Abstract

We analyze analytically and numerically the mechanism for modulational instability of the resonance excitation of a space-charge field by a moving light pattern in a photorefractive sillenite crystal to explain the results of recent experiments with Bi12SiO20 crystals.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. I. Sturman, M. Mann, J. Otten, and K. H. Ringhofer, “Space-charge waves and their parametric excitation,” J. Opt. Soc. Am. B 10, 1919–1932 (1993).
    [CrossRef]
  2. T. E. McClelland, D. J. Webb, B. I. Sturman, and K. H. Ringhofer, “Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling,” Phys. Rev. Lett. 73, 3082–3084 (1994).
    [CrossRef] [PubMed]
  3. H. C. Pedersen and P. M. Johansen, “Parametric oscillation in photorefractive media,” J. Opt. Soc. Am. B 12, 1065–1073 (1995).
    [CrossRef]
  4. 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]
  5. T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. H. Ringhofer, “Low-frequency peculiarities of the photorefractive response in sillenites,” Opt. Commun. 113, 371–377 (1995).
    [CrossRef]
  6. T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
    [CrossRef]
  7. L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, Oxford, 1996).
  8. S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, and J.-P. Huignard, “Generation of spatial subharmonics by two-wave mixing in a nonlinear photorefractive medium,” J. Appl. Phys. 63, 5660–5663 (1988).
    [CrossRef]
  9. D. J. Webb and L. Solymar, “Observation of spatial subharmonics arising during two-wave mixing in BSO,” Opt. Commun. 74, 386–389 (1990).
    [CrossRef]
  10. J. Takacs, M. Schaub, and L. Solymar, “Subharmonics in photorefractive Bi12TiO20 crystals,” Opt. Commun. 91, 252–254 (1992).
    [CrossRef]
  11. J. Takacs and L. Solymar, “Subharmonics in Bi12SiO20 with an applied ac electric field,” Opt. Lett. 17, 247–248 (1992).
    [CrossRef] [PubMed]
  12. P. M. Johansen, R. S. Hansen, and T. Olsen, “Experimental characteristics of spatial subharmonics in BSO,” Opt. Commun. 115, 308–314 (1995).
    [CrossRef]
  13. P. Buchhave, S. Lyuksyutov, and M. Vasnetsov, “Relations between spontaneously occurring beams in bismuth silicon oxide with two frequency-detuned pump beams,” Opt. Lett. 20, 2363–2365 (1995).
    [CrossRef] [PubMed]
  14. M. Vasnetsov, P. Buchhave, and S. Lyuksyutov, “Phasemodulation spectroscopy of space-charge wave resonances in Bi12SiO20,” Opt. Commun. 137, 181–191 (1997).
    [CrossRef]
  15. J.-P. Huignard and A. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals,” Opt. Commun. 38, 249–254 (1981).
    [CrossRef]
  16. P. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
    [CrossRef]
  17. S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
    [CrossRef]
  18. B. I. Sturman, M. Aguilar, F. Agullo-Lopez, and K. H. Ringhofer, “Fundamentals of the nonlinear theory of photorefractive subharmonics,” Phys. Rev. E 55, 6072–6083 (1997).
    [CrossRef]
  19. E. V. Podivilov, H. C. Pedersen, P. M. Johansen, and B. I. Sturman, “Transversal parametric oscillation and its external stability in photorefractive sillenite crystals,” Phys. Rev. E (to be published).
  20. H. Pedersen and P. M. Johansen, “Observation of angularly tilted subharmonic gratings in photorefractive bismuth silicon oxide,” Opt. Lett. 19, 1418–1420 (1994).
    [CrossRef] [PubMed]
  21. H. C. Pedersen and P. M. Johansen, “Longitudinal, degenerate, and transversal parametric oscillation in photore- fractive media,” Phys. Rev. Lett. 77, 3106–3109 (1996).
    [CrossRef] [PubMed]
  22. K. Walsh, A. K. Powell, C. Stace, and T. J. Hall, “Techniques for the enhancement of space-charge fields in photorefractive materials,” J. Opt. Soc. Am. B 7, 288–303 (1990).
    [CrossRef]
  23. B. I. Sturman, M. Mann, and K. H. Ringhofer, “Instability of the resonance enhancement of moving photorefractive gratings,” Opt. Lett. 18, 702–704 (1993).
    [CrossRef] [PubMed]
  24. H. C. Pedersen, D. J. Webb, and P. M. Johansen, “Observation of resonance-instability of running gratings in photorefractive sillenite crystals,” submitted to Phys. Rev. Lett.
  25. S. Lyukslyutov, P. Buchhave, and M. Vasnetsov, “Self-excitation of space-charge waves,” Phys. Rev. Lett. 79, 67–70 (1997).
    [CrossRef]
  26. B. I. Sturman, M. Mann, and K. H. Ringhofer, “Instability of moving gratings in photorefractive crystals,” Appl. Phys. A: Solids Surf. 55, 235–241 (1992).
    [CrossRef]
  27. H. C. Pedersen, D. J. Webb, and P. M. Johansen, “Fundamental characteristics of space-charge waves in photorefractive crystals,” J. Opt. Soc. Am. B 15, 2573–2580 (1998).
    [CrossRef]
  28. H. M. Gibbs, Optical Bistability (Academic, New York, 1985).
  29. B. I. Sturman, A. I. Chernykh, E. Shamonina, V. P. Kamenov, and K. H. Ringhofer, “Rigorous 3D-theory of the subharmonic instability in semiconductors,” J. Opt. Soc. Am. B (to be published).

