Abstract

We investigate experimentally the fundamental characteristics of space-charge waves excited in a photorefractive crystal of Bi12SiO20. Features such as their transient rise and decay as well as their steady-state frequency response are investigated. Based on this, we find the dependence of the space-charge waves’ quality factor on spatial frequency and electric-field biasing. The experimental findings are compared with the linear space-charge wave theory developed previously by Sturman et al. [J. Opt. Soc. Am. B 10, 1919 (1993) ].

© 1998 Optical Society of America

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References

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  1. B. I. Sturman, M. Mann, and K. H. Ringhofer, “Instability of spatial gratings induced by ac fields in photorefractive crystals,” Opt. Lett. 17, 1620–1622 (1992).
    [CrossRef] [PubMed]
  2. 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]
  3. B. I. Sturman, M. Mann, J. Otten, and K. H. Ringhofer, “Space-charge waves in photorefractive crystals and their parametric excitation,” J. Opt. Soc. Am. B 10, 1919–1932 (1993).
    [CrossRef]
  4. N. V. Kukhtarev, “Kinetics of hologram recording and erasure in electrooptic crystals,” Sov. Tech. Phys. Lett. 2, 438–440 (1977).
  5. Ph. Refregier, 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]
  6. H. C. Pedersen and P. M. Johansen, “Parametric oscillation in photorefractive media,” J. Opt. Soc. Am. B 12, 1065–1073 (1995).
    [CrossRef]
  7. 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]
  8. 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 57, 6112–6126 (1998).
    [CrossRef]
  9. B. I. Sturman, M. Mann, J. Otten, K. H. Ringhofer, and A. Bledowski, “Subharmonic generation in photorefractive crystals: application of theory to experiment,” Appl. Phys. A: Solids Surf. 55, 55–60 (1992).
    [CrossRef]
  10. 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]
  11. H. C. Pedersen and P. M. Johansen, “Longitudinal, degenerate, and transversal parametric oscillation in photorefractive media,” Phys. Rev. Lett. 77, 3106–3109 (1996).
    [CrossRef] [PubMed]
  12. H. C. Pedersen and P. M. Johansen, “Longitudinal, degenerate, and transversal photorefractive parametric oscillation: theory and experiment,” J. Opt. Soc. Am. B 14, 1418–1427 (1997).
    [CrossRef]
  13. S. F. Lyuksyutov, P. Buchhave, and M. V. Vasnetsov, “Self-excitation of space-charge waves,” Phys. Rev. Lett. 79, 67–70 (1997).
    [CrossRef]
  14. J. Otten, A. Ozols, M. Reinfelde, and K. H. Ringhofer, “Selfenhancement in lithium niobate,” Opt. Commun. 72, 175 (1989).
    [CrossRef]
  15. H. C. Pedersen, P. M. Johansen, and D. J. Webb, “Photorefractive subharmonics: a beam coupling effect?” J. Opt. Soc. Am. B 15, 1528–1532 (1998).
    [CrossRef]
  16. H. C. Pedersen, D. J. Webb, and P. M. Johansen, “Influence of beam coupling on photorefractive parametric oscillation in a dc-field-biased Bi12SiO20 crystal,” J. Opt. Soc. Am. B 15, 2439–2445 (1998).
    [CrossRef]
  17. G. Hamel de Montchenault, B. Loiseaux, and J. P. Huignard, “Moving grating during erasure in photorefractive Bi12SiO20 crystals,” Electron. Lett. 22, 1030–1032 (1986).
    [CrossRef]
  18. J. M. Heaton and L. Solymar, “Transient effects during dynamic hologram formation in BSO crystals: theory and experiment,” IEEE J. Quantum Electron. 24, 558–567 (1988).
    [CrossRef]
  19. 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]
  20. P. M. Johansen, “Enhanced four-wave mixing in photorefractive BSO produced by temporal phase shifts,” J. Phys. D 22, 247–253 (1989).
    [CrossRef]
  21. A. Marrakchi, R. V. Johnson, and A. R. Tanguay, Jr., “Polarization properties of photorefractive diffraction in electrooptic and optically active sillenite crystals (Bragg regime),” J. Opt. Soc. Am. B 3, 321–336 (1986).
    [CrossRef]
  22. P. M. Johansen, “Vectorial solution to the photorefractive band transport model in the spatial and temporal Fourier transformed domain,” IEEE J. Quantum Electron. 25, 530–539 (1989).
    [CrossRef]

