Abstract

It is shown that spatial gratings in photorefractive crystals, induced by the standing interference pattern of two coherent waves and an external alternating electric field, may be unstable against the excitation of weakly damped eigenmodes. The dependence of the exponential rate of growth of the instability on experimental parameters and crystal characteristics is investigated. The instability influences the amplification of the photorefractive sensitivity by an ac field. A comparison is made between theoretical results and experimental data.

© 1992 Optical Society of America

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References

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  1. S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5600 (1988).
  2. D. J. Webb, L. Solymar, Opt. Commun. 74386 (1990).
  3. D. J. Webb, L. B. Au, D. C. Jones, L. Solymar, Appl. Phys. Lett. 57, 1602 (1990).
  4. J. Takacs, L. Solymar, Opt. Lett. 17247 (1992).
  5. O. P. Nestiorkin, Opt. Commun. 81315 (1991).
  6. B. Sturman, A. Bledowski, J. Otten, K. H. Ringhofer, J. Opt. Soc. Am. B 9, 672 (1992).
  7. B. I. Sturman, M. Mann, J. Otten, K. H. Ringhofer, Appl. Phys. A 55, 55 (1992).
  8. S. I. Stepanov, M. P. Petrov, Opt. Commun. 53, 292 (1985).
  9. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949, 961 (1979).
  10. K. Walsh, A. K. Powell, C. Stace, T. J. Hall, J. Opt. Soc. Am. B 7, 288 (1990).
  11. E. L. Ince, Ordinary Differential Equations (Dover, New York, 1956).

1992 (3)

1991 (1)

O. P. Nestiorkin, Opt. Commun. 81315 (1991).

1990 (3)

D. J. Webb, L. Solymar, Opt. Commun. 74386 (1990).

D. J. Webb, L. B. Au, D. C. Jones, L. Solymar, Appl. Phys. Lett. 57, 1602 (1990).

K. Walsh, A. K. Powell, C. Stace, T. J. Hall, J. Opt. Soc. Am. B 7, 288 (1990).

1988 (1)

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5600 (1988).

1985 (1)

S. I. Stepanov, M. P. Petrov, Opt. Commun. 53, 292 (1985).

1979 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949, 961 (1979).

1956 (1)

E. L. Ince, Ordinary Differential Equations (Dover, New York, 1956).

Au, L. B.

D. J. Webb, L. B. Au, D. C. Jones, L. Solymar, Appl. Phys. Lett. 57, 1602 (1990).

Bledowski, A.

Ducollet, H.

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5600 (1988).

Hall, T. J.

Herriau, J. P.

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5600 (1988).

Huignard, J. P.

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5600 (1988).

Imbert, B.

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5600 (1988).

Ince, E. L.

E. L. Ince, Ordinary Differential Equations (Dover, New York, 1956).

Jones, D. C.

D. J. Webb, L. B. Au, D. C. Jones, L. Solymar, Appl. Phys. Lett. 57, 1602 (1990).

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949, 961 (1979).

Mallick, S.

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5600 (1988).

Mann, M.

B. I. Sturman, M. Mann, J. Otten, K. H. Ringhofer, Appl. Phys. A 55, 55 (1992).

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949, 961 (1979).

Nestiorkin, O. P.

O. P. Nestiorkin, Opt. Commun. 81315 (1991).

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949, 961 (1979).

Otten, J.

B. I. Sturman, M. Mann, J. Otten, K. H. Ringhofer, Appl. Phys. A 55, 55 (1992).

B. Sturman, A. Bledowski, J. Otten, K. H. Ringhofer, J. Opt. Soc. Am. B 9, 672 (1992).

Petrov, M. P.

S. I. Stepanov, M. P. Petrov, Opt. Commun. 53, 292 (1985).

Powell, A. K.

Ringhofer, K. H.

B. I. Sturman, M. Mann, J. Otten, K. H. Ringhofer, Appl. Phys. A 55, 55 (1992).

B. Sturman, A. Bledowski, J. Otten, K. H. Ringhofer, J. Opt. Soc. Am. B 9, 672 (1992).

Solymar, L.

