Abstract

The theory of grating oscillations in photorefractive materials is developed in the linear and nonlinear approximations for the drift mechanism of holographic recording. The resonance dependence of diffraction efficiency on the phase-modulation frequency is predicted for the linear regime in which holograms are recorded by two beams, one of which is phase modulated. For long drift lengths (KgL01) the resonance frequency is shown to be Ωr(τ1KgL0)-1. A more pronounced resonance peak is expected for the non-Bragg diffraction orders. In the nonlinear regime of recording, additional resonance maxima at Ωr/p (p is an integer) are found. Grating oscillations are experimentally studied in thin holograms of Bi12TiO20. A sharp resonance for the non-Bragg order in the interval 100–2000 Hz is detected. The position of the resonance is shown to depend on the experimental conditions. The experiment is in excellent agreement with the theory. At a high contrast ratio and in a high external electric field, distortions in the resonance dependence at Ω<Ωr and even a chaotic frequency dependence are found, which points to the nonlinear character of grating oscillations.

© 1998 Optical Society of America

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References

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  1. M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, Berlin, 1991).
  2. S. I. Stepanov, “Applications of photorefractive crystals,” Rep. Progr. Phys. 57, 39 (1994).
    [Crossref]
  3. T. J. Hall, M. A. Fiddy, and M. S. Ner, “Detector for an optical-fiber accoustic sensor using dynamic holographic interferometry,” Opt. Lett. 5, 485 (1980).
    [Crossref] [PubMed]
  4. V. M. Petrov and M. P. Petrov, “Two- and three-wave mixing in a PRIZ space light modulator,” Tech. Phys. Lett. 21, 403 (1995).
  5. M. P. Petrov, V. M. Petrov, I. S. Zouboulis, and L. P. Xu, “Two-wave and induced three-wave mixing on a thin Bi12TiO20 hologram,” Opt. Commun. 134, 599 (1997).
    [Crossref]
  6. S. Breugnot, M. Defour, and J. P. Huignard, “Photorefractive two-wave mixing: complex amplitudes solutions in the case of a weak signal beam,” Opt. Commun. 134, 599 (1997).
    [Crossref]
  7. S. I. Stepanov, “Photorefractive crystals for adaptive interferometry,” in Optical Holography with Recording in Three-Dimensional Media, Yu. Denisyuk, ed. (Nauka, Leningrad, 1983), in Russian.
  8. S. Bian and J. Frejlich, “Photorefractive response time measurements in GaAs crystals by phase modulation in two wave mixing,” Opt. Lett. 19, 1702 (1994).
    [Crossref] [PubMed]
  9. M. P. Petrov, V. M. Petrov, V. V. Bryksin, I. Zouboulis, A. Gerwens, and E. Krätzig, “Grating oscillations in photorefractive crystals,” Opt. Lett. 22, 1083 (1997).
    [Crossref] [PubMed]
  10. W. R. Klein, “Theoretical Efficiency of Bragg Devices,” Proc. IEEE 54, 803 (1966).
    [Crossref]
  11. M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Non-steady-state photo-electromotive-force induced by dynamic gratings in partially compensated photoconductors,” J. Appl. Phys. 68, 2216 (1990).
    [Crossref]
  12. N. V. Kukhtarev, V. B. Markov, S. G. Odoulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electrooptic crystals,” Ferroelectrics 22, 949 (1979).
    [Crossref]
  13. M. G. Moharam, T. K. Gaylord, R. Magnuson, and L. Young, “Holographic grating formation in photorefractive crystals with arbitrary electron transport length,” J. Appl. Phys. 50, 5642 (1979).
    [Crossref]
  14. P. Günter and J.-P. Huignard, Photorefractive Materials and Their Applications I and II, Vols. 61 and 62 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988).
  15. S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “ ‘Running holograms’ in photorefractive Bi12SiO20 crystals,” Opt. Commun. 44, 19 (1982).
    [Crossref]
  16. P. Refregier, L. Solymar, K. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
    [Crossref]
  17. T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. N. Ringhofer, “Low frequency peculiarities of the photorefractive response in sillenites,” Opt. Commun. 113, 371 (1995).
    [Crossref]
  18. M. Vasnetsov, P. Buchhave, and S. Lyuksyutov, “Phase modulation spectroscopy of space-charge wave resonances in Bi12SiO20,” Opt. Commun. 137, 181 (1997).
    [Crossref]
  19. R. F. Kazarinov, R. A. Suris, and B. I. Fuks, “ ‘Thermal current’ instability in compensated semiconductors,” Phys. Tech. Semicond. 6, 572 (1972), in Russian.
  20. N. G. Zhdanova, M. S. Kagan, R. A. Suris, and B. I. Fuks, “Trap charge exchange waves in compensated germanium,” Pis'ma Zh. Eksp. Teor. Fiz. 74, 346 (1978), in Russian.
  21. R. Orlowski and E. Krätzig, “Holographic method for the determination of photo-induced electron and hole transport in electro-optic crystals,” Solid State Commun. 27, 1351 (1978).
    [Crossref]
  22. F. Rickermann, S. Riehemann, K. Buse, D. Dirksen, and G. von Bally, “Diffraction efficiency enhancement of holographic gratings in Bi12Ti0.76V0.24O20 crystals after recording,” J. Opt. Soc. Am. B 13, 2299 (1996).
    [Crossref]

