Abstract

Space-charge waves have been investigated in the sillenite-type crystals Bi12SiO20, Bi12GeO20, and Bi12TiO20. For the experiments, oscillating light patterns and the effects of spatial and overall rectification have been utilized. Main attention has been paid to the high-frequency branch and to the detailed comparison of experiment and theory. It was found that the theoretical model describes the experimental results for the high- and low-frequency branches quite reasonably; in particular, the dispersion laws are confirmed. By use of the data obtained for both branches, the major characteristics of the crystals (lifetime of the carriers, mobility, Maxwell relaxation time, and screening factor) have been determined.

© 2005 Optical Society of America

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  1. R. F. Kazarinov, R. A. Suris, and B. I. Fuks, "Thermal-current instability in compensated semiconductors," Sov. Phys. Semicond. 6, 500-502 (1972).
  2. S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, "Running holograms in photorefractive Bi12SiO20 crystals," Opt. Commun. 44, 19-23 (1982).
    [CrossRef]
  3. S. Mallick, B. Imbert, H. Ducollet, J.-P. Herriau, and J.-P. Huignard, "Generation of spatial subharmonics by 2-wave mixing in a nonlinear photorefractive medium," J. Appl. Phys. 63, 5660-5663 (1988).
    [CrossRef]
  4. L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials, Vol. 11 of Oxford Series on Optical and Imaging Sciences (Oxford University, 1996).
  5. B. I. Sturman, T. E. McClelland, D. J. Webb, E. Shamonina, and K. H. Ringhofer, "Investigation of photorefractive subharmonics in the absence of wave mixing," J. Opt. Soc. Am. B 12, 1621-1627 (1995).
    [CrossRef]
  6. M. Vasnetsov, P. Buchhave, and S. Lyuksyutov, "Phase modulation spectroscopy of space-charge wave resonances in Bi12SiO20," Opt. Commun. 137, 181-191 (1997).
    [CrossRef]
  7. H. C. Pedersen, D. J. Webb, and P. M. Johansen, "Fundamental characteristics of space-charge waves in photorefractive sillenite crystals," J. Opt. Soc. Am. B 15, 2573-2580 (1998).
    [CrossRef]
  8. S. Mansurova, S. Stepanov, N. Korneev, and C. Dibon, "Giant enhancement of low frequency non-steady-state photo-EMF signal in Bi12SiO20 crystal under external dc bias," Opt. Commun. 152, 207-214 (1998).
    [CrossRef]
  9. M. P. Petrov, V. V. Bryksin, V. M. Petrov, S. Wevering, and E. Krätzig, "Study of the dispersion law of photorefractive waves in sillenites," Phys. Rev. A 60, 2413-2419 (1999).
    [CrossRef]
  10. B. K. Ridley, "Propagation of space-charge waves in a conductor exhibiting a differential negative resistance," Proc. Phys. Soc. London 86, 637-645 (1965).
    [CrossRef]
  11. A. F. Volkov and Sh. M. Kogan, "Physical phenomena in semiconductors with negative differential conductivity," Sov. Phys. Usp. 11, 881-903 (1969).
    [CrossRef]
  12. R. F. Kazarinov, R. A. Suris, and B. I. Fuks, "Instability with respect to waves of spatial charge-exchange in compensated semiconductors," Sov. Phys. Semicond. 7, 480-486 (1973).
  13. J. P. Partanen, J. M. Jonathan, and R. W. Hellwarth, "Direct determination of electron-mobility in photorefractive Bi12SiO20 by a holographic time-of-flight technique," Appl. Phys. Lett. 57, 2404-2406 (1990).
    [CrossRef]
  14. D. Dolfi, Th. Merlet, A. Mestreau, and J. P. Huignard, "Photodetector for microwave signals based on the synchronous drift of photogenerated carriers with a moving interference pattern," Appl. Phys. Lett. 65, 2931-2933 (1994).
    [CrossRef]
  15. G. Pauliat, A. Villing, J. C. Launay, and G. Roosen, "Optical measurements of charge-carriers mobilities in photorefractive sillenite crystals," J. Opt. Soc. Am. B 7, 1481-1486 (1990).
    [CrossRef]
  16. I. A. Sokolov and S. I. Stepanov, "Non-steady-state photoelectromotive force in crystals with long photocarrier lifetimes," J. Opt. Soc. Am. B 10, 1483-1488 (1993).
    [CrossRef]
  17. M. Bryushinin, V. Kulikov, and I. Sokolov, "Giant resonant enhancement of the nonstationary holographic currents in an alternating electric field," Phys. Rev. B 67, 075202 (2003).
    [CrossRef]
  18. V. V. Bryksin, P. Kleinert, and M. P. Petrov, "Theory of space-charge waves in semiconductors with negative differential conductivity," Phys. Solid State 45, 2044-2052 (2003).
    [CrossRef]
  19. S. L. Sochava, K. Buse, and E. Krätzig, "Photoinduced Hall-current measurements in photorefractive sillenites," Phys. Rev. B 51, 4684-4686 (1995).
    [CrossRef]
  20. I. Biaggio, R. W. Hellwarth, and J. P. Partanen, "Band mobility of photoexcited electrons in Bi12SiO20," Phys. Rev. Lett. 78, 891-894 (1997).
    [CrossRef]
  21. M. P. Petrov, V. V. Bryksin, H. Vogt, F. Rahe, and E. Krätzig, "Overall rectification and second-harmonic generation of space charge waves," Phys. Rev. B 66, 085107 (2002).
    [CrossRef]
  22. M. P. Petrov, V. V. Bryksin, F. Rahe, C. E. Rüter, and E. Krätzig, "Space charge wave rectification effects in photorefractive Bi12TiO20 crystals," Opt. Commun. 227, 183-192 (2003).
    [CrossRef]
  23. V. V. Bryksin and M. P. Petrov, "Spatial rectification of fields of photorefractive waves," Phys. Solid State 42, 1854-1860 (2000).
    [CrossRef]
  24. M. P. Petrov, A. P. Paugurt, V. V. Bryksin, S. Wevering, and E. Krätzig, "Spatial rectification of the electric field of space charge waves," Phys. Rev. Lett. 84, 5114-5117 (2000).
    [CrossRef] [PubMed]
  25. A. Grunnet-Jepsen, I. Aubrecht, and L. Solymar, "High-frequency resonances in photorefractive crystals," J. Opt. Soc. Am. B 12, 921-925 (1995).
    [CrossRef]
  26. J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, and B. A. Wechsler, "Measurement of electrooptic and electrogyratory effects in Bi12SiO20," J. Appl. Phys. 57, 2245-2252 (1990).
    [CrossRef]
  27. V. V. Bryksin and M. P. Petrov, "Second harmonic generation and rectification of space-charge waves in photorefractive crystals," Phys. Solid State 44, 1869-1879 (2002).
    [CrossRef]
  28. A. M. Plesovskikh and S. M. Shandarov, "Effect of a dc external field on the photorefractive-response dynamics in crystals with double-donor centers and shallow traps," Phys. Solid State 44, 58-63 (2002).
    [CrossRef]