J. Takacs, L. Solymar, Opt. Lett. 17247 (1992).

D. J. Webb, L. B. Au, D. C. Jones, L. Solymar, Appl. Phys. Lett. 57, 1602 (1990).

D. J. Webb, L. Solymar, Opt. Commun. 74386 (1990).

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949, 961 (1979).

Stace, C.

Stepanov, S. I.

S. I. Stepanov, M. P. Petrov, Opt. Commun. 53, 292 (1985).

Sturman, B.

Sturman, B. I.

B. I. Sturman, M. Mann, J. Otten, K. H. Ringhofer, Appl. Phys. A 55, 55 (1992).

Takacs, J.

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949, 961 (1979).

Walsh, K.

Webb, D. J.

D. J. Webb, L. B. Au, D. C. Jones, L. Solymar, Appl. Phys. Lett. 57, 1602 (1990).

D. J. Webb, L. Solymar, Opt. Commun. 74386 (1990).

Appl. Phys. A (1)

B. I. Sturman, M. Mann, J. Otten, K. H. Ringhofer, Appl. Phys. A 55, 55 (1992).

Appl. Phys. Lett. (1)

D. J. Webb, L. B. Au, D. C. Jones, L. Solymar, Appl. Phys. Lett. 57, 1602 (1990).

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949, 961 (1979).

J. Appl. Phys. (1)

S. Mallick, B. Imbert, H. Ducollet, J. P. Herriau, J. P. Huignard, J. Appl. Phys. 63, 5600 (1988).

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

Opt. Commun. (3)

O. P. Nestiorkin, Opt. Commun. 81315 (1991).

S. I. Stepanov, M. P. Petrov, Opt. Commun. 53, 292 (1985).

D. J. Webb, L. Solymar, Opt. Commun. 74386 (1990).

Opt. Lett. (1)

Ordinary Differential Equations (1)

E. L. Ince, Ordinary Differential Equations (Dover, New York, 1956).

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Figures (2)

Fig. 1
Fig. 1

Dependence mth (k1) in the limit of a quickly oscillating field for μτ = 3 × 107, 4 × 107, and 8 × 107 cm2 V1.

Fig. 2
Fig. 2

Dependence Γ (t0−1) for m = 0.05, μτ = 6 × 107 cm2 V1, and k1/K = 1/2, 1/3, and 1/4.

Equations (13)

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E ex ( t ) = E 0 p ( t ) , p ( t ) { 1 0 t < t 0 / 2 1 t 0 / 2 t < t 0 .
( E x t p ω K E ) x γ E ( K ) E + ( γ N + γ D ) E x x = ω K ( m cos x E 2 ) x .
ω K = e g 0 0 K E 0 , γ E ( K ) = ω K K E 0 μ τ , γ N = g 0 N , γ D = ω K K k B T e E 0 .
γ k = γ E ( K ) + γ N + γ D .
Φ k = ω k ( p t p t 0 / 2 + t 0 / 2 ) .
( t + i p ω K + γ K ) E K = i 2 m ω K .
E K 2 i m γ K t 0 sin ( ω K t 0 / 4 ) exp [ i ( Φ K ω K t 0 / 4 ) ] .
E = E K exp ( i x ) + A 1 K / k 1 exp ( i k 1 K x i Φ k 1 ) + A 2 K / k 2 exp ( i k 2 K x i Φ k 2 ) + c . c .
( t + γ k 1 ) A 1 = κ ω K exp ( i Ψ ) A 2 * , ( t + γ k 2 ) A 2 * = κ ω K exp ( i Ψ ) A 1 .
κ = 2 K k 1 k 2 | E K | , Ψ t = 2 p ω K Δ , Δ = 1 2 ( K 2 k 1 k 2 1 ) .
Γ = t 0 1 ln | Z | .
Z ± = 1 + 2 S ± 2 S + S 2 , S = κ 2 Δ 2 κ 2 sin 2 ( ω K t 0 2 Δ 2 κ 2 ) .
Γ 0 m ω K 2 γ K K k 1 k 2 .

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