1998 (1)

1997 (3)

S. Lyukslyutov, P. Buchhave, and M. Vasnetsov, “Self-excitation of space-charge waves,” Phys. Rev. Lett. 79, 67–70 (1997).
[CrossRef]

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

B. I. Sturman, M. Aguilar, F. Agullo-Lopez, and K. H. Ringhofer, “Fundamentals of the nonlinear theory of photorefractive subharmonics,” Phys. Rev. E 55, 6072–6083 (1997).
[CrossRef]

1996 (2)

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[CrossRef]

H. C. Pedersen and P. M. Johansen, “Longitudinal, degenerate, and transversal parametric oscillation in photore- fractive media,” Phys. Rev. Lett. 77, 3106–3109 (1996).
[CrossRef] [PubMed]

1995 (5)

1994 (2)

H. Pedersen and P. M. Johansen, “Observation of angularly tilted subharmonic gratings in photorefractive bismuth silicon oxide,” Opt. Lett. 19, 1418–1420 (1994).
[CrossRef] [PubMed]

T. E. McClelland, D. J. Webb, B. I. Sturman, and K. H. Ringhofer, “Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling,” Phys. Rev. Lett. 73, 3082–3084 (1994).
[CrossRef] [PubMed]

1993 (2)

1992 (3)

B. I. Sturman, M. Mann, and K. H. Ringhofer, “Instability of moving gratings in photorefractive crystals,” Appl. Phys. A: Solids Surf. 55, 235–241 (1992).
[CrossRef]

J. Takacs, M. Schaub, and L. Solymar, “Subharmonics in photorefractive Bi12TiO20 crystals,” Opt. Commun. 91, 252–254 (1992).
[CrossRef]

J. Takacs and L. Solymar, “Subharmonics in Bi12SiO20 with an applied ac electric field,” Opt. Lett. 17, 247–248 (1992).
[CrossRef] [PubMed]

1990 (2)

D. J. Webb and L. Solymar, “Observation of spatial subharmonics arising during two-wave mixing in BSO,” Opt. Commun. 74, 386–389 (1990).
[CrossRef]

K. Walsh, A. K. Powell, C. Stace, and T. J. Hall, “Techniques for the enhancement of space-charge fields in photorefractive materials,” J. Opt. Soc. Am. B 7, 288–303 (1990).
[CrossRef]

1988 (1)

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

1985 (2)

P. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[CrossRef]

1981 (1)

J.-P. Huignard and A. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

Aguilar, M.