2003 (3)

M. Bryushinin, V. Kulikov, and I. Sokolov, "Giant resonant enhancement of the nonstationary holographic currents in an alternating electric field," Phys. Rev. B 67, 075202 (2003).
[CrossRef]

V. V. Bryksin, P. Kleinert, and M. P. Petrov, "Theory of space-charge waves in semiconductors with negative differential conductivity," Phys. Solid State 45, 2044-2052 (2003).
[CrossRef]

M. P. Petrov, V. V. Bryksin, F. Rahe, C. E. Rüter, and E. Krätzig, "Space charge wave rectification effects in photorefractive Bi12TiO20 crystals," Opt. Commun. 227, 183-192 (2003).
[CrossRef]

2002 (3)

V. V. Bryksin and M. P. Petrov, "Second harmonic generation and rectification of space-charge waves in photorefractive crystals," Phys. Solid State 44, 1869-1879 (2002).
[CrossRef]

A. M. Plesovskikh and S. M. Shandarov, "Effect of a dc external field on the photorefractive-response dynamics in crystals with double-donor centers and shallow traps," Phys. Solid State 44, 58-63 (2002).
[CrossRef]

M. P. Petrov, V. V. Bryksin, H. Vogt, F. Rahe, and E. Krätzig, "Overall rectification and second-harmonic generation of space charge waves," Phys. Rev. B 66, 085107 (2002).
[CrossRef]

2000 (2)

V. V. Bryksin and M. P. Petrov, "Spatial rectification of fields of photorefractive waves," Phys. Solid State 42, 1854-1860 (2000).
[CrossRef]

M. P. Petrov, A. P. Paugurt, V. V. Bryksin, S. Wevering, and E. Krätzig, "Spatial rectification of the electric field of space charge waves," Phys. Rev. Lett. 84, 5114-5117 (2000).
[CrossRef] [PubMed]

1999 (1)

M. P. Petrov, V. V. Bryksin, V. M. Petrov, S. Wevering, and E. Krätzig, "Study of the dispersion law of photorefractive waves in sillenites," Phys. Rev. A 60, 2413-2419 (1999).
[CrossRef]

1998 (2)

H. C. Pedersen, D. J. Webb, and P. M. Johansen, "Fundamental characteristics of space-charge waves in photorefractive sillenite crystals," J. Opt. Soc. Am. B 15, 2573-2580 (1998).
[CrossRef]

S. Mansurova, S. Stepanov, N. Korneev, and C. Dibon, "Giant enhancement of low frequency non-steady-state photo-EMF signal in Bi12SiO20 crystal under external dc bias," Opt. Commun. 152, 207-214 (1998).
[CrossRef]

1997 (2)

M. Vasnetsov, P. Buchhave, and S. Lyuksyutov, "Phase modulation spectroscopy of space-charge wave resonances in Bi12SiO20," Opt. Commun. 137, 181-191 (1997).
[CrossRef]

I. Biaggio, R. W. Hellwarth, and J. P. Partanen, "Band mobility of photoexcited electrons in Bi12SiO20," Phys. Rev. Lett. 78, 891-894 (1997).
[CrossRef]

1995 (3)

1994 (1)

