Abstract

A general formalism based on the Kukhtarev equations is developed to describe the kinetics of holographic recording and erasure in unipolar photorefractive materials containing multiple active centers. One primary relevant result is that the exchange of charge among the various centers and the holographic grating dynamics, involving charge transport, are uncoupled after appropriate linearization of the equations. The formalism is then applied to the simple but physically meaningful case of two active centers, an optical donor and a thermally active trap. Detailed computer simulations have been carried out to investigate the influence of trap energy depth, trap concentration, temperature, and light intensity on the holographic behavior. The results qualitatively account for a number of unexpected features in the kinetics of grating recording and erasure observed in several photorefractive materials.

© 1991 Optical Society of America

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  1. P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–298 (1982).
    [Crossref]
  2. P. Yeh, “Two-wave mixing in non-linear media,” IEEE J. Quantum Electron. 25, 484–512 (1989).
    [Crossref]
  3. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. steady state,” Ferroelectrics 22, 949–960 (1979).
    [Crossref]
  4. A. A. Kamshilin, M. G. Miteva, “Effect of infrared irradiation on holographic recording in BSO,” Opt. Commun. 36, 429–433 (1981).
    [Crossref]
  5. L. Arizmendi, “Thermal fixing of holographic gratings in BSO,” J. Appl. Phys. 65, 423–427 (1989).
    [Crossref]
  6. G. Montaemmezzani, M. Ingold, H. Looser, P. Günter, “Multiple photorefractive gratings in Ce-doped LiNbO3 and KNbO3 crystals,” Ferroelectrics 92, 281–287 (1989).
    [Crossref]
  7. F. P. Strohkendl, “Light-induced dark decays of photorefractive gratings and their observation in BSO,” J. Appl. Phys. 65, 3773–3780 (1989).
    [Crossref]
  8. D. Mahgerefteh, J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195–2198 (1990).
    [Crossref] [PubMed]
  9. G. C. Valley, “Erase rates in photorefractive materials with two photorefractive species,” Appl. Opt. 22, 3160–3164 (1983).
    [Crossref] [PubMed]
  10. M. Carrascosa, F. Agulló-López, “Erasure of holographic gratings in photorefractive materials with two active species,” Appl. Opt. 27, 2851–2857 (1988).
    [Crossref] [PubMed]
  11. G. C. Valley, “Simultaneous electron–hole transport in photorefractive materials,” J. Appl. Phys. 59, 3363–3366 (1986).
    [Crossref]
  12. F. P. Strohkendl, J. M. Jonathan, R. W. Hellwarth, “Hole–electron competition in photorefractive gratings,” Opt. Lett. 11, 312–314(1986).
    [Crossref] [PubMed]
  13. L. M. Bernardo, J. C. Lopes, O. D. Soares, “Hole–electron competition with fast and slow gratings in BSO crystals,” Appl. Opt. 29, 12–14 (1990).
    [Crossref] [PubMed]
  14. S. Zhivkova, M. Miteva, “Holographic recording in photorefractive crystals with simultaneous electron–hole transport and two active centers,” J. Appl. Phys. 68, 3099–3103 (1990).
    [Crossref]
  15. M. C. Bashaw, T. P. Ma, R. C. Barker, S. Mroczkowski, R. R. Dube, “Theory of complementary holograms arising from electron–hole transport in photorefractive media,” J. Opt. Soc. Am. B 7, 2329–2338 (1990).
    [Crossref]
  16. L. Arizmendi, University Autonoma Madrid, Cantoblanco, Madrid, Spain (personal communication).
  17. F. Jariego, F. Agulló-López, “Monotonic versus oscillatory behavior during holographic writing in photorefractive photovoltaic materials,” Opt. Commun. 76, 169–172 (1990).
    [Crossref]
  18. M. Carrascosa, F. Agulló-López, “Kinetics for optical erasure of sinusoidal holographic gratings in photorefractive materials,” IEEE J. Quantum Electron. QE-22, 1369–1375 (1986).
    [Crossref]
  19. D. D. Nolte, D. H. Olson, A. M. Glass, “Nonequilibrium screening of the photorefractive effect,” Phys. Rev. Lett. 68, 891–893 (1989).
    [Crossref]

1990 (5)