1998 (3)

1997 (3)

H. C. Pedersen and P. M. Johansen, “Longitudinal, degenerate, and transversal photorefractive parametric oscillation: theory and experiment,” J. Opt. Soc. Am. B 14, 1418–1427 (1997).
[CrossRef]

S. F. Lyuksyutov, P. Buchhave, and M. V. Vasnetsov, “Self-excitation of space-charge waves,” Phys. Rev. Lett. 79, 67–70 (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 (1)

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

1995 (2)

1994 (1)

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 (1)

1992 (3)

B. I. Sturman, M. Mann, and K. H. Ringhofer, “Instability of spatial gratings induced by ac fields in photorefractive crystals,” Opt. Lett. 17, 1620–1622 (1992).
[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]

B. I. Sturman, M. Mann, J. Otten, K. H. Ringhofer, and A. Bledowski, “Subharmonic generation in photorefractive crystals: application of theory to experiment,” Appl. Phys. A: Solids Surf. 55, 55–60 (1992).
[CrossRef]

1989 (3)

J. Otten, A. Ozols, M. Reinfelde, and K. H. Ringhofer, “Selfenhancement in lithium niobate,” Opt. Commun. 72, 175 (1989).
[CrossRef]

P. M. Johansen, “Enhanced four-wave mixing in photorefractive BSO produced by temporal phase shifts,” J. Phys. D 22, 247–253 (1989).
[CrossRef]

P. M. Johansen, “Vectorial solution to the photorefractive band transport model in the spatial and temporal Fourier transformed domain,” IEEE J. Quantum Electron. 25, 530–539 (1989).
[CrossRef]

1988 (1)

J. M. Heaton and L. Solymar, “Transient effects during dynamic hologram formation in BSO crystals: theory and experiment,” IEEE J. Quantum Electron. 24, 558–567 (1988).
[CrossRef]

1986 (2)

A. Marrakchi, R. V. Johnson, and A. R. Tanguay, Jr., “Polarization properties of photorefractive diffraction in electrooptic and optically active sillenite crystals (Bragg regime),” J. Opt. Soc. Am. B 3, 321–336 (1986).
[CrossRef]

G. Hamel de Montchenault, B. Loiseaux, and J. P. Huignard, “Moving grating during erasure in photorefractive Bi12SiO20 crystals,” Electron. Lett. 22, 1030–1032 (1986).
[CrossRef]

1985 (1)

Ph. Refregier, 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]

1977 (1)

N. V. Kukhtarev, “Kinetics of hologram recording and erasure in electrooptic crystals,” Sov. Tech. Phys. Lett. 2, 438–440 (1977).

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]

Bledowski, A.

B. I. Sturman, M. Mann, J. Otten, K. H. Ringhofer, and A. Bledowski, “Subharmonic generation in photorefractive crystals: application of theory to experiment,” Appl. Phys. A: Solids Surf. 55, 55–60 (1992).
[CrossRef]

Buchhave, P.

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

Hamel de Montchenault, G.

G. Hamel de Montchenault, B. Loiseaux, and J. P. Huignard, “Moving grating during erasure in photorefractive Bi12SiO20 crystals,” Electron. Lett. 22, 1030–1032 (1986).
[CrossRef]

Heaton, J. M.

