Abstract

The benefits of a direct visualization of space-charge grating buildup are described. The visualization is carried out by a simple repetitive computer program, which simulates the basic processes in the band-transport model and displays the result graphically or in the form of numerical data. The simulation sheds light on issues that are not amenable to analytical solutions, such as the spectral content of the wave forms, cross talk in three-beam interaction, and the range of applications of the band-transport model.

© 1998 Optical Society of America

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References

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  1. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949–960 (1979).
    [CrossRef]
  2. N. V. Kukhtarev, P. Buchhave, and S. Lyuksyutov, Phys. Rev. A 55, 3133–3136 (1997).
    [CrossRef]
  3. N. V. Kukhtarev, H. J. Caulfield, T. Kukhtareva, P. Buchhave, and S. Lyuksyutov, in Critical Reviews in Optical Science and Technology, P. Cloeck, ed. Vol. 64 of Critical Reviews Series (SPIE, Bellingham, Wash., 1996), p. 280.
  4. P. E. Andersen, P. Buchhave, P. M. Petersen, and M. V. Vasnetsov, J. Opt. Soc. Am. B 12, 1422–1433 (1995).
    [CrossRef]
  5. P. E. Andersen, P. M. Petersen, and P. Buchhave, J. Opt. Soc. Am. B 12, 2453–2462 (1995).
    [CrossRef]
  6. M. Vasnetsov, S. Lyuksyutov, P. Buchhave, P. E. Andersen, and P. M. Petersen, “Spectral dependence of cross talk between holographic gratings in photorefractive Bi12SiO20,” Appl. Phys. B 65, 523–526 (1997).
    [CrossRef]
  7. P. E. Andersen and P. M. Petersen, presented at the 1997 Topical Meeting on Photorefractive Materials, Effects and Devices (PR’97), June 11–13, 1997, Chiba, Japan.

1997 (2)

N. V. Kukhtarev, P. Buchhave, and S. Lyuksyutov, Phys. Rev. A 55, 3133–3136 (1997).
[CrossRef]

M. Vasnetsov, S. Lyuksyutov, P. Buchhave, P. E. Andersen, and P. M. Petersen, “Spectral dependence of cross talk between holographic gratings in photorefractive Bi12SiO20,” Appl. Phys. B 65, 523–526 (1997).
[CrossRef]

1995 (2)

1979 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Andersen, P. E.

M. Vasnetsov, S. Lyuksyutov, P. Buchhave, P. E. Andersen, and P. M. Petersen, “Spectral dependence of cross talk between holographic gratings in photorefractive Bi12SiO20,” Appl. Phys. B 65, 523–526 (1997).
[CrossRef]

P. E. Andersen, P. M. Petersen, and P. Buchhave, J. Opt. Soc. Am. B 12, 2453–2462 (1995).
[CrossRef]

P. E. Andersen, P. Buchhave, P. M. Petersen, and M. V. Vasnetsov, J. Opt. Soc. Am. B 12, 1422–1433 (1995).
[CrossRef]

P. E. Andersen and P. M. Petersen, presented at the 1997 Topical Meeting on Photorefractive Materials, Effects and Devices (PR’97), June 11–13, 1997, Chiba, Japan.

Buchhave, P.

M. Vasnetsov, S. Lyuksyutov, P. Buchhave, P. E. Andersen, and P. M. Petersen, “Spectral dependence of cross talk between holographic gratings in photorefractive Bi12SiO20,” Appl. Phys. B 65, 523–526 (1997).
[CrossRef]

N. V. Kukhtarev, P. Buchhave, and S. Lyuksyutov, Phys. Rev. A 55, 3133–3136 (1997).
[CrossRef]

P. E. Andersen, P. Buchhave, P. M. Petersen, and M. V. Vasnetsov, J. Opt. Soc. Am. B 12, 1422–1433 (1995).
[CrossRef]

P. E. Andersen, P. M. Petersen, and P. Buchhave, J. Opt. Soc. Am. B 12, 2453–2462 (1995).
[CrossRef]

N. V. Kukhtarev, H. J. Caulfield, T. Kukhtareva, P. Buchhave, and S. Lyuksyutov, in Critical Reviews in Optical Science and Technology, P. Cloeck, ed. Vol. 64 of Critical Reviews Series (SPIE, Bellingham, Wash., 1996), p. 280.

Caulfield, H. J.

N. V. Kukhtarev, H. J. Caulfield, T. Kukhtareva, P. Buchhave, and S. Lyuksyutov, in Critical Reviews in Optical Science and Technology, P. Cloeck, ed. Vol. 64 of Critical Reviews Series (SPIE, Bellingham, Wash., 1996), p. 280.

Kukhtarev, N. V.

N. V. Kukhtarev, P. Buchhave, and S. Lyuksyutov, Phys. Rev. A 55, 3133–3136 (1997).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949–960 (1979).
[CrossRef]

N. V. Kukhtarev, H. J. Caulfield, T. Kukhtareva, P. Buchhave, and S. Lyuksyutov, in Critical Reviews in Optical Science and Technology, P. Cloeck, ed. Vol. 64 of Critical Reviews Series (SPIE, Bellingham, Wash., 1996), p. 280.

Kukhtareva, T.