1997 (4)

M. P. Petrov, V. M. Petrov, I. S. Zouboulis, and L. P. Xu, “Two-wave and induced three-wave mixing on a thin Bi12TiO20 hologram,” Opt. Commun. 134, 599 (1997).
[Crossref]

S. Breugnot, M. Defour, and J. P. Huignard, “Photorefractive two-wave mixing: complex amplitudes solutions in the case of a weak signal beam,” Opt. Commun. 134, 599 (1997).
[Crossref]

M. P. Petrov, V. M. Petrov, V. V. Bryksin, I. Zouboulis, A. Gerwens, and E. Krätzig, “Grating oscillations in photorefractive crystals,” Opt. Lett. 22, 1083 (1997).
[Crossref] [PubMed]

M. Vasnetsov, P. Buchhave, and S. Lyuksyutov, “Phase modulation spectroscopy of space-charge wave resonances in Bi12SiO20,” Opt. Commun. 137, 181 (1997).
[Crossref]

1996 (1)

1995 (2)

V. M. Petrov and M. P. Petrov, “Two- and three-wave mixing in a PRIZ space light modulator,” Tech. Phys. Lett. 21, 403 (1995).

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. N. Ringhofer, “Low frequency peculiarities of the photorefractive response in sillenites,” Opt. Commun. 113, 371 (1995).
[Crossref]

1994 (2)

1990 (1)

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Non-steady-state photo-electromotive-force induced by dynamic gratings in partially compensated photoconductors,” J. Appl. Phys. 68, 2216 (1990).
[Crossref]

1985 (1)

P. Refregier, L. Solymar, K. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[Crossref]

1982 (1)

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “ ‘Running holograms’ in photorefractive Bi12SiO20 crystals,” Opt. Commun. 44, 19 (1982).
[Crossref]

1980 (1)

1979 (2)

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

M. G. Moharam, T. K. Gaylord, R. Magnuson, and L. Young, “Holographic grating formation in photorefractive crystals with arbitrary electron transport length,” J. Appl. Phys. 50, 5642 (1979).
[Crossref]

1978 (2)

N. G. Zhdanova, M. S. Kagan, R. A. Suris, and B. I. Fuks, “Trap charge exchange waves in compensated germanium,” Pis'ma Zh. Eksp. Teor. Fiz. 74, 346 (1978), in Russian.

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

1972 (1)

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, “ ‘Thermal current’ instability in compensated semiconductors,” Phys. Tech. Semicond. 6, 572 (1972), in Russian.

1966 (1)

W. R. Klein, “Theoretical Efficiency of Bragg Devices,” Proc. IEEE 54, 803 (1966).
[Crossref]

Bian, S.

Breugnot, S.

S. Breugnot, M. Defour, and J. P. Huignard, “Photorefractive two-wave mixing: complex amplitudes solutions in the case of a weak signal beam,” Opt. Commun. 134, 599 (1997).
[Crossref]

Bryksin, V. V.

