II: Beam coupling, light amplification,” Ferroelectrics 22, 961–964 (1990).
[CrossRef]

N. V. Kukhtarev, G. E. Dogvalenko, V. N. Markov, “Influence of the optical activity on hologram formation in photorefractive crystals,” Appl. Phys. A 33, 227–230 (1984).
[CrossRef]

Kulikov, V. V.

V. V. Kulikov, S. I. Stepanov, “Mechanisms of holographic recording and thermal fixing in photorefractive LiNbO3:Fe,” Sov. Phys. Solid State 21, 1849–1851 (1979).

Kuz’minov, Yu. S.

E. I. Bondarenko, V. A. Zagorulko, Yu. S. Kuz’minov, A. N. Pavlov, E. M. Panchenko, O. I. Prokopalo, “Model of the electret state in oxygen-octahedral materials,” Sov. Phys. Solid State 27, 629–630 (1985).

Looser, H.

G. Montemezzani, M. Ingold, H. Looser, P. Günter, “Multiple photorefractive gratings in Ce-doped LiNbO3and KNbO3crystals,” Ferroelectrics 92, 281–287 (1989).
[CrossRef]

Ma, T.-P.

M. C. Bashaw, T.-P. Ma, R. C. Barker, S. Mroczkowski, R. R. Dube, “Introduction, revelation, and evolution of complementary gratings in photorefractive bismuth silicon oxide,” Phys. Rev. B 42, 5641–5648 (1990).
[CrossRef]

M. C. Bashaw, T.-P. Ma, R. C. Barker, S. Mroczkowski, R. R. Dube, “Theory of complementary holograms arising from electron-hole transport in photorefractive media,” J. Opt. Soc. Am. B 7, 2329–2338 (1990).
[CrossRef]

Mallick, S.

A. Delboulbe, C. Fromont, J. P. Herriau, S. Mallick, J.-P. Huignard, “Quasi-nondestructive readout of holographically stored information in photorefractive Bi12SiO20crystals,” Appl. Phys. Lett. 55, 713–715 (1989).
[CrossRef]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. II: Beam coupling, light amplification,” Ferroelectrics 22, 961–964 (1990).
[CrossRef]

N. K. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I: Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Markov, V. N.

N. V. Kukhtarev, G. E. Dogvalenko, V. N. Markov, “Influence of the optical activity on hologram formation in photorefractive crystals,” Appl. Phys. A 33, 227–230 (1984).
[CrossRef]

Meyer, W.

W. Meyer, P. Würfel, R. Munser, G. Miller-Vogt, “Kinetics of fixation of phase holograms in LiNbO3,” Phys. Status Solidi A 53171–180 (1979),
[CrossRef]

Micheron, F.

F. Micheron, G. Bismuth, “Electrical control of fixation and erasure of holographic patterns in ferroelectric materials,” Appl. Phys. Lett. 20, 79–81 (1972).
[CrossRef]

Miller-Vogt, G.

W. Meyer, P. Würfel, R. Munser, G. Miller-Vogt, “Kinetics of fixation of phase holograms in LiNbO3,” Phys. Status Solidi A 53171–180 (1979),
[CrossRef]

Miteva, M.

S. Zhivkova, M. Miteva, “Holographic recording in photorefractive crystals with simultaneous electron-hole transport and two active centers,” J. Appl. Phys. 68, 3099–3103 (1990).
[CrossRef]

M. Miteva, L. Nikolova, “Oscillating behaviour of diffracted light on uniform illumination of holograms in photorefractive Bi12TiO20crystals,” Opt. Commun. 67, 192–194 (1988).
[CrossRef]

Montemezzani, G.

G. Montemezzani, P. Günter, “Thermal hologram fixing in pure and doped KNbO3crystals,” J. Opt. Soc. Am. B 7, 2323–2328 (1990).
[CrossRef]

G. Montemezzani, M. Ingold, H. Looser, P. Günter, “Multiple photorefractive gratings in Ce-doped LiNbO3and KNbO3crystals,” Ferroelectrics 92, 281–287 (1989).
[CrossRef]

Mroczkowski, S.