B. I. Sturman, M. Aguilar, F. Agullo-Lopez, and K. H. Ringhofer, “Fundamentals of the nonlinear theory of photorefractive subharmonics,” Phys. Rev. E 55, 6072–6083 (1997).
[CrossRef]

Agullo-Lopez, F.

B. I. Sturman, M. Aguilar, F. Agullo-Lopez, and K. H. Ringhofer, “Fundamentals of the nonlinear theory of photorefractive subharmonics,” Phys. Rev. E 55, 6072–6083 (1997).
[CrossRef]

Buchhave, P.

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

S. Lyukslyutov, P. Buchhave, and M. Vasnetsov, “Self-excitation of space-charge waves,” Phys. Rev. Lett. 79, 67–70 (1997).
[CrossRef]

P. Buchhave, S. Lyuksyutov, and M. Vasnetsov, “Relations between spontaneously occurring beams in bismuth silicon oxide with two frequency-detuned pump beams,” Opt. Lett. 20, 2363–2365 (1995).
[CrossRef] [PubMed]

Ducollet, H.

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

Hall, T. J.

Hansen, R. S.

P. M. Johansen, R. S. Hansen, and T. Olsen, “Experimental characteristics of spatial subharmonics in BSO,” Opt. Commun. 115, 308–314 (1995).
[CrossRef]

Herriau, J. P.

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

Huignard, J.-P.

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

P. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

J.-P. Huignard and A. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

Imbert, B.

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

Johansen, P. M.

Lyukslyutov, S.

S. Lyukslyutov, P. Buchhave, and M. Vasnetsov, “Self-excitation of space-charge waves,” Phys. Rev. Lett. 79, 67–70 (1997).
[CrossRef]

Lyuksyutov, S.

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

P. Buchhave, S. Lyuksyutov, and M. Vasnetsov, “Relations between spontaneously occurring beams in bismuth silicon oxide with two frequency-detuned pump beams,” Opt. Lett. 20, 2363–2365 (1995).
[CrossRef] [PubMed]

Mallick, S.

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

Mann, M.

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. H. Ringhofer, “Low-frequency peculiarities of the photorefractive response in sillenites,” Opt. Commun. 113, 371–377 (1995).
[CrossRef]

B. I. Sturman, M. Mann, J. Otten, and K. H. Ringhofer, “Space-charge waves and their parametric excitation,” J. Opt. Soc. Am. B 10, 1919–1932 (1993).
[CrossRef]

B. I. Sturman, M. Mann, and K. H. Ringhofer, “Instability of the resonance enhancement of moving photorefractive gratings,” Opt. Lett. 18, 702–704 (1993).
[CrossRef] [PubMed]

B. I. Sturman, M. Mann, and K. H. Ringhofer, “Instability of moving gratings in photorefractive crystals,” Appl. Phys. A: Solids Surf. 55, 235–241 (1992).
[CrossRef]

Marrakchi, A.

J.-P. Huignard and A. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

McClelland, T. E.

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[CrossRef]

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]

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. H. Ringhofer, “Low-frequency peculiarities of the photorefractive response in sillenites,” Opt. Commun. 113, 371–377 (1995).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, and K. H. Ringhofer, “Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling,” Phys. Rev. Lett. 73, 3082–3084 (1994).
[CrossRef] [PubMed]

Olsen, T.

P. M. Johansen, R. S. Hansen, and T. Olsen, “Experimental characteristics of spatial subharmonics in BSO,” Opt. Commun. 115, 308–314 (1995).
[CrossRef]

Otten, J.

Pedersen, H.

Pedersen, H. C.

Petrov, M. P.

S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[CrossRef]

Powell, A. K.

Rajbenbach, H.

P. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Réfrégier, P.

P. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Ringhofer, K. H.