D. Dolfi, Th. Merlet, A. Mestreau, and J. P. Huignard, "Photodetector for microwave signals based on the synchronous drift of photogenerated carriers with a moving interference pattern," Appl. Phys. Lett. 65, 2931-2933 (1994).
[CrossRef]

1993 (1)

1990 (3)

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, and B. A. Wechsler, "Measurement of electrooptic and electrogyratory effects in Bi12SiO20," J. Appl. Phys. 57, 2245-2252 (1990).
[CrossRef]

G. Pauliat, A. Villing, J. C. Launay, and G. Roosen, "Optical measurements of charge-carriers mobilities in photorefractive sillenite crystals," J. Opt. Soc. Am. B 7, 1481-1486 (1990).
[CrossRef]

J. P. Partanen, J. M. Jonathan, and R. W. Hellwarth, "Direct determination of electron-mobility in photorefractive Bi12SiO20 by a holographic time-of-flight technique," Appl. Phys. Lett. 57, 2404-2406 (1990).
[CrossRef]

1988 (1)

S. Mallick, B. Imbert, H. Ducollet, J.-P. Herriau, and J.-P. Huignard, "Generation of spatial subharmonics by 2-wave mixing in a nonlinear photorefractive medium," J. Appl. Phys. 63, 5660-5663 (1988).
[CrossRef]

1982 (1)

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, "Running holograms in photorefractive Bi12SiO20 crystals," Opt. Commun. 44, 19-23 (1982).
[CrossRef]

1973 (1)

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, "Instability with respect to waves of spatial charge-exchange in compensated semiconductors," Sov. Phys. Semicond. 7, 480-486 (1973).

1972 (1)

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, "Thermal-current instability in compensated semiconductors," Sov. Phys. Semicond. 6, 500-502 (1972).

1969 (1)

A. F. Volkov and Sh. M. Kogan, "Physical phenomena in semiconductors with negative differential conductivity," Sov. Phys. Usp. 11, 881-903 (1969).
[CrossRef]

1965 (1)

B. K. Ridley, "Propagation of space-charge waves in a conductor exhibiting a differential negative resistance," Proc. Phys. Soc. London 86, 637-645 (1965).
[CrossRef]

Aubrecht, I.

Biaggio, I.

I. Biaggio, R. W. Hellwarth, and J. P. Partanen, "Band mobility of photoexcited electrons in Bi12SiO20," Phys. Rev. Lett. 78, 891-894 (1997).
[CrossRef]

Bryksin, V. V.

V. V. Bryksin, P. Kleinert, and M. P. Petrov, "Theory of space-charge waves in semiconductors with negative differential conductivity," Phys. Solid State 45, 2044-2052 (2003).
[CrossRef]

M. P. Petrov, V. V. Bryksin, F. Rahe, C. E. Rüter, and E. Krätzig, "Space charge wave rectification effects in photorefractive Bi12TiO20 crystals," Opt. Commun. 227, 183-192 (2003).
[CrossRef]

V. V. Bryksin and M. P. Petrov, "Second harmonic generation and rectification of space-charge waves in photorefractive crystals," Phys. Solid State 44, 1869-1879 (2002).
[CrossRef]

M. P. Petrov, V. V. Bryksin, H. Vogt, F. Rahe, and E. Krätzig, "Overall rectification and second-harmonic generation of space charge waves," Phys. Rev. B 66, 085107 (2002).
[CrossRef]

V. V. Bryksin and M. P. Petrov, "Spatial rectification of fields of photorefractive waves," Phys. Solid State 42, 1854-1860 (2000).
[CrossRef]

M. P. Petrov, A. P. Paugurt, V. V. Bryksin, S. Wevering, and E. Krätzig, "Spatial rectification of the electric field of space charge waves," Phys. Rev. Lett. 84, 5114-5117 (2000).
[CrossRef] [PubMed]

M. P. Petrov, V. V. Bryksin, V. M. Petrov, S. Wevering, and E. Krätzig, "Study of the dispersion law of photorefractive waves in sillenites," Phys. Rev. A 60, 2413-2419 (1999).
[CrossRef]

Bryushinin, M.

M. Bryushinin, V. Kulikov, and I. Sokolov, "Giant resonant enhancement of the nonstationary holographic currents in an alternating electric field," Phys. Rev. B 67, 075202 (2003).
[CrossRef]

Buchhave, P.

M. Vasnetsov, P. Buchhave, and S. Lyuksyutov, "Phase modulation spectroscopy of space-charge wave resonances in Bi12SiO20," Opt. Commun. 137, 181-191 (1997).
[CrossRef]

Buse, K.

S. L. Sochava, K. Buse, and E. Krätzig, "Photoinduced Hall-current measurements in photorefractive sillenites," Phys. Rev. B 51, 4684-4686 (1995).
[CrossRef]

Dibon, C.

S. Mansurova, S. Stepanov, N. Korneev, and C. Dibon, "Giant enhancement of low frequency non-steady-state photo-EMF signal in Bi12SiO20 crystal under external dc bias," Opt. Commun. 152, 207-214 (1998).
[CrossRef]

Dolfi, D.

D. Dolfi, Th. Merlet, A. Mestreau, and J. P. Huignard, "Photodetector for microwave signals based on the synchronous drift of photogenerated carriers with a moving interference pattern," Appl. Phys. Lett. 65, 2931-2933 (1994).
[CrossRef]

Ducollet, H.