J. M. Heaton and L. Solymar, “Transient effects during dynamic hologram formation in BSO crystals: theory and experiment,” IEEE J. Quantum Electron. 24, 558–567 (1988).
[CrossRef]

Huignard, J. P.

G. Hamel de Montchenault, B. Loiseaux, and J. P. Huignard, “Moving grating during erasure in photorefractive Bi12SiO20 crystals,” Electron. Lett. 22, 1030–1032 (1986).
[CrossRef]

Huignard, J.-P.

Ph. Refregier, 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]

Johansen, P. M.

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 57, 6112–6126 (1998).
[CrossRef]

H. C. Pedersen, P. M. Johansen, and D. J. Webb, “Photorefractive subharmonics: a beam coupling effect?” J. Opt. Soc. Am. B 15, 1528–1532 (1998).
[CrossRef]

H. C. Pedersen, D. J. Webb, and P. M. Johansen, “Influence of beam coupling on photorefractive parametric oscillation in a dc-field-biased Bi12SiO20 crystal,” J. Opt. Soc. Am. B 15, 2439–2445 (1998).
[CrossRef]

H. C. Pedersen and P. M. Johansen, “Longitudinal, degenerate, and transversal photorefractive parametric oscillation: theory and experiment,” J. Opt. Soc. Am. B 14, 1418–1427 (1997).
[CrossRef]

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

H. C. Pedersen and P. M. Johansen, “Parametric oscillation in photorefractive media,” J. Opt. Soc. Am. B 12, 1065–1073 (1995).
[CrossRef]

P. M. Johansen, “Vectorial solution to the photorefractive band transport model in the spatial and temporal Fourier transformed domain,” IEEE J. Quantum Electron. 25, 530–539 (1989).
[CrossRef]

P. M. Johansen, “Enhanced four-wave mixing in photorefractive BSO produced by temporal phase shifts,” J. Phys. D 22, 247–253 (1989).
[CrossRef]

Johnson, R. V.

Kukhtarev, N. V.

N. V. Kukhtarev, “Kinetics of hologram recording and erasure in electrooptic crystals,” Sov. Tech. Phys. Lett. 2, 438–440 (1977).

Loiseaux, B.

G. Hamel de Montchenault, B. Loiseaux, and J. P. Huignard, “Moving grating during erasure in photorefractive Bi12SiO20 crystals,” Electron. Lett. 22, 1030–1032 (1986).
[CrossRef]

Lyuksyutov, S. F.

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

Mann, M.

B. I. Sturman, M. Mann, J. Otten, and K. H. Ringhofer, “Space-charge waves in photorefractive crystals 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 spatial gratings induced by ac fields in photorefractive crystals,” Opt. Lett. 17, 1620–1622 (1992).
[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]

B. I. Sturman, M. Mann, J. Otten, K. H. Ringhofer, and A. Bledowski, “Subharmonic generation in photorefractive crystals: application of theory to experiment,” Appl. Phys. A: Solids Surf. 55, 55–60 (1992).
[CrossRef]

Marrakchi, A.

McClelland, T. E.

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]

Otten, J.

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

B. I. Sturman, M. Mann, J. Otten, K. H. Ringhofer, and A. Bledowski, “Subharmonic generation in photorefractive crystals: application of theory to experiment,” Appl. Phys. A: Solids Surf. 55, 55–60 (1992).
[CrossRef]

J. Otten, A. Ozols, M. Reinfelde, and K. H. Ringhofer, “Selfenhancement in lithium niobate,” Opt. Commun. 72, 175 (1989).
[CrossRef]

Ozols, A.

J. Otten, A. Ozols, M. Reinfelde, and K. H. Ringhofer, “Selfenhancement in lithium niobate,” Opt. Commun. 72, 175 (1989).
[CrossRef]

Pedersen, H. C.

Podivilov, E. V.

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 57, 6112–6126 (1998).
[CrossRef]

Rajbenbach, H.