B. I. Sturman, M. Aguilar, F. Agullo-Lopez, and K. H. Ringhofer, “Fundamentals of the nonlinear theory of photorefractive subharmonics,” Phys. Rev. E 55, 6072–6083 (1997).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. H. Ringhofer, “Low-frequency peculiarities of the photorefractive response in sillenites,” Opt. Commun. 113, 371–377 (1995).
[CrossRef]

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]

T. E. McClelland, D. J. Webb, B. I. Sturman, and K. H. Ringhofer, “Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling,” Phys. Rev. Lett. 73, 3082–3084 (1994).
[CrossRef] [PubMed]

B. I. Sturman, M. Mann, J. Otten, and K. H. Ringhofer, “Space-charge waves and their parametric excitation,” J. Opt. Soc. Am. B 10, 1919–1932 (1993).
[CrossRef]

B. I. Sturman, M. Mann, and K. H. Ringhofer, “Instability of the resonance enhancement of moving photorefractive gratings,” Opt. Lett. 18, 702–704 (1993).
[CrossRef] [PubMed]

B. I. Sturman, M. Mann, and K. H. Ringhofer, “Instability of moving gratings in photorefractive crystals,” Appl. Phys. A: Solids Surf. 55, 235–241 (1992).
[CrossRef]

Schaub, M.

J. Takacs, M. Schaub, and L. Solymar, “Subharmonics in photorefractive Bi12TiO20 crystals,” Opt. Commun. 91, 252–254 (1992).
[CrossRef]

Shamonina, E.

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[CrossRef]

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]

Solymar, L.

J. Takacs, M. Schaub, and L. Solymar, “Subharmonics in photorefractive Bi12TiO20 crystals,” Opt. Commun. 91, 252–254 (1992).
[CrossRef]

J. Takacs and L. Solymar, “Subharmonics in Bi12SiO20 with an applied ac electric field,” Opt. Lett. 17, 247–248 (1992).
[CrossRef] [PubMed]

D. J. Webb and L. Solymar, “Observation of spatial subharmonics arising during two-wave mixing in BSO,” Opt. Commun. 74, 386–389 (1990).
[CrossRef]

P. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Stace, C.

Stepanov, S. I.

S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[CrossRef]

Sturman, B. I.

B. I. Sturman, M. Aguilar, F. Agullo-Lopez, and K. H. Ringhofer, “Fundamentals of the nonlinear theory of photorefractive subharmonics,” Phys. Rev. E 55, 6072–6083 (1997).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. H. Ringhofer, “Low-frequency peculiarities of the photorefractive response in sillenites,” Opt. Commun. 113, 371–377 (1995).
[CrossRef]

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]

T. E. McClelland, D. J. Webb, B. I. Sturman, and K. H. Ringhofer, “Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling,” Phys. Rev. Lett. 73, 3082–3084 (1994).
[CrossRef] [PubMed]

B. I. Sturman, M. Mann, J. Otten, and K. H. Ringhofer, “Space-charge waves and their parametric excitation,” J. Opt. Soc. Am. B 10, 1919–1932 (1993).
[CrossRef]

B. I. Sturman, M. Mann, and K. H. Ringhofer, “Instability of the resonance enhancement of moving photorefractive gratings,” Opt. Lett. 18, 702–704 (1993).
[CrossRef] [PubMed]

B. I. Sturman, M. Mann, and K. H. Ringhofer, “Instability of moving gratings in photorefractive crystals,” Appl. Phys. A: Solids Surf. 55, 235–241 (1992).
[CrossRef]

Takacs, J.

J. Takacs and L. Solymar, “Subharmonics in Bi12SiO20 with an applied ac electric field,” Opt. Lett. 17, 247–248 (1992).
[CrossRef] [PubMed]

J. Takacs, M. Schaub, and L. Solymar, “Subharmonics in photorefractive Bi12TiO20 crystals,” Opt. Commun. 91, 252–254 (1992).
[CrossRef]

Vasnetsov, M.

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

S. Lyukslyutov, P. Buchhave, and M. Vasnetsov, “Self-excitation of space-charge waves,” Phys. Rev. Lett. 79, 67–70 (1997).
[CrossRef]

P. Buchhave, S. Lyuksyutov, and M. Vasnetsov, “Relations between spontaneously occurring beams in bismuth silicon oxide with two frequency-detuned pump beams,” Opt. Lett. 20, 2363–2365 (1995).
[CrossRef] [PubMed]

Walsh, K.

