Abstract

Erase rates for uniformly illuminated refractive-index gratings are derived for a model of photorefractivity in which two photoactive ions participate as donors and acceptors. The model leads naturally to decay of gratings at two separate rates. In some conditions the amplitudes of the components that decay at each rate are nearly equal, while the rates are substantially different. These conditions should be readily observable in crystals with two photoactive species. In other conditions, one amplitude greatly exceeds the other or the time constants are nearly equal, and a single rate would be observed. The ratios of the rates and amplitudes are insensitive to erase irradiance but very sensitive to grating period and absorption cross section. Illustrative parameters for Bi12SiO20 suggest that if two photoactive species are present, two decay rates should be observable.

© 1983 Optical Society of America

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References

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  1. M. B. Klein, Hughes Research Laboratories; private communication (1982).
  2. R. A. Mullen, R. W. Hellwarth, in Technical Digest, Conference on Lasers and Electrooptics (Optical Society of America, Washington, D.C., 1983), paper THH3.
  3. M. Peltier, F. Micheron, J. Appl. Phys. 48, 3686 (1977).
    [CrossRef]
  4. N. V. Kukhtarev, Sov. Tech. Phys. Lett. 2, 438 (1976).
  5. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
    [CrossRef]
  6. G. C. Valley, “Short Pulse Grating Formation in Photorefractive Materials,” to be published IEEE J. Quantum Electron.QE-19, Nov. (1983).
  7. L. Young, W. K. Y. Wong, M. L. W. Thewalt, W. D. Cornish, Appl. Phys. Lett 24, 264 (1974).
    [CrossRef]
  8. J. J. Amodei, RCA Rev. 32, 185 (1971).
  9. J. P. Huignard, J. P. Herriau, P. Aubourg, E. Spitz, Opt. Lett. 4, 21 (1979).
    [CrossRef] [PubMed]
  10. J. P. Huignard, J. P. Herriau, Appl. Opt. 17, 2671 (1978).
    [CrossRef] [PubMed]
  11. A. Marrakchi, J. P. Huignard, Appl. Phys. 24, 131 (1981).
    [CrossRef]
  12. L. Pichon, J. P. Huignard, Opt. Commun. 36, 277 (1981).
    [CrossRef]
  13. Y. H. Ja, Opt. Quantum Electron. 14, 363 (1982).
    [CrossRef]
  14. P. Gunter, Phys. Rep. 93, 200 (1983).
  15. G. C. Valley, M. B. Klein, “Optimal Properties of Photorefractive Materials for Optical Data Processing,” to be published in Opt. Eng.22, Dec. (1983).
    [CrossRef]

1983 (1)

P. Gunter, Phys. Rep. 93, 200 (1983).

1982 (1)

Y. H. Ja, Opt. Quantum Electron. 14, 363 (1982).
[CrossRef]

1981 (2)

A. Marrakchi, J. P. Huignard, Appl. Phys. 24, 131 (1981).
[CrossRef]

L. Pichon, J. P. Huignard, Opt. Commun. 36, 277 (1981).
[CrossRef]

1979 (2)

J. P. Huignard, J. P. Herriau, P. Aubourg, E. Spitz, Opt. Lett. 4, 21 (1979).
[CrossRef] [PubMed]

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

1978 (1)

1977 (1)

M. Peltier, F. Micheron, J. Appl. Phys. 48, 3686 (1977).
[CrossRef]

1976 (1)

N. V. Kukhtarev, Sov. Tech. Phys. Lett. 2, 438 (1976).

1974 (1)

L. Young, W. K. Y. Wong, M. L. W. Thewalt, W. D. Cornish, Appl. Phys. Lett 24, 264 (1974).
[CrossRef]

1971 (1)

J. J. Amodei, RCA Rev. 32, 185 (1971).

Amodei, J. J.

J. J. Amodei, RCA Rev. 32, 185 (1971).

Aubourg, P.

Cornish, W. D.

L. Young, W. K. Y. Wong, M. L. W. Thewalt, W. D. Cornish, Appl. Phys. Lett 24, 264 (1974).
[CrossRef]

Gunter, P.

P. Gunter, Phys. Rep. 93, 200 (1983).

Hellwarth, R. W.