Ph. Refregier, 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]

Refregier, Ph.

Ph. Refregier, 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]

Reinfelde, M.

J. Otten, A. Ozols, M. Reinfelde, and K. H. Ringhofer, “Selfenhancement in lithium niobate,” Opt. Commun. 72, 175 (1989).
[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]

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 in photorefractive crystals 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 spatial gratings induced by ac fields in photorefractive crystals,” Opt. Lett. 17, 1620–1622 (1992).
[CrossRef] [PubMed]

B. I. Sturman, M. Mann, J. Otten, K. H. Ringhofer, and A. Bledowski, “Subharmonic generation in photorefractive crystals: application of theory to experiment,” Appl. Phys. A: Solids Surf. 55, 55–60 (1992).
[CrossRef]

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. Otten, A. Ozols, M. Reinfelde, and K. H. Ringhofer, “Selfenhancement in lithium niobate,” Opt. Commun. 72, 175 (1989).
[CrossRef]

Shamonina, E.

Solymar, L.

J. M. Heaton and L. Solymar, “Transient effects during dynamic hologram formation in BSO crystals: theory and experiment,” IEEE J. Quantum Electron. 24, 558–567 (1988).
[CrossRef]

Ph. Refregier, 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]

Sturman, B. I.

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 57, 6112–6126 (1998).
[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]

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 in photorefractive crystals 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 spatial gratings induced by ac fields in photorefractive crystals,” Opt. Lett. 17, 1620–1622 (1992).
[CrossRef] [PubMed]

B. I. Sturman, M. Mann, J. Otten, K. H. Ringhofer, and A. Bledowski, “Subharmonic generation in photorefractive crystals: application of theory to experiment,” Appl. Phys. A: Solids Surf. 55, 55–60 (1992).
[CrossRef]

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]

Tanguay Jr., A. R.

Vasnetsov, M. V.

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

Webb, D. J.

Appl. Phys. A: Solids Surf. (2)

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]

B. I. Sturman, M. Mann, J. Otten, K. H. Ringhofer, and A. Bledowski, “Subharmonic generation in photorefractive crystals: application of theory to experiment,” Appl. Phys. A: Solids Surf. 55, 55–60 (1992).
[CrossRef]

Electron. Lett. (1)

G. Hamel de Montchenault, B. Loiseaux, and J. P. Huignard, “Moving grating during erasure in photorefractive Bi12SiO20 crystals,” Electron. Lett. 22, 1030–1032 (1986).
[CrossRef]

IEEE J. Quantum Electron. (2)

J. M. Heaton and L. Solymar, “Transient effects during dynamic hologram formation in BSO crystals: theory and experiment,” IEEE J. Quantum Electron. 24, 558–567 (1988).
[CrossRef]

P. M. Johansen, “Vectorial solution to the photorefractive band transport model in the spatial and temporal Fourier transformed domain,” IEEE J. Quantum Electron. 25, 530–539 (1989).
[CrossRef]

J. Appl. Phys. (1)

Ph. Refregier, 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 (7)

J. Phys. D (1)

P. M. Johansen, “Enhanced four-wave mixing in photorefractive BSO produced by temporal phase shifts,” J. Phys. D 22, 247–253 (1989).
[CrossRef]

Opt. Commun. (1)

J. Otten, A. Ozols, M. Reinfelde, and K. H. Ringhofer, “Selfenhancement in lithium niobate,” Opt. Commun. 72, 175 (1989).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. E (2)

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]

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 57, 6112–6126 (1998).
[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. F. Lyuksyutov, P. Buchhave, and M. V. 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 photorefractive media,” Phys. Rev. Lett. 77, 3106–3109 (1996).
[CrossRef] [PubMed]

Sov. Tech. Phys. Lett. (1)

N. V. Kukhtarev, “Kinetics of hologram recording and erasure in electrooptic crystals,” Sov. Tech. Phys. Lett. 2, 438–440 (1977).