D. Mahgerefteh, J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195–2198 (1990).
[Crossref] [PubMed]

S. Zhivkova, M. Miteva, “Holographic recording in photorefractive crystals with simultaneous electron–hole transport and two active centers,” J. Appl. Phys. 68, 3099–3103 (1990).
[Crossref]

F. Jariego, F. Agulló-López, “Monotonic versus oscillatory behavior during holographic writing in photorefractive photovoltaic materials,” Opt. Commun. 76, 169–172 (1990).
[Crossref]

M. C. Bashaw, T. P. Ma, R. C. Barker, S. Mroczkowski, R. R. Dube, “Theory of complementary holograms arising from electron–hole transport in photorefractive media,” J. Opt. Soc. Am. B 7, 2329–2338 (1990).
[Crossref]

L. M. Bernardo, J. C. Lopes, O. D. Soares, “Hole–electron competition with fast and slow gratings in BSO crystals,” Appl. Opt. 29, 12–14 (1990).
[Crossref] [PubMed]

1989 (5)

D. D. Nolte, D. H. Olson, A. M. Glass, “Nonequilibrium screening of the photorefractive effect,” Phys. Rev. Lett. 68, 891–893 (1989).
[Crossref]

L. Arizmendi, “Thermal fixing of holographic gratings in BSO,” J. Appl. Phys. 65, 423–427 (1989).
[Crossref]

G. Montaemmezzani, M. Ingold, H. Looser, P. Günter, “Multiple photorefractive gratings in Ce-doped LiNbO3 and KNbO3 crystals,” Ferroelectrics 92, 281–287 (1989).
[Crossref]

F. P. Strohkendl, “Light-induced dark decays of photorefractive gratings and their observation in BSO,” J. Appl. Phys. 65, 3773–3780 (1989).
[Crossref]

P. Yeh, “Two-wave mixing in non-linear media,” IEEE J. Quantum Electron. 25, 484–512 (1989).
[Crossref]

1988 (1)

1986 (3)

F. P. Strohkendl, J. M. Jonathan, R. W. Hellwarth, “Hole–electron competition in photorefractive gratings,” Opt. Lett. 11, 312–314(1986).
[Crossref] [PubMed]

M. Carrascosa, F. Agulló-López, “Kinetics for optical erasure of sinusoidal holographic gratings in photorefractive materials,” IEEE J. Quantum Electron. QE-22, 1369–1375 (1986).
[Crossref]

G. C. Valley, “Simultaneous electron–hole transport in photorefractive materials,” J. Appl. Phys. 59, 3363–3366 (1986).
[Crossref]

1983 (1)

1982 (1)

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–298 (1982).
[Crossref]

1981 (1)

A. A. Kamshilin, M. G. Miteva, “Effect of infrared irradiation on holographic recording in BSO,” Opt. Commun. 36, 429–433 (1981).
[Crossref]

1979 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. steady state,” Ferroelectrics 22, 949–960 (1979).
[Crossref]

Agulló-López, F.

F. Jariego, F. Agulló-López, “Monotonic versus oscillatory behavior during holographic writing in photorefractive photovoltaic materials,” Opt. Commun. 76, 169–172 (1990).
[Crossref]

M. Carrascosa, F. Agulló-López, “Erasure of holographic gratings in photorefractive materials with two active species,” Appl. Opt. 27, 2851–2857 (1988).
[Crossref] [PubMed]

M. Carrascosa, F. Agulló-López, “Kinetics for optical erasure of sinusoidal holographic gratings in photorefractive materials,” IEEE J. Quantum Electron. QE-22, 1369–1375 (1986).
[Crossref]

Arizmendi, L.

L. Arizmendi, “Thermal fixing of holographic gratings in BSO,” J. Appl. Phys. 65, 423–427 (1989).
[Crossref]

L. Arizmendi, University Autonoma Madrid, Cantoblanco, Madrid, Spain (personal communication).

Barker, R. C.

Bashaw, M. C.

Bernardo, L. M.

Carrascosa, M.

M. Carrascosa, F. Agulló-López, “Erasure of holographic gratings in photorefractive materials with two active species,” Appl. Opt. 27, 2851–2857 (1988).
[Crossref] [PubMed]

M. Carrascosa, F. Agulló-López, “Kinetics for optical erasure of sinusoidal holographic gratings in photorefractive materials,” IEEE J. Quantum Electron. QE-22, 1369–1375 (1986).
[Crossref]

Dube, R. R.