S. Mallick, B. Imbert, H. Ducollet, J.-P. Herriau, and J.-P. Huignard, "Generation of spatial subharmonics by 2-wave mixing in a nonlinear photorefractive medium," J. Appl. Phys. 63, 5660-5663 (1988).
[CrossRef]

Fuks, B. I.

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, "Instability with respect to waves of spatial charge-exchange in compensated semiconductors," Sov. Phys. Semicond. 7, 480-486 (1973).

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, "Thermal-current instability in compensated semiconductors," Sov. Phys. Semicond. 6, 500-502 (1972).

Grunnet-Jepsen, A.

A. Grunnet-Jepsen, I. Aubrecht, and L. Solymar, "High-frequency resonances in photorefractive crystals," J. Opt. Soc. Am. B 12, 921-925 (1995).
[CrossRef]

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials, Vol. 11 of Oxford Series on Optical and Imaging Sciences (Oxford University, 1996).

Hellwarth, R. W.

I. Biaggio, R. W. Hellwarth, and J. P. Partanen, "Band mobility of photoexcited electrons in Bi12SiO20," Phys. Rev. Lett. 78, 891-894 (1997).
[CrossRef]

J. P. Partanen, J. M. Jonathan, and R. W. Hellwarth, "Direct determination of electron-mobility in photorefractive Bi12SiO20 by a holographic time-of-flight technique," Appl. Phys. Lett. 57, 2404-2406 (1990).
[CrossRef]

Herriau, J.-P.

S. Mallick, B. Imbert, H. Ducollet, J.-P. Herriau, and J.-P. Huignard, "Generation of spatial subharmonics by 2-wave mixing in a nonlinear photorefractive medium," J. Appl. Phys. 63, 5660-5663 (1988).
[CrossRef]

Hesselink, L.

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, and B. A. Wechsler, "Measurement of electrooptic and electrogyratory effects in Bi12SiO20," J. Appl. Phys. 57, 2245-2252 (1990).
[CrossRef]

Huignard, J. P.

D. Dolfi, Th. Merlet, A. Mestreau, and J. P. Huignard, "Photodetector for microwave signals based on the synchronous drift of photogenerated carriers with a moving interference pattern," Appl. Phys. Lett. 65, 2931-2933 (1994).
[CrossRef]

Huignard, J.-P.

S. Mallick, B. Imbert, H. Ducollet, J.-P. Herriau, and J.-P. Huignard, "Generation of spatial subharmonics by 2-wave mixing in a nonlinear photorefractive medium," J. Appl. Phys. 63, 5660-5663 (1988).
[CrossRef]

Imbert, B.

S. Mallick, B. Imbert, H. Ducollet, J.-P. Herriau, and J.-P. Huignard, "Generation of spatial subharmonics by 2-wave mixing in a nonlinear photorefractive medium," J. Appl. Phys. 63, 5660-5663 (1988).
[CrossRef]

Johansen, P. M.

Jonathan, J. M.

J. P. Partanen, J. M. Jonathan, and R. W. Hellwarth, "Direct determination of electron-mobility in photorefractive Bi12SiO20 by a holographic time-of-flight technique," Appl. Phys. Lett. 57, 2404-2406 (1990).
[CrossRef]

Kazarinov, R. F.

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, "Instability with respect to waves of spatial charge-exchange in compensated semiconductors," Sov. Phys. Semicond. 7, 480-486 (1973).

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, "Thermal-current instability in compensated semiconductors," Sov. Phys. Semicond. 6, 500-502 (1972).

Klein, M. B.

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, and B. A. Wechsler, "Measurement of electrooptic and electrogyratory effects in Bi12SiO20," J. Appl. Phys. 57, 2245-2252 (1990).
[CrossRef]

Kleinert, P.

V. V. Bryksin, P. Kleinert, and M. P. Petrov, "Theory of space-charge waves in semiconductors with negative differential conductivity," Phys. Solid State 45, 2044-2052 (2003).
[CrossRef]

Kogan, Sh. M.

A. F. Volkov and Sh. M. Kogan, "Physical phenomena in semiconductors with negative differential conductivity," Sov. Phys. Usp. 11, 881-903 (1969).
[CrossRef]

Korneev, N.

S. Mansurova, S. Stepanov, N. Korneev, and C. Dibon, "Giant enhancement of low frequency non-steady-state photo-EMF signal in Bi12SiO20 crystal under external dc bias," Opt. Commun. 152, 207-214 (1998).
[CrossRef]

Krätzig, E.

M. P. Petrov, V. V. Bryksin, F. Rahe, C. E. Rüter, and E. Krätzig, "Space charge wave rectification effects in photorefractive Bi12TiO20 crystals," Opt. Commun. 227, 183-192 (2003).
[CrossRef]

M. P. Petrov, V. V. Bryksin, H. Vogt, F. Rahe, and E. Krätzig, "Overall rectification and second-harmonic generation of space charge waves," Phys. Rev. B 66, 085107 (2002).
[CrossRef]

M. P. Petrov, A. P. Paugurt, V. V. Bryksin, S. Wevering, and E. Krätzig, "Spatial rectification of the electric field of space charge waves," Phys. Rev. Lett. 84, 5114-5117 (2000).
[CrossRef] [PubMed]

M. P. Petrov, V. V. Bryksin, V. M. Petrov, S. Wevering, and E. Krätzig, "Study of the dispersion law of photorefractive waves in sillenites," Phys. Rev. A 60, 2413-2419 (1999).
[CrossRef]

S. L. Sochava, K. Buse, and E. Krätzig, "Photoinduced Hall-current measurements in photorefractive sillenites," Phys. Rev. B 51, 4684-4686 (1995).
[CrossRef]

Kulikov, V.