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Figures (8)

Fig. 1
Fig. 1

Schematical setup for the moving grating experiment.

Fig. 2
Fig. 2

Transient growth of the diffraction efficiency versus normalized time for four values of QK.

Fig. 3
Fig. 3

Schematical diagram of the experimental setup.

Fig. 4
Fig. 4

Normalized diffraction efficiencies measured for Λ=20 μm and E0=8.3 kV/cm. (a) Steady-state, normalized diffraction efficiency versus Ω; the open circles represent measurements, and the curves represent theory. The solid curve is obtained from Eq. (8) with γK=3.8 s-1 and ωK=11.8 s-1; the dashed curve is obtained from Eq. (8) with γK=2.8 s-1, ωK=11.8 s-1, and a renormalization factor of 1.3. The arrows show the FWHM’s of the two theoretical curves. (b) Transient decay of normalized diffraction efficiency at Ω=0. (c) Natural logarithm of the data in (b); the two lines mark two tangents. (d) Transient rise of normalized diffraction efficiency at Ω=0; the open circles represent experiments, and the curve is obtained theoretically from Eq. (10) with γK=2.4 s-1 and ωK=11.3 s-1. The low-frequency peak in (a) is simply a transient peak that occurs when the smooth movement of the piezomirror is turned on, and thus it does not reflect a real peak in frequency response. In obtaining (b) and (d) we switched, at t=0, the driving voltage of the piezomirror between a rapid sine voltage and a constant dc voltage.

Fig. 5
Fig. 5

Schematical illustration of the rough modeling of nonuniform illumination.

Fig. 6
Fig. 6

(a) New resonance curve (thin dashed curve) obtained from the simple model of including nonuniform illumination. Average values of γK=2.8 s-1 and ωK=11.8 s-1 were used as well as a renormalization factor of 1.3. The thick dashed curve and the circles are taken from Fig. 4(a). (b) New rise curve (thin dashed curve) obtained from the simple model of including nonuniform illumination. Average values of γK=2.4 s-1 and ωK=11.3 s-1 were used. The solid curve and the circles are taken from Fig. 4(d).

Fig. 7
Fig. 7

Rise curves for different values of Λ and E0.

Fig. 8
Fig. 8

Quality factor versus fringe spacing for three values of E0. The curves are obtained theoretically from Eqs. (5) by using the crystal parameters listed in Table 1 and a value of μ that was chosen to be 7×10-6 m2 V-1 s-1 to give the best theoretical fit. The symbols represent experimental values extracted from the r values in Fig. 7. The error bars reflect the uncertainty in determination of the steady-state levels in Fig. 7.

Tables (1)

Tables Icon

Table 1 Material Parameters Relevant to Bi12SiO20a

Equations (15)

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I=I0+I1=I0[1+m cos(Kx-Ωt)],
kBTq 2E˙1x2+E0 E˙1x-1μτ E˙1+kBTq ω0 2E1x2
+ω0E0 E1x-ζI0E1=ζI1E0+kBTq ζ I1x.
E1=E0e1(t)exp(iKx)+c.c.,
e˙1+(γK+iωK)e1=-i m2 ωK exp(-iΩt).
γK=ω01+EM,KEq,KE02+ED,KEq,KE02,
ωK=ω0 Eq,KE0,
Eq,KE0ED,K, EM,K.
e1=m2 ωKΩ-ωK+iγK exp(-iΩt).
η|e12|η(i)=γK2(Ω-ωK)2+γK2,
e1=e1(0)exp(-γKt-iωKt)  ηη(ii)=exp(-2γKt),
e1=-m2 ωKωK-iγK [1-exp(-γKt-iωKt)]ηη(iii)=|1-exp(-QK-1t-it)|2,
r[1+exp(-π/QK)]2,
QK=-πln(r-1).
ηN-2p=1Ne1(p)2,

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