M. C. Bashaw, T.-P. Ma, R. C. Barker, S. Mroczkowski, R. R. Dube, “Introduction, revelation, and evolution of complementary gratings in photorefractive bismuth silicon oxide,” Phys. Rev. B 42, 5641–5648 (1990).
[CrossRef]

M. C. Bashaw, T.-P. Ma, R. C. Barker, S. Mroczkowski, R. R. Dube, “Theory of complementary holograms arising from electron-hole transport in photorefractive media,” J. Opt. Soc. Am. B 7, 2329–2338 (1990).
[CrossRef]

Munser, R.

W. Meyer, P. Würfel, R. Munser, G. Miller-Vogt, “Kinetics of fixation of phase holograms in LiNbO3,” Phys. Status Solidi A 53171–180 (1979),
[CrossRef]

Nikolova, L.

M. Miteva, L. Nikolova, “Oscillating behaviour of diffracted light on uniform illumination of holograms in photorefractive Bi12TiO20crystals,” Opt. Commun. 67, 192–194 (1988).
[CrossRef]

Nouchi, P.

J. P. Partanen, P. Nouchi, J. M. C. Jonathan, R. W. Hellwarth, “Comparison between holographic and transient-photocurrent measurements of electron mobility in photorefractive Bi12SiO20,” Phys. Rev. B 44, 1487–1491 (1991).
[CrossRef]

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. II: Beam coupling, light amplification,” Ferroelectrics 22, 961–964 (1990).
[CrossRef]

N. K. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I: Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Panchenko, E. M.

E. I. Bondarenko, V. A. Zagorulko, Yu. S. Kuz’minov, A. N. Pavlov, E. M. Panchenko, O. I. Prokopalo, “Model of the electret state in oxygen-octahedral materials,” Sov. Phys. Solid State 27, 629–630 (1985).

Partanen, J. P.

J. P. Partanen, P. Nouchi, J. M. C. Jonathan, R. W. Hellwarth, “Comparison between holographic and transient-photocurrent measurements of electron mobility in photorefractive Bi12SiO20,” Phys. Rev. B 44, 1487–1491 (1991).
[CrossRef]

Pavlov, A. N.

E. I. Bondarenko, V. A. Zagorulko, Yu. S. Kuz’minov, A. N. Pavlov, E. M. Panchenko, O. I. Prokopalo, “Model of the electret state in oxygen-octahedral materials,” Sov. Phys. Solid State 27, 629–630 (1985).

Prokopalo, O. I.

E. I. Bondarenko, V. A. Zagorulko, Yu. S. Kuz’minov, A. N. Pavlov, E. M. Panchenko, O. I. Prokopalo, “Model of the electret state in oxygen-octahedral materials,” Sov. Phys. Solid State 27, 629–630 (1985).

Redfield, S.

Ringhofer, K. H.

P. Hertel, K. H. Ringhofer, R. Sommerfeldt, “Theory of thermal hologram fixing and application to LiNbO3:Cu,” Phys. Status Solidi A 104, 855–862 (1987).
[CrossRef]

Rogers, K. F.

D. Von der Linde, A. M. Glass, K. F. Rogers, “High-sensitivity optical recording in KTN by two photon absorption,” Appl. Phys. Lett. 26, 22–24 (1975).
[CrossRef]

D. Von der Linde, A. M. Glass, K. F. Rogers, “Multiphoton photorefractive processes for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
[CrossRef]

Ruzhnikov, A. V.

E. V. Bursian, Ya. G. Girshberg, A. V. Ruzhnikov, “The correlation between optical absorption spectra, carrier mobility, and phase transition temperature in some ferroelectrics,” Phys. Status Solidi B 74, 689–693 (1976).
[CrossRef]

Sommerfeldt, R.

P. Hertel, K. H. Ringhofer, R. Sommerfeldt, “Theory of thermal hologram fixing and application to LiNbO3:Cu,” Phys. Status Solidi A 104, 855–862 (1987).
[CrossRef]

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. II: Beam coupling, light amplification,” Ferroelectrics 22, 961–964 (1990).
[CrossRef]

N. K. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I: Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Staebler, D. L.