Feinberg, J.

D. Mahgerefteh, J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195–2198 (1990).
[Crossref] [PubMed]

Glass, A. M.

D. D. Nolte, D. H. Olson, A. M. Glass, “Nonequilibrium screening of the photorefractive effect,” Phys. Rev. Lett. 68, 891–893 (1989).
[Crossref]

Günter, P.

G. Montaemmezzani, M. Ingold, H. Looser, P. Günter, “Multiple photorefractive gratings in Ce-doped LiNbO3 and KNbO3 crystals,” Ferroelectrics 92, 281–287 (1989).
[Crossref]

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–298 (1982).
[Crossref]

Hellwarth, R. W.

Ingold, M.

G. Montaemmezzani, M. Ingold, H. Looser, P. Günter, “Multiple photorefractive gratings in Ce-doped LiNbO3 and KNbO3 crystals,” Ferroelectrics 92, 281–287 (1989).
[Crossref]

Jariego, F.

F. Jariego, F. Agulló-López, “Monotonic versus oscillatory behavior during holographic writing in photorefractive photovoltaic materials,” Opt. Commun. 76, 169–172 (1990).
[Crossref]

Jonathan, J. M.

Kamshilin, A. A.

A. A. Kamshilin, M. G. Miteva, “Effect of infrared irradiation on holographic recording in BSO,” Opt. Commun. 36, 429–433 (1981).
[Crossref]

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. steady state,” Ferroelectrics 22, 949–960 (1979).
[Crossref]

Looser, H.

G. Montaemmezzani, M. Ingold, H. Looser, P. Günter, “Multiple photorefractive gratings in Ce-doped LiNbO3 and KNbO3 crystals,” Ferroelectrics 92, 281–287 (1989).
[Crossref]

Lopes, J. C.

Ma, T. P.

Mahgerefteh, D.

D. Mahgerefteh, J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195–2198 (1990).
[Crossref] [PubMed]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. steady state,” Ferroelectrics 22, 949–960 (1979).
[Crossref]

Miteva, M.

S. Zhivkova, M. Miteva, “Holographic recording in photorefractive crystals with simultaneous electron–hole transport and two active centers,” J. Appl. Phys. 68, 3099–3103 (1990).
[Crossref]

Miteva, M. G.

A. A. Kamshilin, M. G. Miteva, “Effect of infrared irradiation on holographic recording in BSO,” Opt. Commun. 36, 429–433 (1981).
[Crossref]

Montaemmezzani, G.

G. Montaemmezzani, M. Ingold, H. Looser, P. Günter, “Multiple photorefractive gratings in Ce-doped LiNbO3 and KNbO3 crystals,” Ferroelectrics 92, 281–287 (1989).
[Crossref]

Mroczkowski, S.

Nolte, D. D.

D. D. Nolte, D. H. Olson, A. M. Glass, “Nonequilibrium screening of the photorefractive effect,” Phys. Rev. Lett. 68, 891–893 (1989).
[Crossref]

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. steady state,” Ferroelectrics 22, 949–960 (1979).
[Crossref]

Olson, D. H.

D. D. Nolte, D. H. Olson, A. M. Glass, “Nonequilibrium screening of the photorefractive effect,” Phys. Rev. Lett. 68, 891–893 (1989).
[Crossref]

Soares, O. D.

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. steady state,” Ferroelectrics 22, 949–960 (1979).
[Crossref]

Strohkendl, F. P.

F. P. Strohkendl, “Light-induced dark decays of photorefractive gratings and their observation in BSO,” J. Appl. Phys. 65, 3773–3780 (1989).
[Crossref]

F. P. Strohkendl, J. M. Jonathan, R. W. Hellwarth, “Hole–electron competition in photorefractive gratings,” Opt. Lett. 11, 312–314(1986).
[Crossref] [PubMed]

Valley, G. C.

G. C. Valley, “Simultaneous electron–hole transport in photorefractive materials,” J. Appl. Phys. 59, 3363–3366 (1986).
[Crossref]

G. C. Valley, “Erase rates in photorefractive materials with two photorefractive species,” Appl. Opt. 22, 3160–3164 (1983).
[Crossref] [PubMed]

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. steady state,” Ferroelectrics 22, 949–960 (1979).
[Crossref]

Yeh, P.