M. Bryushinin, V. Kulikov, and I. Sokolov, "Giant resonant enhancement of the nonstationary holographic currents in an alternating electric field," Phys. Rev. B 67, 075202 (2003).
[CrossRef]

Kulikov, V. V.

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, "Running holograms in photorefractive Bi12SiO20 crystals," Opt. Commun. 44, 19-23 (1982).
[CrossRef]

Launay, J. C.

Lyuksyutov, S.

M. Vasnetsov, P. Buchhave, and S. Lyuksyutov, "Phase modulation spectroscopy of space-charge wave resonances in Bi12SiO20," Opt. Commun. 137, 181-191 (1997).
[CrossRef]

Mallick, S.

S. Mallick, B. Imbert, H. Ducollet, J.-P. Herriau, and J.-P. Huignard, "Generation of spatial subharmonics by 2-wave mixing in a nonlinear photorefractive medium," J. Appl. Phys. 63, 5660-5663 (1988).
[CrossRef]

Mansurova, S.

S. Mansurova, S. Stepanov, N. Korneev, and C. Dibon, "Giant enhancement of low frequency non-steady-state photo-EMF signal in Bi12SiO20 crystal under external dc bias," Opt. Commun. 152, 207-214 (1998).
[CrossRef]

McCahon, S. W.

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, and B. A. Wechsler, "Measurement of electrooptic and electrogyratory effects in Bi12SiO20," J. Appl. Phys. 57, 2245-2252 (1990).
[CrossRef]

McClelland, T. E.

Merlet, Th.

D. Dolfi, Th. Merlet, A. Mestreau, and J. P. Huignard, "Photodetector for microwave signals based on the synchronous drift of photogenerated carriers with a moving interference pattern," Appl. Phys. Lett. 65, 2931-2933 (1994).
[CrossRef]

Mestreau, A.

D. Dolfi, Th. Merlet, A. Mestreau, and J. P. Huignard, "Photodetector for microwave signals based on the synchronous drift of photogenerated carriers with a moving interference pattern," Appl. Phys. Lett. 65, 2931-2933 (1994).
[CrossRef]

Partanen, J. P.

I. Biaggio, R. W. Hellwarth, and J. P. Partanen, "Band mobility of photoexcited electrons in Bi12SiO20," Phys. Rev. Lett. 78, 891-894 (1997).
[CrossRef]

J. P. Partanen, J. M. Jonathan, and R. W. Hellwarth, "Direct determination of electron-mobility in photorefractive Bi12SiO20 by a holographic time-of-flight technique," Appl. Phys. Lett. 57, 2404-2406 (1990).
[CrossRef]

Paugurt, A. P.

M. P. Petrov, A. P. Paugurt, V. V. Bryksin, S. Wevering, and E. Krätzig, "Spatial rectification of the electric field of space charge waves," Phys. Rev. Lett. 84, 5114-5117 (2000).
[CrossRef] [PubMed]

Pauliat, G.

Pedersen, H. C.

Petrov, M. P.

V. V. Bryksin, P. Kleinert, and M. P. Petrov, "Theory of space-charge waves in semiconductors with negative differential conductivity," Phys. Solid State 45, 2044-2052 (2003).
[CrossRef]

M. P. Petrov, V. V. Bryksin, F. Rahe, C. E. Rüter, and E. Krätzig, "Space charge wave rectification effects in photorefractive Bi12TiO20 crystals," Opt. Commun. 227, 183-192 (2003).
[CrossRef]

M. P. Petrov, V. V. Bryksin, H. Vogt, F. Rahe, and E. Krätzig, "Overall rectification and second-harmonic generation of space charge waves," Phys. Rev. B 66, 085107 (2002).
[CrossRef]

V. V. Bryksin and M. P. Petrov, "Second harmonic generation and rectification of space-charge waves in photorefractive crystals," Phys. Solid State 44, 1869-1879 (2002).
[CrossRef]

V. V. Bryksin and M. P. Petrov, "Spatial rectification of fields of photorefractive waves," Phys. Solid State 42, 1854-1860 (2000).
[CrossRef]

M. P. Petrov, A. P. Paugurt, V. V. Bryksin, S. Wevering, and E. Krätzig, "Spatial rectification of the electric field of space charge waves," Phys. Rev. Lett. 84, 5114-5117 (2000).
[CrossRef] [PubMed]

M. P. Petrov, V. V. Bryksin, V. M. Petrov, S. Wevering, and E. Krätzig, "Study of the dispersion law of photorefractive waves in sillenites," Phys. Rev. A 60, 2413-2419 (1999).
[CrossRef]

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, "Running holograms in photorefractive Bi12SiO20 crystals," Opt. Commun. 44, 19-23 (1982).
[CrossRef]

Petrov, V. M.