J. J. Amodei, D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
[CrossRef]

D. L. Staebler, “Ferroelectric crystals,” in Holographic Recording Materials, H. M. Smith, ed. (Springer-Verlag, Berlin, 1977), pp. 101–132.
[CrossRef]

Stepanov, S. I.

G. S. Trofimov, S. I. Stepanov, “Electrical development of a hologram in a Bi12SiO20crystal,” Sov. Tech. Phys. Lett. 10, 282–283 (1984).

V. V. Kulikov, S. I. Stepanov, “Mechanisms of holographic recording and thermal fixing in photorefractive LiNbO3:Fe,” Sov. Phys. Solid State 21, 1849–1851 (1979).

Strohkendl, F. P.

F. P. Strohkendl, “Light-induced dark decays of photorefractive gratings and their observation in Bi12SiO20,” J. Appl. Phys. 65, 3773–3780 (1989).
[CrossRef]

Thaxter, J. B.

Trofimov, G. S.

G. S. Trofimov, S. I. Stepanov, “Electrical development of a hologram in a Bi12SiO20crystal,” Sov. Tech. Phys. Lett. 10, 282–283 (1984).

Valley, G. C.

G. C. Valley, “Simultaneous electron/hole transport in photorefractive materials,” J. Appl. Phys. 59, 3363–3366 (1986).
[CrossRef]

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. II: Beam coupling, light amplification,” Ferroelectrics 22, 961–964 (1990).
[CrossRef]

N. K. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I: Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Von der Linde, D.

D. Von der Linde, A. M. Glass, K. F. Rogers, “High-sensitivity optical recording in KTN by two photon absorption,” Appl. Phys. Lett. 26, 22–24 (1975).
[CrossRef]

D. Von der Linde, A. M. Glass, K. F. Rogers, “Multiphoton photorefractive processes for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
[CrossRef]

Vormann, H.

H. Vormann, G. Weber, S. Kapphan, M. Wöhlecke, “Hydrogen as origin of themal fixing of LiNbOe:Fe,” Solid State Commun. 57, 543–545 (1981).
[CrossRef]

Weber, G.

H. Vormann, G. Weber, S. Kapphan, M. Wöhlecke, “Hydrogen as origin of themal fixing of LiNbOe:Fe,” Solid State Commun. 57, 543–545 (1981).
[CrossRef]

Wöhlecke, M.

H. Vormann, G. Weber, S. Kapphan, M. Wöhlecke, “Hydrogen as origin of themal fixing of LiNbOe:Fe,” Solid State Commun. 57, 543–545 (1981).
[CrossRef]

Würfel, P.

W. Meyer, P. Würfel, R. Munser, G. Miller-Vogt, “Kinetics of fixation of phase holograms in LiNbO3,” Phys. Status Solidi A 53171–180 (1979),
[CrossRef]

Zagorulko, V. A.

E. I. Bondarenko, V. A. Zagorulko, Yu. S. Kuz’minov, A. N. Pavlov, E. M. Panchenko, O. I. Prokopalo, “Model of the electret state in oxygen-octahedral materials,” Sov. Phys. Solid State 27, 629–630 (1985).

Zgonik, M.

I. Biaggio, M. Zgonik, P. Günter, “Photorefractive effects induced by picosecond light pulses in reduced KNbO3,” J. Opt. Soc. Am. B 9, 1480–1487 (1992).
[CrossRef]

I. Biaggio, M. Zgonik, P. Günter, “Build-up and dark decay of transient photorefractive gratings in reduced KNbO3,” Opt. Commun. 77, 312–317 (1990).
[CrossRef]

Zhivkova, S.

S. Zhivkova, M. Miteva, “Holographic recording in photorefractive crystals with simultaneous electron-hole transport and two active centers,” J. Appl. Phys. 68, 3099–3103 (1990).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. A (1)

N. V. Kukhtarev, G. E. Dogvalenko, V. N. Markov, “Influence of the optical activity on hologram formation in photorefractive crystals,” Appl. Phys. A 33, 227–230 (1984).
[CrossRef]

Appl. Phys. Lett. (6)

D. Von der Linde, A. M. Glass, K. F. Rogers, “Multiphoton photorefractive processes for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
[CrossRef]