R. A. Mullen, R. W. Hellwarth, in Technical Digest, Conference on Lasers and Electrooptics (Optical Society of America, Washington, D.C., 1983), paper THH3.

Herriau, J. P.

Huignard, J. P.

Ja, Y. H.

Y. H. Ja, Opt. Quantum Electron. 14, 363 (1982).
[CrossRef]

Klein, M. B.

G. C. Valley, M. B. Klein, “Optimal Properties of Photorefractive Materials for Optical Data Processing,” to be published in Opt. Eng.22, Dec. (1983).
[CrossRef]

M. B. Klein, Hughes Research Laboratories; private communication (1982).

Kukhtarev, N. V.

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

N. V. Kukhtarev, Sov. Tech. Phys. Lett. 2, 438 (1976).

Markov, V. B.

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

Marrakchi, A.

A. Marrakchi, J. P. Huignard, Appl. Phys. 24, 131 (1981).
[CrossRef]

Micheron, F.

M. Peltier, F. Micheron, J. Appl. Phys. 48, 3686 (1977).
[CrossRef]

Mullen, R. A.

R. A. Mullen, R. W. Hellwarth, in Technical Digest, Conference on Lasers and Electrooptics (Optical Society of America, Washington, D.C., 1983), paper THH3.

Odulov, S. G.

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

Peltier, M.

M. Peltier, F. Micheron, J. Appl. Phys. 48, 3686 (1977).
[CrossRef]

Pichon, L.

L. Pichon, J. P. Huignard, Opt. Commun. 36, 277 (1981).
[CrossRef]

Soskin, M. S.

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

Spitz, E.

Thewalt, M. L. W.

L. Young, W. K. Y. Wong, M. L. W. Thewalt, W. D. Cornish, Appl. Phys. Lett 24, 264 (1974).
[CrossRef]

Valley, G. C.

G. C. Valley, “Short Pulse Grating Formation in Photorefractive Materials,” to be published IEEE J. Quantum Electron.QE-19, Nov. (1983).

G. C. Valley, M. B. Klein, “Optimal Properties of Photorefractive Materials for Optical Data Processing,” to be published in Opt. Eng.22, Dec. (1983).
[CrossRef]

Vinetskii, V. L.

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

Wong, W. K. Y.

L. Young, W. K. Y. Wong, M. L. W. Thewalt, W. D. Cornish, Appl. Phys. Lett 24, 264 (1974).
[CrossRef]

Young, L.

L. Young, W. K. Y. Wong, M. L. W. Thewalt, W. D. Cornish, Appl. Phys. Lett 24, 264 (1974).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. (1)

A. Marrakchi, J. P. Huignard, Appl. Phys. 24, 131 (1981).
[CrossRef]

Appl. Phys. Lett (1)

L. Young, W. K. Y. Wong, M. L. W. Thewalt, W. D. Cornish, Appl. Phys. Lett 24, 264 (1974).
[CrossRef]

Ferroelectrics (1)

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

J. Appl. Phys. (1)

M. Peltier, F. Micheron, J. Appl. Phys. 48, 3686 (1977).
[CrossRef]

Opt. Commun. (1)

L. Pichon, J. P. Huignard, Opt. Commun. 36, 277 (1981).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

Y. H. Ja, Opt. Quantum Electron. 14, 363 (1982).
[CrossRef]

Phys. Rep. (1)

P. Gunter, Phys. Rep. 93, 200 (1983).

RCA Rev. (1)

J. J. Amodei, RCA Rev. 32, 185 (1971).

Sov. Tech. Phys. Lett. (1)

N. V. Kukhtarev, Sov. Tech. Phys. Lett. 2, 438 (1976).

Other (4)

M. B. Klein, Hughes Research Laboratories; private communication (1982).

R. A. Mullen, R. W. Hellwarth, in Technical Digest, Conference on Lasers and Electrooptics (Optical Society of America, Washington, D.C., 1983), paper THH3.

G. C. Valley, “Short Pulse Grating Formation in Photorefractive Materials,” to be published IEEE J. Quantum Electron.QE-19, Nov. (1983).

G. C. Valley, M. B. Klein, “Optimal Properties of Photorefractive Materials for Optical Data Processing,” to be published in Opt. Eng.22, Dec. (1983).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Ratios of the two time constants τ+/τ and of the amplitudes A+/A as a function of the ratio of dielectric relaxation time to the diffusion time τdi/τdiff for values of the parameters given in the figure.