Buchhave, P.

M. Vasnetsov, P. Buchhave, and S. Lyuksyutov, “Phase modulation spectroscopy of space-charge wave resonances in Bi12SiO20,” Opt. Commun. 137, 181 (1997).
[Crossref]

Buse, K.

Defour, M.

S. Breugnot, M. Defour, and J. P. Huignard, “Photorefractive two-wave mixing: complex amplitudes solutions in the case of a weak signal beam,” Opt. Commun. 134, 599 (1997).
[Crossref]

Dirksen, D.

Fiddy, M. A.

Frejlich, J.

Fuks, B. I.

N. G. Zhdanova, M. S. Kagan, R. A. Suris, and B. I. Fuks, “Trap charge exchange waves in compensated germanium,” Pis'ma Zh. Eksp. Teor. Fiz. 74, 346 (1978), in Russian.

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, “ ‘Thermal current’ instability in compensated semiconductors,” Phys. Tech. Semicond. 6, 572 (1972), in Russian.

Gaylord, T. K.

M. G. Moharam, T. K. Gaylord, R. Magnuson, and L. Young, “Holographic grating formation in photorefractive crystals with arbitrary electron transport length,” J. Appl. Phys. 50, 5642 (1979).
[Crossref]

Gerwens, A.

Günter, P.

P. Günter and J.-P. Huignard, Photorefractive Materials and Their Applications I and II, Vols. 61 and 62 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988).

Hall, T. J.

Huignard, J. P.

S. Breugnot, M. Defour, and J. P. Huignard, “Photorefractive two-wave mixing: complex amplitudes solutions in the case of a weak signal beam,” Opt. Commun. 134, 599 (1997).
[Crossref]

P. Refregier, L. Solymar, K. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[Crossref]

Huignard, J.-P.

P. Günter and J.-P. Huignard, Photorefractive Materials and Their Applications I and II, Vols. 61 and 62 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988).

Kagan, M. S.

N. G. Zhdanova, M. S. Kagan, R. A. Suris, and B. I. Fuks, “Trap charge exchange waves in compensated germanium,” Pis'ma Zh. Eksp. Teor. Fiz. 74, 346 (1978), in Russian.

Kazarinov, R. F.

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, “ ‘Thermal current’ instability in compensated semiconductors,” Phys. Tech. Semicond. 6, 572 (1972), in Russian.

Khomenko, A. V.

M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, Berlin, 1991).

Klein, W. R.

W. R. Klein, “Theoretical Efficiency of Bragg Devices,” Proc. IEEE 54, 803 (1966).
[Crossref]

Krätzig, E.

M. P. Petrov, V. M. Petrov, V. V. Bryksin, I. Zouboulis, A. Gerwens, and E. Krätzig, “Grating oscillations in photorefractive crystals,” Opt. Lett. 22, 1083 (1997).
[Crossref] [PubMed]

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

Kukhtarev, N. V.

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

Kulikov, V. V.

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “ ‘Running holograms’ in photorefractive Bi12SiO20 crystals,” Opt. Commun. 44, 19 (1982).
[Crossref]

Lyuksyutov, S.

M. Vasnetsov, P. Buchhave, and S. Lyuksyutov, “Phase modulation spectroscopy of space-charge wave resonances in Bi12SiO20,” Opt. Commun. 137, 181 (1997).
[Crossref]

Magnuson, R.

M. G. Moharam, T. K. Gaylord, R. Magnuson, and L. Young, “Holographic grating formation in photorefractive crystals with arbitrary electron transport length,” J. Appl. Phys. 50, 5642 (1979).
[Crossref]

Mann, M.

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. N. Ringhofer, “Low frequency peculiarities of the photorefractive response in sillenites,” Opt. Commun. 113, 371 (1995).
[Crossref]

Markov, V. B.

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

McClelland, T. E.

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. N. Ringhofer, “Low frequency peculiarities of the photorefractive response in sillenites,” Opt. Commun. 113, 371 (1995).
[Crossref]

Moharam, M. G.

M. G. Moharam, T. K. Gaylord, R. Magnuson, and L. Young, “Holographic grating formation in photorefractive crystals with arbitrary electron transport length,” J. Appl. Phys. 50, 5642 (1979).
[Crossref]

Ner, M. S.