D. Von der Linde, A. M. Glass, K. F. Rogers, “High-sensitivity optical recording in KTN by two photon absorption,” Appl. Phys. Lett. 26, 22–24 (1975).
[CrossRef]

J. J. Amodei, D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
[CrossRef]

F. Micheron, G. Bismuth, “Electrical control of fixation and erasure of holographic patterns in ferroelectric materials,” Appl. Phys. Lett. 20, 79–81 (1972).
[CrossRef]

J. P. Herriau, J.-P. Huignard, “Hologram fixing process at room temperature in photorefractive Bi12SiO20crystals,” Appl. Phys. Lett. 49, 1140–1142 (1986).
[CrossRef]

A. Delboulbe, C. Fromont, J. P. Herriau, S. Mallick, J.-P. Huignard, “Quasi-nondestructive readout of holographically stored information in photorefractive Bi12SiO20crystals,” Appl. Phys. Lett. 55, 713–715 (1989).
[CrossRef]

Ferroelectrics (3)

G. Montemezzani, M. Ingold, H. Looser, P. Günter, “Multiple photorefractive gratings in Ce-doped LiNbO3and KNbO3crystals,” Ferroelectrics 92, 281–287 (1989).
[CrossRef]

N. K. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I: Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. II: Beam coupling, light amplification,” Ferroelectrics 22, 961–964 (1990).
[CrossRef]

J. Appl. Phys. (4)

G. C. Valley, “Simultaneous electron/hole transport in photorefractive materials,” J. Appl. Phys. 59, 3363–3366 (1986).
[CrossRef]

S. Zhivkova, M. Miteva, “Holographic recording in photorefractive crystals with simultaneous electron-hole transport and two active centers,” J. Appl. Phys. 68, 3099–3103 (1990).
[CrossRef]

F. P. Strohkendl, “Light-induced dark decays of photorefractive gratings and their observation in Bi12SiO20,” J. Appl. Phys. 65, 3773–3780 (1989).
[CrossRef]

L. Arizmendi, “Thermal fixing of holographic gratings in Bi12SiO20,” J. Appl. Phys. 65, 423–427 (1989).
[CrossRef]

J. Opt. Soc. Am. B (5)

Opt. Commun. (2)

I. Biaggio, M. Zgonik, P. Günter, “Build-up and dark decay of transient photorefractive gratings in reduced KNbO3,” Opt. Commun. 77, 312–317 (1990).
[CrossRef]

M. Miteva, L. Nikolova, “Oscillating behaviour of diffracted light on uniform illumination of holograms in photorefractive Bi12TiO20crystals,” Opt. Commun. 67, 192–194 (1988).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (2)

J. P. Partanen, P. Nouchi, J. M. C. Jonathan, R. W. Hellwarth, “Comparison between holographic and transient-photocurrent measurements of electron mobility in photorefractive Bi12SiO20,” Phys. Rev. B 44, 1487–1491 (1991).
[CrossRef]

M. C. Bashaw, T.-P. Ma, R. C. Barker, S. Mroczkowski, R. R. Dube, “Introduction, revelation, and evolution of complementary gratings in photorefractive bismuth silicon oxide,” Phys. Rev. B 42, 5641–5648 (1990).
[CrossRef]

Phys. Status Solidi A (2)

W. Meyer, P. Würfel, R. Munser, G. Miller-Vogt, “Kinetics of fixation of phase holograms in LiNbO3,” Phys. Status Solidi A 53171–180 (1979),
[CrossRef]

P. Hertel, K. H. Ringhofer, R. Sommerfeldt, “Theory of thermal hologram fixing and application to LiNbO3:Cu,” Phys. Status Solidi A 104, 855–862 (1987).
[CrossRef]

Phys. Status Solidi B (1)

E. V. Bursian, Ya. G. Girshberg, A. V. Ruzhnikov, “The correlation between optical absorption spectra, carrier mobility, and phase transition temperature in some ferroelectrics,” Phys. Status Solidi B 74, 689–693 (1976).
[CrossRef]

Solid State Commun. (1)

H. Vormann, G. Weber, S. Kapphan, M. Wöhlecke, “Hydrogen as origin of themal fixing of LiNbOe:Fe,” Solid State Commun. 57, 543–545 (1981).
[CrossRef]

Sov. Phys. Solid State (2)

V. V. Kulikov, S. I. Stepanov, “Mechanisms of holographic recording and thermal fixing in photorefractive LiNbO3:Fe,” Sov. Phys. Solid State 21, 1849–1851 (1979).