M. P. Petrov, V. V. Bryksin, V. M. Petrov, S. Wevering, and E. Krätzig, "Study of the dispersion law of photorefractive waves in sillenites," Phys. Rev. A 60, 2413-2419 (1999).
[CrossRef]

Plesovskikh, A. M.

A. M. Plesovskikh and S. M. Shandarov, "Effect of a dc external field on the photorefractive-response dynamics in crystals with double-donor centers and shallow traps," Phys. Solid State 44, 58-63 (2002).
[CrossRef]

Rahe, F.

M. P. Petrov, V. V. Bryksin, F. Rahe, C. E. Rüter, and E. Krätzig, "Space charge wave rectification effects in photorefractive Bi12TiO20 crystals," Opt. Commun. 227, 183-192 (2003).
[CrossRef]

M. P. Petrov, V. V. Bryksin, H. Vogt, F. Rahe, and E. Krätzig, "Overall rectification and second-harmonic generation of space charge waves," Phys. Rev. B 66, 085107 (2002).
[CrossRef]

Ridley, B. K.

B. K. Ridley, "Propagation of space-charge waves in a conductor exhibiting a differential negative resistance," Proc. Phys. Soc. London 86, 637-645 (1965).
[CrossRef]

Ringhofer, K. H.

Roosen, G.

Rüter, C. E.

M. P. Petrov, V. V. Bryksin, F. Rahe, C. E. Rüter, and E. Krätzig, "Space charge wave rectification effects in photorefractive Bi12TiO20 crystals," Opt. Commun. 227, 183-192 (2003).
[CrossRef]

Rytz, D.

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, and B. A. Wechsler, "Measurement of electrooptic and electrogyratory effects in Bi12SiO20," J. Appl. Phys. 57, 2245-2252 (1990).
[CrossRef]

Shamonina, E.

Shandarov, S. M.

A. M. Plesovskikh and S. M. Shandarov, "Effect of a dc external field on the photorefractive-response dynamics in crystals with double-donor centers and shallow traps," Phys. Solid State 44, 58-63 (2002).
[CrossRef]

Sochava, S. L.

S. L. Sochava, K. Buse, and E. Krätzig, "Photoinduced Hall-current measurements in photorefractive sillenites," Phys. Rev. B 51, 4684-4686 (1995).
[CrossRef]

Sokolov, I.

M. Bryushinin, V. Kulikov, and I. Sokolov, "Giant resonant enhancement of the nonstationary holographic currents in an alternating electric field," Phys. Rev. B 67, 075202 (2003).
[CrossRef]

Sokolov, I. A.

Solymar, L.

A. Grunnet-Jepsen, I. Aubrecht, and L. Solymar, "High-frequency resonances in photorefractive crystals," J. Opt. Soc. Am. B 12, 921-925 (1995).
[CrossRef]

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials, Vol. 11 of Oxford Series on Optical and Imaging Sciences (Oxford University, 1996).

Stepanov, S.

S. Mansurova, S. Stepanov, N. Korneev, and C. Dibon, "Giant enhancement of low frequency non-steady-state photo-EMF signal in Bi12SiO20 crystal under external dc bias," Opt. Commun. 152, 207-214 (1998).
[CrossRef]

Stepanov, S. I.

I. A. Sokolov and S. I. Stepanov, "Non-steady-state photoelectromotive force in crystals with long photocarrier lifetimes," J. Opt. Soc. Am. B 10, 1483-1488 (1993).
[CrossRef]

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, "Running holograms in photorefractive Bi12SiO20 crystals," Opt. Commun. 44, 19-23 (1982).
[CrossRef]

Sturman, B. I.

Suris, R. A.

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, "Instability with respect to waves of spatial charge-exchange in compensated semiconductors," Sov. Phys. Semicond. 7, 480-486 (1973).

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, "Thermal-current instability in compensated semiconductors," Sov. Phys. Semicond. 6, 500-502 (1972).

Vasnetsov, M.

M. Vasnetsov, P. Buchhave, and S. Lyuksyutov, "Phase modulation spectroscopy of space-charge wave resonances in Bi12SiO20," Opt. Commun. 137, 181-191 (1997).
[CrossRef]

Villing, A.

Vogt, H.

M. P. Petrov, V. V. Bryksin, H. Vogt, F. Rahe, and E. Krätzig, "Overall rectification and second-harmonic generation of space charge waves," Phys. Rev. B 66, 085107 (2002).
[CrossRef]

Volkov, A. F.

A. F. Volkov and Sh. M. Kogan, "Physical phenomena in semiconductors with negative differential conductivity," Sov. Phys. Usp. 11, 881-903 (1969).
[CrossRef]

Webb, D. J.

Wechsler, B. A.

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, and B. A. Wechsler, "Measurement of electrooptic and electrogyratory effects in Bi12SiO20," J. Appl. Phys. 57, 2245-2252 (1990).
[CrossRef]

Wevering, S.