Fig. 2
Fig. 2

Ratios τ+/τ and A+/A as a function of τdi/τdiff for a smaller ratio of dielectric relaxation time to recombination times than in Fig. 1.

Fig. 3
Fig. 3

Ratio of τ+/τ as a function of τdi/τIA for a range of parameters τdi/τdiff = τdi/τD = τdiA = 102–107.

Fig. 4
Fig. 4

Ratio A+/A as a function of τdi/τIA for a small ratio of dielectric relaxation time to diffusion and recombination times, τdi/τdiff = τdi/τD = τdi/τA = 103.

Fig. 5
Fig. 5

Ratio A+/A as a function of τdi/τIA for a large ratio of dielectric relaxation time to diffusion and recombination times, τdi/τdiff = τdi/τD = τdi/τA = 106.

Fig. 6
Fig. 6

Oscillation frequency ω times 2T1 as a function of τdi/τdiff for values of the ratio τdi/τD with τdi/τIA = τdi/τID = 104.

Fig. 7
Fig. 7

Ratios τ+/τ and A+/A as a function of grating periods Λg for illustrative parameters for BSO derived from the work of Peltier and Micheron.3

Equations (25)

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n t + N A i t N D i t = 1 e j z ,
N D i t = s D I ( N D N D i ) γ D n N D i ,
N A i t = s A I N A i + γ A n ( N A N A i ) ,
j = e μ n E μ k B T n z ,
E z = 4 π e ( n + N A i N D i ) .
n D ( N D N D 0 i ) n 0 N D 0 i = 0 ,
n 0 ( N A N A 0 i ) n A N A 0 i = 0 ,
n 0 = N D 0 i N A 0 i ,
n D ( N D N A 0 i n A N A 0 i N A N A 0 i ) n A N A 0 i N A N A 0 i ( N A 0 i + n A N A 0 i N A N A 0 i ) = 0 .
N A 0 2 i ( 1 n A / n D ) ( N D + N A ) N A 0 i + N A N D = 0 .
n A N A N A 0 i 1 .
s A I γ R N A ( 1 + N D N A ) 1 .
n 0 t = s D I ( N D N D 0 i ) γ D n 0 N D 0 i γ A n 0 ( N A N A 0 i ) + s A I N A 0 i .
n 0 = [ s D ( N D N D 0 i ) + s A N A 0 i ] I γ D N D 0 i + γ A ( N A N A 0 i ) × ( 1 exp { t [ γ D N D 0 i + γ A ( N A N A 0 i ) } ) .
n 0 = s D ( N D N D 0 i ) I γ D N D 0 i .
T 3 3 δ E t 3 + 2 δ E t 2 + 1 T 1 δ E t + 1 T 2 2 δ E = 0 ,
1 T 3 = ( 1 τ diff + 1 τ di + 1 τ I D + 1 τ I A + 1 τ D + 1 τ A ) ,
1 T 1 = T 3 ( 1 τ I D τ diff + 1 τ I A τ diff + 1 τ I D τ di + 1 τ I A τ di + 1 τ I A τ I D + 1 τ D τ di + 1 τ A τ di + 1 τ D τ I A + 1 τ A τ I D ) ,
1 T 2 2 = T 3 ( 1 τ I D τ I A τ diff + 1 τ I D τ I A τ di + 1 τ I D τ A τ di + 1 τ I A τ D τ di ) .
δ E ( 0 ) = E g ,
δ E t t = 0 = E g τ di ,
δ E ( t ) δ E ( 0 ) = τ + exp ( t / τ + ) ( τ τ + ) ( 1 τ τ di ) + τ exp ( t / τ ) ( τ τ + ) ( 1 τ + τ di ) ,
1 τ ± = 1 2 T 1 [ 1 ± ( 1 4 T 1 2 T 2 2 ) 1 / 2 ] .
A + A = ( τ di / τ 1 ) ( τ di / τ + 1 ) .
N D = 10 19 cm 3 , μ = 0.03 cm 2 / V sec , N A = 10 16 cm 3 γ D = 2 × 10 11 cm 3 / sec , s D = 2 × 10 19 cm 2 , γ A 8 × 10 11 cm 3 / sec .

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