Odoulov, S. G.

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

Orlowski, R.

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

Petrov, M. P.

M. P. Petrov, V. M. Petrov, V. V. Bryksin, I. Zouboulis, A. Gerwens, and E. Krätzig, “Grating oscillations in photorefractive crystals,” Opt. Lett. 22, 1083 (1997).
[Crossref] [PubMed]

M. P. Petrov, V. M. Petrov, I. S. Zouboulis, and L. P. Xu, “Two-wave and induced three-wave mixing on a thin Bi12TiO20 hologram,” Opt. Commun. 134, 599 (1997).
[Crossref]

V. M. Petrov and M. P. Petrov, “Two- and three-wave mixing in a PRIZ space light modulator,” Tech. Phys. Lett. 21, 403 (1995).

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Non-steady-state photo-electromotive-force induced by dynamic gratings in partially compensated photoconductors,” J. Appl. Phys. 68, 2216 (1990).
[Crossref]

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “ ‘Running holograms’ in photorefractive Bi12SiO20 crystals,” Opt. Commun. 44, 19 (1982).
[Crossref]

M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, Berlin, 1991).

Petrov, V. M.

M. P. Petrov, V. M. Petrov, I. S. Zouboulis, and L. P. Xu, “Two-wave and induced three-wave mixing on a thin Bi12TiO20 hologram,” Opt. Commun. 134, 599 (1997).
[Crossref]

M. P. Petrov, V. M. Petrov, V. V. Bryksin, I. Zouboulis, A. Gerwens, and E. Krätzig, “Grating oscillations in photorefractive crystals,” Opt. Lett. 22, 1083 (1997).
[Crossref] [PubMed]

V. M. Petrov and M. P. Petrov, “Two- and three-wave mixing in a PRIZ space light modulator,” Tech. Phys. Lett. 21, 403 (1995).

Rajbenbach, K.

P. Refregier, L. Solymar, K. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[Crossref]

Refregier, P.

P. Refregier, L. Solymar, K. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[Crossref]

Rickermann, F.

Riehemann, S.

Ringhofer, K. N.

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. N. Ringhofer, “Low frequency peculiarities of the photorefractive response in sillenites,” Opt. Commun. 113, 371 (1995).
[Crossref]

Sokolov, I. A.

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Non-steady-state photo-electromotive-force induced by dynamic gratings in partially compensated photoconductors,” J. Appl. Phys. 68, 2216 (1990).
[Crossref]

Solymar, L.

P. Refregier, L. Solymar, K. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[Crossref]

Soskin, M. S.

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

Stepanov, S. I.

S. I. Stepanov, “Applications of photorefractive crystals,” Rep. Progr. Phys. 57, 39 (1994).
[Crossref]

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Non-steady-state photo-electromotive-force induced by dynamic gratings in partially compensated photoconductors,” J. Appl. Phys. 68, 2216 (1990).
[Crossref]

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “ ‘Running holograms’ in photorefractive Bi12SiO20 crystals,” Opt. Commun. 44, 19 (1982).
[Crossref]

M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, Berlin, 1991).

S. I. Stepanov, “Photorefractive crystals for adaptive interferometry,” in Optical Holography with Recording in Three-Dimensional Media, Yu. Denisyuk, ed. (Nauka, Leningrad, 1983), in Russian.

Sturman, B. I.

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. N. Ringhofer, “Low frequency peculiarities of the photorefractive response in sillenites,” Opt. Commun. 113, 371 (1995).
[Crossref]

Suris, R. A.

N. G. Zhdanova, M. S. Kagan, R. A. Suris, and B. I. Fuks, “Trap charge exchange waves in compensated germanium,” Pis'ma Zh. Eksp. Teor. Fiz. 74, 346 (1978), in Russian.

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, “ ‘Thermal current’ instability in compensated semiconductors,” Phys. Tech. Semicond. 6, 572 (1972), in Russian.

Trofimov, G. S.

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Non-steady-state photo-electromotive-force induced by dynamic gratings in partially compensated photoconductors,” J. Appl. Phys. 68, 2216 (1990).
[Crossref]

Vasnetsov, M.