M. P. Petrov, A. P. Paugurt, V. V. Bryksin, S. Wevering, and E. Krätzig, "Spatial rectification of the electric field of space charge waves," Phys. Rev. Lett. 84, 5114-5117 (2000).
[CrossRef] [PubMed]

M. P. Petrov, V. V. Bryksin, V. M. Petrov, S. Wevering, and E. Krätzig, "Study of the dispersion law of photorefractive waves in sillenites," Phys. Rev. A 60, 2413-2419 (1999).
[CrossRef]

Wilde, J. P.

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, and B. A. Wechsler, "Measurement of electrooptic and electrogyratory effects in Bi12SiO20," J. Appl. Phys. 57, 2245-2252 (1990).
[CrossRef]

Appl. Phys. Lett. (2)

J. P. Partanen, J. M. Jonathan, and R. W. Hellwarth, "Direct determination of electron-mobility in photorefractive Bi12SiO20 by a holographic time-of-flight technique," Appl. Phys. Lett. 57, 2404-2406 (1990).
[CrossRef]

D. Dolfi, Th. Merlet, A. Mestreau, and J. P. Huignard, "Photodetector for microwave signals based on the synchronous drift of photogenerated carriers with a moving interference pattern," Appl. Phys. Lett. 65, 2931-2933 (1994).
[CrossRef]

J. Appl. Phys. (2)

S. Mallick, B. Imbert, H. Ducollet, J.-P. Herriau, and J.-P. Huignard, "Generation of spatial subharmonics by 2-wave mixing in a nonlinear photorefractive medium," J. Appl. Phys. 63, 5660-5663 (1988).
[CrossRef]

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, and B. A. Wechsler, "Measurement of electrooptic and electrogyratory effects in Bi12SiO20," J. Appl. Phys. 57, 2245-2252 (1990).
[CrossRef]

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

Opt. Commun. (4)

M. Vasnetsov, P. Buchhave, and S. Lyuksyutov, "Phase modulation spectroscopy of space-charge wave resonances in Bi12SiO20," Opt. Commun. 137, 181-191 (1997).
[CrossRef]

S. Mansurova, S. Stepanov, N. Korneev, and C. Dibon, "Giant enhancement of low frequency non-steady-state photo-EMF signal in Bi12SiO20 crystal under external dc bias," Opt. Commun. 152, 207-214 (1998).
[CrossRef]

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, "Running holograms in photorefractive Bi12SiO20 crystals," Opt. Commun. 44, 19-23 (1982).
[CrossRef]

M. P. Petrov, V. V. Bryksin, F. Rahe, C. E. Rüter, and E. Krätzig, "Space charge wave rectification effects in photorefractive Bi12TiO20 crystals," Opt. Commun. 227, 183-192 (2003).
[CrossRef]

Phys. Rev. A (1)

M. P. Petrov, V. V. Bryksin, V. M. Petrov, S. Wevering, and E. Krätzig, "Study of the dispersion law of photorefractive waves in sillenites," Phys. Rev. A 60, 2413-2419 (1999).
[CrossRef]

Phys. Rev. B (3)

S. L. Sochava, K. Buse, and E. Krätzig, "Photoinduced Hall-current measurements in photorefractive sillenites," Phys. Rev. B 51, 4684-4686 (1995).
[CrossRef]

M. Bryushinin, V. Kulikov, and I. Sokolov, "Giant resonant enhancement of the nonstationary holographic currents in an alternating electric field," Phys. Rev. B 67, 075202 (2003).
[CrossRef]

M. P. Petrov, V. V. Bryksin, H. Vogt, F. Rahe, and E. Krätzig, "Overall rectification and second-harmonic generation of space charge waves," Phys. Rev. B 66, 085107 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

M. P. Petrov, A. P. Paugurt, V. V. Bryksin, S. Wevering, and E. Krätzig, "Spatial rectification of the electric field of space charge waves," Phys. Rev. Lett. 84, 5114-5117 (2000).
[CrossRef] [PubMed]

I. Biaggio, R. W. Hellwarth, and J. P. Partanen, "Band mobility of photoexcited electrons in Bi12SiO20," Phys. Rev. Lett. 78, 891-894 (1997).
[CrossRef]

Phys. Solid State (4)

V. V. Bryksin, P. Kleinert, and M. P. Petrov, "Theory of space-charge waves in semiconductors with negative differential conductivity," Phys. Solid State 45, 2044-2052 (2003).
[CrossRef]

V. V. Bryksin and M. P. Petrov, "Second harmonic generation and rectification of space-charge waves in photorefractive crystals," Phys. Solid State 44, 1869-1879 (2002).
[CrossRef]

A. M. Plesovskikh and S. M. Shandarov, "Effect of a dc external field on the photorefractive-response dynamics in crystals with double-donor centers and shallow traps," Phys. Solid State 44, 58-63 (2002).
[CrossRef]

V. V. Bryksin and M. P. Petrov, "Spatial rectification of fields of photorefractive waves," Phys. Solid State 42, 1854-1860 (2000).
[CrossRef]

Proc. Phys. Soc. London (1)

B. K. Ridley, "Propagation of space-charge waves in a conductor exhibiting a differential negative resistance," Proc. Phys. Soc. London 86, 637-645 (1965).
[CrossRef]

Sov. Phys. Semicond. (2)

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, "Thermal-current instability in compensated semiconductors," Sov. Phys. Semicond. 6, 500-502 (1972).