N. V. Kukhtarev, H. J. Caulfield, T. Kukhtareva, P. Buchhave, and S. Lyuksyutov, in Critical Reviews in Optical Science and Technology, P. Cloeck, ed. Vol. 64 of Critical Reviews Series (SPIE, Bellingham, Wash., 1996), p. 280.

Lyuksyutov, S.

N. V. Kukhtarev, P. Buchhave, and S. Lyuksyutov, Phys. Rev. A 55, 3133–3136 (1997).
[CrossRef]

M. Vasnetsov, S. Lyuksyutov, P. Buchhave, P. E. Andersen, and P. M. Petersen, “Spectral dependence of cross talk between holographic gratings in photorefractive Bi12SiO20,” Appl. Phys. B 65, 523–526 (1997).
[CrossRef]

N. V. Kukhtarev, H. J. Caulfield, T. Kukhtareva, P. Buchhave, and S. Lyuksyutov, in Critical Reviews in Optical Science and Technology, P. Cloeck, ed. Vol. 64 of Critical Reviews Series (SPIE, Bellingham, Wash., 1996), p. 280.

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Petersen, P. M.

M. Vasnetsov, S. Lyuksyutov, P. Buchhave, P. E. Andersen, and P. M. Petersen, “Spectral dependence of cross talk between holographic gratings in photorefractive Bi12SiO20,” Appl. Phys. B 65, 523–526 (1997).
[CrossRef]

P. E. Andersen, P. M. Petersen, and P. Buchhave, J. Opt. Soc. Am. B 12, 2453–2462 (1995).
[CrossRef]

P. E. Andersen, P. Buchhave, P. M. Petersen, and M. V. Vasnetsov, J. Opt. Soc. Am. B 12, 1422–1433 (1995).
[CrossRef]

P. E. Andersen and P. M. Petersen, presented at the 1997 Topical Meeting on Photorefractive Materials, Effects and Devices (PR’97), June 11–13, 1997, Chiba, Japan.

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Vasnetsov, M.

M. Vasnetsov, S. Lyuksyutov, P. Buchhave, P. E. Andersen, and P. M. Petersen, “Spectral dependence of cross talk between holographic gratings in photorefractive Bi12SiO20,” Appl. Phys. B 65, 523–526 (1997).
[CrossRef]

Vasnetsov, M. V.

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Appl. Phys. B (1)

M. Vasnetsov, S. Lyuksyutov, P. Buchhave, P. E. Andersen, and P. M. Petersen, “Spectral dependence of cross talk between holographic gratings in photorefractive Bi12SiO20,” Appl. Phys. B 65, 523–526 (1997).
[CrossRef]

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949–960 (1979).
[CrossRef]

J. Opt. Soc. Am. B (2)

Phys. Rev. A (1)

N. V. Kukhtarev, P. Buchhave, and S. Lyuksyutov, Phys. Rev. A 55, 3133–3136 (1997).
[CrossRef]

Other (2)

N. V. Kukhtarev, H. J. Caulfield, T. Kukhtareva, P. Buchhave, and S. Lyuksyutov, in Critical Reviews in Optical Science and Technology, P. Cloeck, ed. Vol. 64 of Critical Reviews Series (SPIE, Bellingham, Wash., 1996), p. 280.

P. E. Andersen and P. M. Petersen, presented at the 1997 Topical Meeting on Photorefractive Materials, Effects and Devices (PR’97), June 11–13, 1997, Chiba, Japan.

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Figures (4)

Fig. 1
Fig. 1

Flow diagram of the simulation program.

Fig. 2
Fig. 2

Grating variables at different stages of the time development: First row, incident intensity (I); second row, intensity (I), electron density (n), density of ionized donors (v), and space-charge field (w) during transient development; third row, the same grating variables at steady state. The bottom three rows show Fourier spectra of electron density (n), density of ionized donors (v) and space-charge field (w) in the steady-state condition. The spectrum of the electron density is indistinguishable from that of the intensity. (a) The pure diffusion case (no applied field), (b) a mixed situation with both diffusion and drift, (c) the drift-dominated case.

Fig. 3
Fig. 3

Grating variables in the three-beam case as a function of position. The abscissa covers one and one-half periods of the difference frequency between the two closely spaced beams (object beams). The curves (top to bottom) are space-charge field, incident intensity, ionized donor density, and free-electron density.

Fig. 4
Fig. 4

(a) Harmonics of the three-beam case corresponding to the parameters of Ref. 5. The abscissa covers zero to the sixth harmonic. (b) A more detailed view of the spectral components near the first and the second harmonics.

Equations (15)

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Generation(P-Qv)(1+m¯cos u),
Recombinationnv,
Diffusionλn,
Driftnw.
w=1+n-v.
Generationandrecombination
n˙=-v˙=(P-Qv)(1+m¯cos u)-nv,
Totalcurrentdensityj=nw-λn,
Gaussslaww=1+n-v,
Externalcircuitj=0.
n=n0(1+a1 cos u+b1 sin u)=n0[1+a cos(u+φ)],
w=λ nn-λ n2n2,
v=1+n-λ nn+λ n2n2.
P(1+m¯cos u)=[Q(1+m¯cos u)-n]×1+n-λ nn+λ n2n2.
P(1+m¯cos u)=-n+λn-λ n2n,

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