M. Vasnetsov, P. Buchhave, and S. Lyuksyutov, “Phase modulation spectroscopy of space-charge wave resonances in Bi12SiO20,” Opt. Commun. 137, 181 (1997).
[Crossref]

Vinetskii, V. L.

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

von Bally, G.

Webb, D. J.

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. N. Ringhofer, “Low frequency peculiarities of the photorefractive response in sillenites,” Opt. Commun. 113, 371 (1995).
[Crossref]

Xu, L. P.

M. P. Petrov, V. M. Petrov, I. S. Zouboulis, and L. P. Xu, “Two-wave and induced three-wave mixing on a thin Bi12TiO20 hologram,” Opt. Commun. 134, 599 (1997).
[Crossref]

Young, L.

M. G. Moharam, T. K. Gaylord, R. Magnuson, and L. Young, “Holographic grating formation in photorefractive crystals with arbitrary electron transport length,” J. Appl. Phys. 50, 5642 (1979).
[Crossref]

Zhdanova, N. G.

N. G. Zhdanova, M. S. Kagan, R. A. Suris, and B. I. Fuks, “Trap charge exchange waves in compensated germanium,” Pis'ma Zh. Eksp. Teor. Fiz. 74, 346 (1978), in Russian.

Zouboulis, I.

Zouboulis, I. S.

M. P. Petrov, V. M. Petrov, I. S. Zouboulis, and L. P. Xu, “Two-wave and induced three-wave mixing on a thin Bi12TiO20 hologram,” Opt. Commun. 134, 599 (1997).
[Crossref]

Ferroelectrics (1)

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

J. Appl. Phys. (3)

M. G. Moharam, T. K. Gaylord, R. Magnuson, and L. Young, “Holographic grating formation in photorefractive crystals with arbitrary electron transport length,” J. Appl. Phys. 50, 5642 (1979).
[Crossref]

M. P. Petrov, I. A. Sokolov, S. I. Stepanov, and G. S. Trofimov, “Non-steady-state photo-electromotive-force induced by dynamic gratings in partially compensated photoconductors,” J. Appl. Phys. 68, 2216 (1990).
[Crossref]

P. Refregier, L. Solymar, K. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[Crossref]

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

Opt. Commun. (5)

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. N. Ringhofer, “Low frequency peculiarities of the photorefractive response in sillenites,” Opt. Commun. 113, 371 (1995).
[Crossref]

M. Vasnetsov, P. Buchhave, and S. Lyuksyutov, “Phase modulation spectroscopy of space-charge wave resonances in Bi12SiO20,” Opt. Commun. 137, 181 (1997).
[Crossref]

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “ ‘Running holograms’ in photorefractive Bi12SiO20 crystals,” Opt. Commun. 44, 19 (1982).
[Crossref]

M. P. Petrov, V. M. Petrov, I. S. Zouboulis, and L. P. Xu, “Two-wave and induced three-wave mixing on a thin Bi12TiO20 hologram,” Opt. Commun. 134, 599 (1997).
[Crossref]

S. Breugnot, M. Defour, and J. P. Huignard, “Photorefractive two-wave mixing: complex amplitudes solutions in the case of a weak signal beam,” Opt. Commun. 134, 599 (1997).
[Crossref]

Opt. Lett. (3)

Phys. Tech. Semicond. (1)

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, “ ‘Thermal current’ instability in compensated semiconductors,” Phys. Tech. Semicond. 6, 572 (1972), in Russian.

Pis'ma Zh. Eksp. Teor. Fiz. (1)

N. G. Zhdanova, M. S. Kagan, R. A. Suris, and B. I. Fuks, “Trap charge exchange waves in compensated germanium,” Pis'ma Zh. Eksp. Teor. Fiz. 74, 346 (1978), in Russian.

Proc. IEEE (1)

W. R. Klein, “Theoretical Efficiency of Bragg Devices,” Proc. IEEE 54, 803 (1966).
[Crossref]

Rep. Progr. Phys. (1)

S. I. Stepanov, “Applications of photorefractive crystals,” Rep. Progr. Phys. 57, 39 (1994).
[Crossref]

Solid State Commun. (1)

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

Tech. Phys. Lett. (1)

V. M. Petrov and M. P. Petrov, “Two- and three-wave mixing in a PRIZ space light modulator,” Tech. Phys. Lett. 21, 403 (1995).