E. I. Bondarenko, V. A. Zagorulko, Yu. S. Kuz’minov, A. N. Pavlov, E. M. Panchenko, O. I. Prokopalo, “Model of the electret state in oxygen-octahedral materials,” Sov. Phys. Solid State 27, 629–630 (1985).

Sov. Tech. Phys. Lett. (2)

N. K. Kukhtarev, “Kinetics of hologram recording and erasure in electrooptic crystals,” Sov. Tech. Phys. Lett. 2, 438–440 (1976).

G. S. Trofimov, S. I. Stepanov, “Electrical development of a hologram in a Bi12SiO20crystal,” Sov. Tech. Phys. Lett. 10, 282–283 (1984).

Other (2)

J. Mort, D. M. Pai, eds., Photoconductivity and Related Phenomena (Elsevier, Amsterdam, 1976).

D. L. Staebler, “Ferroelectric crystals,” in Holographic Recording Materials, H. M. Smith, ed. (Springer-Verlag, Berlin, 1977), pp. 101–132.
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Dynamic behavior of the photorefractive space-charge field amplitude |E1| observed in KNbO3 crystals at elevated temperatures (≈100°C). In regions A and B the crystal is illuminated with two laser beams used for recording. In regions C and D the crystal is in the dark or is illuminated by only one homogeneous beam. Charge compensation of a primary space-charge grating by secondary charge carriers and the subsequent revelation of the secondary grating are the underlying processes (see Ref. 15). The value of |E1| at point 2 is not to scale.

Fig. 2
Fig. 2

Grating spacing dependence of the total space-charge field amplitude |E1| and the electronic contribution to it |Ee1| in the steady state. Solid curve, |E1|, no applied field, Eq. (12a); dashed–dotted line curve, |E1|, applied field E0 = 10 kV/cm, Eq. (8); dashed curve, |Ee1|, Eq. (12b). The model parameters used are summarized in Table 1.

Fig. 3
Fig. 3

Grating spacing dependence of the time rate Γ2 for E0 = 0. The solid curves show the approximate analytical expression (20) for the model parameters of Table 1 (lower curve) and a 10-times increased ionic mobility [μI = 2 × 10−14 m2(V s)−1, upper curve]. The dashed curves are exact solutions of Eq. (14) for the corresponding parameters.

Fig. 4
Fig. 4

Grating spacing dependence of the time rate Γ3 for E0 = 0. The solid curves show the approximate analytical expression (21) for the model parameters of Table 1 (lower curve) and a 10-times increased ionic mobility [μI = 2 × 10−14 m2(V s)−1, upper curve]. The dashed curves are exact solutions of Eq. (14) for the corresponding parameters. For the smaller value of μI the solid and the dashed curves also overlap at small grating spacings.

Fig. 5
Fig. 5

Exact solution of the dynamic Eqs. (4a)(4c) for the model parameters of Table 1 except for a 10-times increased ionic mobility [μI = 2 × 10−14 m(V s−1]. Solid curves, total space-charge field E1Ee1 + EI1; dashed curves, electronic (primary) space-charge field Ee1; dotted–dashed curves, ionic (secondary) space-charge field EI1. Note the different scales for both the x and y axes in (a) and (b). The numerical values of all the parameters describing the solution for the field E1(t) following Eq. (13) are given. (a) Grating spacing Λ = 0.5 μm. Recording: Γ1 = 1.0 × 107 s−1; Γ2 = 23.25 s−1; Γ3 = 4.97 s−1. E1(Γ1) = 0.07 V/m; E1(Γ2) = −41784 V/m; E1(Γ3) = +41060 V/m; E1sat = 723 V/m. Erasure: Γ1 = 1.0 × 107 s−1; Γ2 = 17.57 s−1; Γ3 = 4.78 s−1. E1(Γ1) = −0.05 V/m; E1(Γ2) = +43402 V/m; E1(Γ3) = −42679 V/m; E1sat = 0. (b) Grating spacing Λ = 2 μm. Recording: Γ1 = 5.3 × 106 s−1; Γ2 = 16.31 s−1; Γ3 = 0.85 s−1. E1(Γ1) = +0.05 V/m; E1(Γ2) = −24271 V/m; E1(Γ3) = +24088 V/m; Elsat = 184 V/m. Erasure: Γ1 = 5.3 × 106 s−1; Γ2 = 13.53 s−1; Γ3 = 0.75 s−1. E1(Γ1) = −0.05 V/m; E1(Γ2) = +21342 V/m; E1(Γ3) = −21158 V/m; Elsat = 0.