Webb, D. J.

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

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[CrossRef]

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]

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. H. Ringhofer, “Low-frequency peculiarities of the photorefractive response in sillenites,” Opt. Commun. 113, 371–377 (1995).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, and K. H. Ringhofer, “Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling,” Phys. Rev. Lett. 73, 3082–3084 (1994).
[CrossRef] [PubMed]

D. J. Webb and L. Solymar, “Observation of spatial subharmonics arising during two-wave mixing in BSO,” Opt. Commun. 74, 386–389 (1990).
[CrossRef]

Appl. Phys. A: Solids Surf. (1)

B. I. Sturman, M. Mann, and K. H. Ringhofer, “Instability of moving gratings in photorefractive crystals,” Appl. Phys. A: Solids Surf. 55, 235–241 (1992).
[CrossRef]

J. Appl. Phys. (2)

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

P. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

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

Opt. Commun. (8)

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

J.-P. Huignard and A. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, M. Mann, and K. H. Ringhofer, “Low-frequency peculiarities of the photorefractive response in sillenites,” Opt. Commun. 113, 371–377 (1995).
[CrossRef]

T. E. McClelland, D. J. Webb, B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Excitation of higher spatial harmonics by a moving light pattern in sillenites,” Opt. Commun. 131, 315–321 (1996).
[CrossRef]

D. J. Webb and L. Solymar, “Observation of spatial subharmonics arising during two-wave mixing in BSO,” Opt. Commun. 74, 386–389 (1990).
[CrossRef]

J. Takacs, M. Schaub, and L. Solymar, “Subharmonics in photorefractive Bi12TiO20 crystals,” Opt. Commun. 91, 252–254 (1992).
[CrossRef]

P. M. Johansen, R. S. Hansen, and T. Olsen, “Experimental characteristics of spatial subharmonics in BSO,” Opt. Commun. 115, 308–314 (1995).
[CrossRef]

S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. E (1)

B. I. Sturman, M. Aguilar, F. Agullo-Lopez, and K. H. Ringhofer, “Fundamentals of the nonlinear theory of photorefractive subharmonics,” Phys. Rev. E 55, 6072–6083 (1997).
[CrossRef]

Phys. Rev. Lett. (3)

T. E. McClelland, D. J. Webb, B. I. Sturman, and K. H. Ringhofer, “Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling,” Phys. Rev. Lett. 73, 3082–3084 (1994).
[CrossRef] [PubMed]

S. Lyukslyutov, P. Buchhave, and M. Vasnetsov, “Self-excitation of space-charge waves,” Phys. Rev. Lett. 79, 67–70 (1997).
[CrossRef]

H. C. Pedersen and P. M. Johansen, “Longitudinal, degenerate, and transversal parametric oscillation in photore- fractive media,” Phys. Rev. Lett. 77, 3106–3109 (1996).
[CrossRef] [PubMed]

Other (5)

H. M. Gibbs, Optical Bistability (Academic, New York, 1985).

B. I. Sturman, A. I. Chernykh, E. Shamonina, V. P. Kamenov, and K. H. Ringhofer, “Rigorous 3D-theory of the subharmonic instability in semiconductors,” J. Opt. Soc. Am. B (to be published).

H. C. Pedersen, D. J. Webb, and P. M. Johansen, “Observation of resonance-instability of running gratings in photorefractive sillenite crystals,” submitted to Phys. Rev. Lett.

E. V. Podivilov, H. C. Pedersen, P. M. Johansen, and B. I. Sturman, “Transversal parametric oscillation and its external stability in photorefractive sillenite crystals,” Phys. Rev. E (to be published).

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, Oxford, 1996).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Schematic of an experiment on excitation of SCW’s: Fundamental grating vector K equals the difference between the light-wave vectors, and Ω is the difference between the optical frequencies of the pump waves.

Fig. 2
Fig. 2

Dependence of |eK| on the distance to linear resonance for several values of contrast m obtained from analytical theory. Curves 1, 2, 3, 4, and 5 refer to (m/mc)2=0.2, 0.5, 1.0, 1.5, 2, respectively. The dashed portions of curves 4 and 5 correspond to nonphysical steady states. Thick solid curve, the boundary of the nonphysical region.