Other (3)

M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, Berlin, 1991).

S. I. Stepanov, “Photorefractive crystals for adaptive interferometry,” in Optical Holography with Recording in Three-Dimensional Media, Yu. Denisyuk, ed. (Nauka, Leningrad, 1983), in Russian.

P. Günter and J.-P. Huignard, Photorefractive Materials and Their Applications I and II, Vols. 61 and 62 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988).

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Fig. 1
Fig. 1

Diagram of the direction of propagation for different diffraction orders: The incident beams R and S are writing a thin grating into the crystal and are simultaneously diffracted from it into the first orders (●)1 and ()-1, the second orders (●)2 and ()-2, and the third orders (●)3 and ()-3.

Fig. 2
Fig. 2

(a) Experimental setup showing the incident beams R and S and the beams Bragg (Pos N1) and non-Bragg (Pos N2) diffracted from a thin hologram: 1, argon-ion laser; 2, mirror; 3, electro-optic modulator; 4, polarizer; 5, BTO crystal; 6, analyzer of polarization; 7, photoreceiver; 8, lock-in detector; b, beamsplitter. (b) Magnified view of the BTO crystal interaction volume: 1, electrodes; 2, BTO crystal; 3, holographic grating. Kg, grating wavevector; E0, external electric field.

Fig. 3
Fig. 3

Two-wave mixing signal I2W as a function of Ω/2π for three different externally applied electric fields E0. The total light intensity is I0=IS+IR=600 W m-2, the contrast of the interference pattern is m=0.24, the wave number of the grating is Kg=5.54×104 m-1, and the amplitude of modulation is Θ=0.58 rad. Symbols, measured data; solid curves, fits according to Eq. (29).

Fig. 4
Fig. 4

Non-Bragg diffraction signal INB as a function of Ω/2π for three different externally applied electric fields E0 (I0=600 W m-2, m=0.24, Kg=5.54×104 m-1, Θ=0.58 rad). Symbols, measured data; solid curve, a fit according to Eq. (26).

Fig. 5
Fig. 5

The dependence of the maximum value of INB on the externally applied electric field is shown. Symbols, measured values; solid curve, fit of the relation INB,maxE03 to the experimental data. The experimental parameters are m=0.22, Kg=12.6×104 m-1, and Θ=0.58 rad.

Fig. 6
Fig. 6

Dependence of the non-Bragg diffraction signal INB on frequency Ω/2π for an externally applied of E0=6.25 kV cm-1. The contrast of the interference pattern is m=0.22, the wave number of the grating is Kg=89.7×104 m-1, and the amplitude of modulation is Θ=0.58 rad. Symbols, measured data; solid curve, fit according to Eq. (26).

Fig. 7
Fig. 7

Non-Bragg diffraction signal INB versus frequency Ω 2π for an externally applied field of E0=6.25 kV cm-1. The total light intensity is I0=2000 W m-2, and the contrast of the interference pattern is m1. The wave number of the grating is Kg=28.9×104 m-1, and the amplitude of modulation is Θ=0.56 rad. Symbols, measured data; solid curve, fit according to Eq. (26).

Fig. 8
Fig. 8

Dependence of non-Bragg diffraction signal INB on frequency Ω/2π for maximum possible externally applied electric field E0=11.25 kV cm-1 and low light intensity I0=5 W m-2. The contrast of the interference pattern is m1. The wave number of the grating is Kg=89.7×104 m-1, and the amplitude of modulation is Θ=0.58 rad.