Fig. 6
Fig. 6

Exact solution of the dynamic equations (4a)(4c) for Λ = 0.5 μm. The parameters are the same as in Fig. 5(a), except for a 40-times-smaller number of ions (NIo = 2.5 × 1022 m−3) and a 40-times-larger conductivity for the ions (μI = 8 × 10−13 m2(V S)−1, giving an unchanged dielectric relaxation rate for the ions. The meaning of the curves is the same as in Fig. 5. The numerical values of all the parameters describing the solution for the field E1(t) following Eq. (13) are given. Recording: Γ1 = 1.0 × 107 s−1; Γ2 = 23.76 s−1; Γ3 = 8.71 s−1. E1(Γ1) = 0.07 V/m; E1(Γ2) = −41,671 V/m; E1(Γ3) = +25,519 s−1. E1sat = 16,152 V/m. Erasure: Γ1 = 1.0 × 107 s−1; Γ2 = 18.43 s−1; Γ3 = 8.17 s−1. E1(Γ1) = −0.05 V/m; E1(Γ2) = +41,557 V/m; E1(Γ3) = −25,404 V/m; Elsat = 0.

Fig. 7
Fig. 7

Intensity dependence of the time rate Γ3 as predicted from Eq. (19b) for Λ = 2 μm. The values are divided with the value of Γ3 in the dark. The solid curve is drawn with the parameters of Table 1. The other curves are obtained by modifying only the indicated parameter to the given value.

Fig. 8
Fig. 8

Real and imaginary parts of the time rate Γ2* as a function of the externally applied electric field E0. Solid curves, real part from relation (30); dashed curves, imaginary part from relation (31). The usual parameters of Table 1 are taken, and the curves for the three indicated values of the grating spacing Λ are shown.

Fig. 9
Fig. 9

Real (solid curves) and imaginary (dashed curves) parts of the time rate Γ3* as a function of the externally applied electric field E0. The curves are drawn following relation (19b) with the parameters of Table 1 for the indicated values of the grating spacing Λ.

Fig. 10
Fig. 10

Band scheme for the electron–hole model for charge compensation. The hole–photoexcitation rate constant sh is assumed to be zero.

Fig. 11
Fig. 11

Grating spacing dependence of the handling time τ3 = (Γ3)−1 in a pure KNbO3 sample measured at the temperature T = 107°C with an erasing intensity I = 40 mW/cm2. The solid curve indicates the best fit to Eq. (21). From the fitted parameters we determine that τdiI = (6.5 ± 0.7) s and Neff = (0.75 ± 0.15) × 1015 cm−3.

Fig. 12
Fig. 12

Normalized diffraction efficiencies observed during the erasure process in pure KNbO3. For time t < 0, two recording beams were illuminating the crystal until saturation of the primary and secondary gratings was reached. At time t = 0, one of the recording beams was switched off, and the erasure proceeded as shown in regions C and D in Fig. 1. The curves shown compare the decay rates for three values of the applied field E0 at the grating spacing Λ = 2.96 μm. The values for the decay time constants τ3 ≡ 1/Γ3 are τ3(E0 = 0) = 18 s, τ3(E0 = 1 kV/cm) = 13 s, τ3(E0 = 2 kV/cm) = 8.2 s.

Fig. 13
Fig. 13

Electric-field dependence of the diffraction efficiency η measured during the handling process at the grating spacing Λ = 18 μm. During the recording and the beginning of the erasure process the electric field E0 = 2 k/cm is on. After the grating compensation has reached saturation, one of the recording beams is switched off at time t = 5 s. Later, the field is switched off (dashed curves) and on again (solid curves) several times in order to show the jumps in diffraction efficiency. The inset shows the same kind of measurement but for the grating spacing Λ = 0.7 μm.