R. F. Kazarinov, R. A. Suris, and B. I. Fuks, "Instability with respect to waves of spatial charge-exchange in compensated semiconductors," Sov. Phys. Semicond. 7, 480-486 (1973).

Sov. Phys. Usp. (1)

A. F. Volkov and Sh. M. Kogan, "Physical phenomena in semiconductors with negative differential conductivity," Sov. Phys. Usp. 11, 881-903 (1969).
[CrossRef]

Other (1)

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials, Vol. 11 of Oxford Series on Optical and Imaging Sciences (Oxford University, 1996).

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram used for theoretical calculations. Here, R cr is the ohmic resistance of the crystal with ideal electrodes. R cont and C are the effective resistance and the specific capacity of the contact area, respectively, responsible for screening effects. A 1 and A 2 are the complex amplitudes of the recording light beams.

Fig. 2
Fig. 2

Experimental setup (schematically). Here, P C is the photorefractive crystal with real electrodes, R L is the loading resistance, and A 1 and A 2 are the complex amplitudes of the recording light beams.

Fig. 3
Fig. 3

ac current amplitude I 1 as a function of frequency f for (a) BGO and (b) BTO. The symbols are measured values, and the curves are fits of Eq. (6) with the fitting parameters given in the text. The insets show a magnification of the ac current amplitude at high frequencies.

Fig. 4
Fig. 4

dc current Δ I 0 I 0 = [ I 0 ( ϴ = 0.3 π ) I ( ϴ = 0 ) ] I 0 as a function of frequency f for (a) BGO and (b) BTO. The symbols are measured values, and the curves are fits of Eq. (16) with the fitting parameters given in the text.

Fig. 5
Fig. 5

Resonance frequency f HR as a function of K for BSO, BGO, and BTO. The symbols are measured values, and the curves are fits of Eq. (11) with the fitting parameters given in the text.

Fig. 6
Fig. 6

Resonance frequency f LR as a function of K for BSO, BGO, and BTO. The symbols are measured values, and the curves are fits of Eq. (7) with the fitting parameters given in the text.

Fig. 7
Fig. 7

Product f HR f LR for BSO and BGO as a function of (a) K and (b) E 0 , respectively. The symbols are measured values, and the curves are fits of Eq. (12) with the fitting parameters given in the text.

Fig. 8
Fig. 8

Resonance frequency f HR as a function of E 0 for BSO, BGO, and BTO. The symbols are measured values, and the curves are fits of Eq. (11) with the fitting parameters given in the text.

Equations (18)

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Ω L = 1 ( μ τ τ m K W E int ) .
Ω H = μ K W E int .
Ω H Ω L = 1 τ τ M .
W ( x , t ) = W 0 { 1 + m cos [ K x + ϴ cos ( Ω t ) ] } W 0 + W 0 m cos ( K x ) 1 2 W 0 m ϴ sin ( K x Ω t ) 1 2 W 0 m ϴ sin ( K x + Ω t ) .
I 1 ( Ω ) = i σ E int ϴ m 2 1 + q ( 1 + i ω ) ( 1 + i h ω ) 1 τ M 8 τ
× { 2 + ω E D E int + i ω [ ω τ m τ ( d + i + i d E D E int ) ] [ ω + ( d + i + i d E D E int ) 1 ] 2 ω E D E int + i ω [ ω + τ m τ ( d + i + i d E D E int ) ] [ ω ( d + i + i d E D E int ) 1 ] } .
I 1 ( Ω ) L = 1 2 σ E int m 2 ϴ ( 1 + Ω 2 τ M 2 4 ) 1 2 Ω τ M d [ ( 1 + q ) 2 + q 2 Ω 2 τ M 2 ] 1 2
× { 1 [ ( 1 Ω τ M d ) 2 + Ω 2 τ M 2 ] [ ( 1 + Ω τ M d ) 2 + Ω 2 τ M 2 ] } 1 2 .
Ω LR = 1 τ M 1 d 2 + 1 .
I 1 L = 1 4 σ E int m 2 ϴ d 1 + q .
I 1 pl = 1 4 σ E int m 2 ϴ 1 + q h d d 2 + 1 .
I 1 ( Ω ) = 1 4 σ E int m 2 ϴ ( 1 + q h ) d [ Ω 4 τ 2 2 Ω 2 τ 2 ( d 2 1 ) + ( d 2 + 1 ) 2 ] 1 2 .
Ω HR = ( d 2 1 ) 1 2 τ .
Ω HR Ω LR = 1 τ τ M ( d 2 1 d 2 + 1 ) 1 2 .
I 1 H = 1 8 σ E int m 2 ϴ 1 + q h .
I 1 H I 1 L ( 1 + q ) 2 d ( 1 + q h ) .
I 1 pl I 1 H = 2 d d 2 + 1 .
I 0 ( Ω ) = σ E 0 1 + q { 1 m 2 2 ( 1 + q ) + m 2 ϴ 2 8 ( 1 + q ) [ 2 1 ( 1 Ω τ M d ) 2 + Ω 2 τ M 2 1 ( 1 + Ω τ M d ) 2 + Ω 2 τ M 2 ] } .

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