Fig. 3
Fig. 3

Wave-vector diagram for analyzing instability.

Fig. 4
Fig. 4

Instability regions for five values of angle ϕ. Curves 1, 2, 3, 4, and 5 refer to ϕ=90°, 45°, 35°, 9°, 0°, respectively. The region restricted by curve 1 coincides with the forbidden region.

Fig. 5
Fig. 5

Dependences |eK|(δ) for E0=7 kV/cm, Nt=2×1016 cm-3, μτ=8×10-7 cm2/V, and 2π/K18 µm (which corresponds to QK9.8) obtained numerically. Curves 1, 2, 3, 4, and 5 correspond to (m/mc)2=0.2, 0.5, 1.0, 1.5, 2, respectively, and to mc0.106. Thick curve, boundary of the forbidden region.

Fig. 6
Fig. 6

Ratio Γ/Ω versus κ. Curves 1, 2, 3, and 4 correspond to N=5, 8, 11, 20, respectively. The values of the material and experimental parameters are the same as in the caption to Fig. 5.

Fig. 7
Fig. 7

Ratio Γ/Ω as a function of k and κ for N=8; the other parameters are the same as for Fig. 6. The distance between the contour lines is 0.04.

Equations (37)

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

I=I0[1+m cos(Kz-Ωt)].
2Ω=ωk1+ωk2,
2K=k1+k2,
Δφzt-ω0lsΔφ-1l0Δφt+ω0Δφz+lD2l0Δ2φt
=-e0g˜z+e01E0div(g˜φ)+1E0div(Δφtφ),
ω0=g0/Nt,l0=μτ E0,
lD=(μτ kbT/e)1/2,ls=0 E0/eNt,
ωk=eg00E0kz,
γk=g01Nt+e0μτE02kz2+kbT0k2E02kz2.
eK=m2ωKΩ-ωK+iγK.
Ep=E0n=1enK exp(inξ)+c.c.,
e2K- eK2.
δωK=53|eK|2ωK.
m˜2=4y[(53y-δ)2+1],
y=(2δ±δ2-3).
δφ=a1 exp(ik 1r)+a2 exp(ik 2r)+c.c.,
ddt+iωk1+γk1a1=iV1a2* exp(-2iΩt),
ddt-iωk2+γk2a2*=-iV2*a1 exp(2iΩt),
V1=-KΩk12k1z4(k1·k2)+k22k1zk2ze2K,
δωk1ωk1δωk2ωk22|eK|2(5/3-cos2 ϕ),
δV=-2ωK eK2 cos2 ϕ.
V˜=ωK eK2(53-2 cos2 ϕ).
(γk1-iΔ1)a1=iV˜a2*
(γk2+iΔ2)a2*=-iV˜*a1,
|V˜|2=γ2+Δ2.
Δ=Ω-ωK(1+qz2/K2)+2ωK|eK|2(cos2 ϕ-5/3).
5(5-4 cos2 ϕ)y2-4(5-3 cos2 ϕ)δy+3(δ2+1)0,
|eK|th2=3QK,mth=26QK3/2.
5y=4(δ-d)±[(δ-d)2-15]1/2,
mth=23QK3/2.
Ω-ωK=5ωK/QK,|q|/K=1/QK1/2,
|eK|th2=3/QK.
u=exp(iκξ)s=-NNus exp(isξ),
(Csδss-Ass)us=0.
Cs=[(s+κ)2+θ2]-i(s+κ)ν-(s+κ)2+-i(s+κ)Kls+1kl0[ν-i(s+κ)]+Kld2l0[(s+κ)2+θ2][ν-i(s+κ)],
Ass=-m2(δss+1+δss-1)[(s+κ)(s+κ)+θ2]+e(s-s)K{(s-s)2[(s+κ)(s+κ)+θ2]+(s+κ)[(s+κ)2+θ2](s+κ+iν)},
Det(Csδss-Ass)=0,

Metrics