Tables (1)

Tables Icon

Table 1 Values of the Crystal Parameters and of the External Conditions Used for Modeling the Photorefractive Response

Equations (59)

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n t = ( s I + β ) ( N D o - N D + ) - γ n N D + + 1 e J e x ,
N D + t = ( s I + β ) ( N D o - N D + ) - γ n N D + ,
N I t = - 1 e J I x ,
J e = e μ e n E + μ e k B T n x ,
J I = e μ I N I E - μ I k B T N I x ,
0 E x 0 E e x + 0 E I x = e ( N D + - n - N A ) + e ( N I - N I o ) .
I ( x ) I 0 + I 1 exp ( i K x ) ,
F ( x ) = F 0 + F 1 exp ( i K x ) ,
n 1 t = - ( Γ R e + Γ D e + Γ die - i Γ E e ) n 1 + ( Γ die - Γ I e ) N D 1 + + Γ die N I 1 + s ( N D o - N D o + ) I 1 ,
N D 1 + t = - Γ R e n 1 - Γ I e N D 1 + + s ( N D o - N D o + ) I 1 ,
N I 1 t = Γ di I n 1 - Γ di I N D 1 + - ( Γ di I + Γ D I + i Γ E I ) N I 1 ,
Γ die e μ e n 0 0 ,
Γ I e s I 0 + β + γ n 0 ,
Γ R e γ ( N A + n 0 ) ,
Γ D e K 2 k B T μ e e ,
Γ E e K μ e E 0 ,
Γ di I e μ I N I o 0 ,
Γ D I K 2 k B T μ I e ,
Γ E I K μ I E 0 .
n 0 = ( s I 0 + β ) γ ( N D o - N A ) N A .
E 1 = e 0 i K [ s ( N D - N D o + ) I 1 ( Γ D I + i Γ E I ) ( Γ D e - i Γ E e ) ] / [ Γ I e ( Γ di I + Γ D I + i Γ E I ) ( Γ D e - i Γ E e ) + Γ die ( Γ I e + Γ R e ) ( Γ D I + i Γ E I ) ] .
E 1 = - i m E q ( E D 2 + E 0 2 ) ( E q I + E D + i E 0 ) ( E D - i E 0 ) + E q ( E D + i E 0 ) ,
E q = e 0 K N A ( N D o - N A ) N D o = e 0 K N eff
E q I = e N I o 0 K ,
E e 1 = - i m E q ( E q I + E D + i E 0 ) ( E D - i E 0 ) ( E q I + E D + i E 0 ) ( E D - i E 0 ) + E q ( E D + i E o ) ,
E I 1 = + i m E q E q I ( E D - i E 0 ) ( E q I + E D + i E 0 ) ( E D - i E 0 ) + E q ( E D + i E o ) .
E 1 = - i m E D 1 + E D E q + E q I E q ,
E e 1 = - i m E q ( E D + E q I ) E q + E D + E q I ,
E I 1 = + i m E q E q I E q + E D + E q I .
G 1 ( t ) = G 1 ( Γ 1 ) exp ( - Γ 1 t ) + G 1 ( Γ 2 ) exp ( - Γ 2 t ) + G 1 ( Γ 3 ) exp ( - Γ 3 t ) + G 1 sat .
Γ 3 - ( Γ tot ) Γ 2 + ( Γ b ) 2 Γ - ( Γ c ) 3 = 0 ,
Γ tot Γ die + Γ I e + Γ R e + Γ D e + Γ di I + Γ D I ,
Γ b [ Γ die ( Γ D I + Γ I e + Γ R e ) + Γ di I ( Γ D e + Γ I e + Γ R e ) + Γ D I ( Γ D e + Γ I e + Γ R e ) + Γ D e Γ I e ] 1 / 2 ;