Equations (46)

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(λh/nΛ2)1/2<1.
AS=AS0 exp(-iKSx),
AR=AR0 exp{-i[KRx+Θ cos(Ωt)]},
I(x, t)=I0{1+m cos[Kgx+Θ cos(Ωt)]},
dE(t)dt=-mE0 exp[iΘ cos(Ωt)]+E(t)τ1(1-id),
Esc(x, t)=½E(t)exp(iKgx)+c.c.
E(t)=-mE0+δE(Ω)exp(iΩt)+δE(-Ω)exp(-iΩt),
δE(Ω)=-imE0Θ2(1+ig+gd),
δE(-Ω)=-imE0Θ2(1-ig-gd),g=Ωτ1.
E(t)=-mE0(1+F+iF),
F=Θgd cos(Ωt+γ)[1+2g2(1-d2)+g4(1+d2)2]1/2,
γ=arctang2(1+d2)-12g,
F=Θ[1+g2(3-2d2)+g4(3+d4)+g6(1+d3)2]1/2 cos(Ωt+β)1+2g2(1-d2)+g4(1+d2)2,
β=arctang[1+g2(1+d2)]1+g2+(1-d2).
Ωr=1τ1(d2+1)1/2.
Esc(x)=E0(1-m2)1/21+m cos(Kgx)-1.
Ep0=-m1+(1-m2)1/2|p|E0.
G(x, t)=G0{1+m cos[Kgx+Θ cos(Ωt)]}.
Esc(x, t)=Esc(x)+Re[δE(x)exp(iΩt)],
gdKg-1(1-m2)1/2δE(x)+i[1+m cos(Kgx)]
×[1+m cos(Kgx)+ig]δE(x)
=imΘE0(1-m2)1/2{sin(Kgx)
+A[1+m cos(Kgx)]}.
δE(x)=pδEp(Ω)exp(ipKgx)
δE2(Ω)=i4 m2ΘE0 2+ig(1+ig+gd)(1+ig+2gd),
δE2(-Ω)=i4 m2ΘE0 2-ig(1-ig-gd)(1-ig-2gd),
δE2(t)=δE2(Ω)exp(iΩt)+δE2(-Ω)exp(-iΩt).
Esc(x, t)=Re[E1(t)exp(iKgx)]+Re[E2(t)exp(i2Kgx)].
T(x, t)=exp[iΔϕ(x, t)].
Δϕ(x, t)=ρEsc(x, t),
T(x, t)=uiuJu[Δϕ(t)]exp[iu(Kgx+F)],
INB=i2 AS0ρE*(t)2=14 ISρ2(mE0)2(1+2F)=Iconst+2ISηNBΘgd cos(Ωt+γ)[1+2g2(1-d2)+g4(1+d2)2]1/2,
ηNB=14 (mE0ρ)2
I2W= |AS0 cos(α)+iAR0 exp[iΘ cos(Ωt)]½Δϕ(t)×sin(α)exp(-iF)|2=IconstB+2(sin2 α)IRηBF-sin(2α)×(IRISηB)1/2[Θ cos(Ωt)-F].
I2WIconstB-sin(2α)(ISIRηB)1/2Θg [1+g2(3+d4)+g4(1+d2)2(3-2d2)+g6(1+d2)4]1/21+2g2(1-d2)+g4(1+d2)2 cos(Ωt+ϕ),
ϕ=arctan1+g2(1+d2)g[1-d2+g2(1+d2)2].
T(x, t)=expiρp Re[Ep(t)exp(ipKgx)],
I2NB= |(i/2)AS0ρE2*(t)|2=Iconst2NB-2ISη2NB3ΘgdW(g, d)cos(Ωt+χ),
η2NB=14 ρ2 m4E02[1+(1-m2)1/2]4.
W(g, d)2(1-g2d2)(1-4g2d2)
χ=arctan2-10g2d2+8g4d4g(1-5g2d2+4g4d4).
IΣ=i ρ2 AS0E1*(t)+iAR0 exp[iΘ cos(Ωt)]E2*(t)2=IconstΣ+2(ISηNB)1/2[F(ISηNB)1/2-Φ(IRη2NB)1/2]×1-IRη2NBISηNB1/2,
m=m=2(ISIR)1/2IS+IR,ISIR1/2=1±(1-m2)1/2m.
IΣ=IconstΣ+2(ISηNB)1/2[F(ISηNB)1/2-Φ(IRη2NB)1/2]×1-m2[1±(1-m2)1/2][1+(1-m2)1/2].
Erw(x, t)=Eg exp[i(Ωt-Kgx)],
Ω1/τ1KgL0.

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