Γ c [ Γ die Γ D I ( Γ I e + Γ R e ) + Γ D e Γ I e ( Γ di I + Γ D I ) ] 1 / 3 .
Γ 1 = Γ tot ,
Γ 2 = ( Γ b ) 2 Γ tot - ( Γ c ) 3 ( Γ b ) 2 - Γ tot ( Γ c ) 6 ( Γ b ) 6 - 2 ( Γ tot ) 2 ( Γ c ) 9 ( Γ b ) 10 - 5 ( Γ out ) 3 ( Γ c ) 12 ( Γ b ) 14 - = ( Γ b ) 2 Γ tot - Γ 3 ,
Γ 3 = ( Γ c ) 3 ( Γ b ) 2 + Γ tot ( Γ c ) 6 ( Γ b ) 6 + 2 ( Γ tot ) 2 ( Γ c ) 9 ( Γ b ) 10 + 5 ( Γ tot ) 3 ( Γ c ) 12 ( Γ b ) 14 + .
Γ 2 ( Γ b ) 2 Γ tot ,
Γ 3 ( Γ c ) 3 ( Γ b ) 2 .
Γ 2 = Γ di I [ 1 + K 2 K o I 2 ] + Γ di e [ 1 + K 2 K o e 2 1 + K 2 K e 2 ] ,
Γ 3 = Γ di I Γ di e [ K 2 K o I 2 + K 2 K o e 2 ( 1 + K 2 K o I 2 ) ] Γ di e [ 1 + K 2 K o e 2 ] + Γ di I [ ( 1 + K 2 K e 2 ) ( 1 + K 2 K o I 2 ) ] ,
K o e 2 = e 2 N A ( N D o - N A ) 0 k B T N D o = e 2 N eff 0 k B T
K o I 2 = e 2 N I o 0 k B T
K e 2 = e γ N A μ e k B T
Γ 3 Γ di I K 2 K o e 2 + K 2 .
Γ 3 Γ di I K 2 K o e 2 + K 2 + K 2 Γ di e Γ D .
Γ tot * Γ tot + i ( Γ E I - Γ E e ) ,
( Γ b 2 ) * Γ b 2 + Γ E e Γ E I + i [ Γ E I ( Γ di e + Γ I e + Γ R e + Γ D e ) - Γ E e ( Γ di I + Γ D I + Γ I e ) ] ,
( Γ c 3 ) * Γ c 3 + Γ I e Γ E e Γ E I + i [ Γ di e Γ E I ( Γ R e + Γ I e ) + Γ D e Γ I e Γ E I - Γ E e Γ I e ( Γ di I + Γ D I ) ] .
Re ( Γ 2 * ) Γ di I [ 1 + K 2 K o I 2 + K 2 K D 2 ( K 2 + K e 2 ) 2 + K 2 K D 2 ] + Γ di e [ K e 2 ( K 2 + K e 2 ) ( 1 + K 2 K o e 2 ) + K e 2 K 2 K o e 2 K D 2 ( K 2 + K e 2 ) 2 + K 2 K D 2 ]
Im ( Γ 2 * ) Γ di I K K D K o I 2 + Γ di e [ K e 2 ( 1 - K e 2 K o e 2 ) K K D ( K 2 + K e 2 ) 2 + K 2 K D 2 ]
K D e E 0 K B T
E q e = ( e / 0 K ) [ N D o + ( N D o - N D o + ) / N D o ] , E q h = ( e / 0 K ) [ N A o - ( N A o - N A o - ) / N A o ]
E 1 = - i m E D E q e E D + E q e + E q h ,
Γ 2 = Γ di h [ 1 + K 2 K o h 2 1 + K 2 K h 2 ] + Γ di e [ 1 + K 2 K o e 2 1 + K 2 K e 2 ]
Γ 3 = Γ di h Γ di e [ K 2 K o h 2 + K 2 K o e 2 ( 1 + K 2 K o h 2 ) ] Γ di e [ ( 1 + K 2 K h 2 ) ( 1 + K 2 K o e 2 ) ] + Γ di h [ ( 1 + K 2 K e 2 ) ( 1 + K 2 K o h 2 ) ]
K o h 2 = e 2 N A o - ( N A o - N A o - ) 0 k B T N A o
K h 2 = e γ h N A o - μ h k B T
Γ di h e p 0 μ h 0 ,

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