P. Yeh, “Two-wave mixing in non-linear media,” IEEE J. Quantum Electron. 25, 484–512 (1989).
[Crossref]

Zhivkova, S.

S. Zhivkova, M. Miteva, “Holographic recording in photorefractive crystals with simultaneous electron–hole transport and two active centers,” J. Appl. Phys. 68, 3099–3103 (1990).
[Crossref]

Appl. Opt. (3)

Ferroelectrics (2)

G. Montaemmezzani, M. Ingold, H. Looser, P. Günter, “Multiple photorefractive gratings in Ce-doped LiNbO3 and KNbO3 crystals,” Ferroelectrics 92, 281–287 (1989).
[Crossref]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. steady state,” Ferroelectrics 22, 949–960 (1979).
[Crossref]

IEEE J. Quantum Electron. (2)

P. Yeh, “Two-wave mixing in non-linear media,” IEEE J. Quantum Electron. 25, 484–512 (1989).
[Crossref]

M. Carrascosa, F. Agulló-López, “Kinetics for optical erasure of sinusoidal holographic gratings in photorefractive materials,” IEEE J. Quantum Electron. QE-22, 1369–1375 (1986).
[Crossref]

J. Appl. Phys. (4)

G. C. Valley, “Simultaneous electron–hole transport in photorefractive materials,” J. Appl. Phys. 59, 3363–3366 (1986).
[Crossref]

F. P. Strohkendl, “Light-induced dark decays of photorefractive gratings and their observation in BSO,” J. Appl. Phys. 65, 3773–3780 (1989).
[Crossref]

L. Arizmendi, “Thermal fixing of holographic gratings in BSO,” J. Appl. Phys. 65, 423–427 (1989).
[Crossref]

S. Zhivkova, M. Miteva, “Holographic recording in photorefractive crystals with simultaneous electron–hole transport and two active centers,” J. Appl. Phys. 68, 3099–3103 (1990).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Commun. (2)

F. Jariego, F. Agulló-López, “Monotonic versus oscillatory behavior during holographic writing in photorefractive photovoltaic materials,” Opt. Commun. 76, 169–172 (1990).
[Crossref]

A. A. Kamshilin, M. G. Miteva, “Effect of infrared irradiation on holographic recording in BSO,” Opt. Commun. 36, 429–433 (1981).
[Crossref]

Opt. Lett. (1)

Phys. Rep. (1)

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–298 (1982).
[Crossref]

Phys. Rev. Lett. (2)

D. Mahgerefteh, J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195–2198 (1990).
[Crossref] [PubMed]

D. D. Nolte, D. H. Olson, A. M. Glass, “Nonequilibrium screening of the photorefractive effect,” Phys. Rev. Lett. 68, 891–893 (1989).
[Crossref]

Other (1)

L. Arizmendi, University Autonoma Madrid, Cantoblanco, Madrid, Spain (personal communication).

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Figures (3)

Fig. 1
Fig. 1

Effect of trap depth, measured by the thermal ionization rate βT on (a) recording and (b) dark erasure. The trap concentration is NT = 1018 cm−3 (initially empty). Photoactive donor and acceptor concentrations are N 1 0 = 10 17 cm 3 and N 1 + 0 = 10 18 cm 3. The thermal ionization rate for the donors is βT = 10−4 s−1, the photoionization cross sections σ1 = 10−19 cm2, the trapping coefficients γ1 = γ2 = 10−9 cm−3, the mobility μ = 10−1 cm2 V−1 s−1 and χ1 = 8 × 10−46 C cm3.

Fig. 2
Fig. 2

Effect of trap concentration NT on (a) recording and (b) dark erasure. The trap depth corresponds to βT = 10−5 s−1. Photoactive donor and acceptor concentrations are N T 0 = 10 17 cm 3 and N T + 0 = 10 18 cm 3. The thermal ionization rate for the donors is β1 = 10−4 s−1, the photoionization cross sections are σ1 = 10−19 cm2, the trapping coefficients γ1 = γ2 = 10−9 cm−3, the mobility μ = 10−1 cm2 V−1 s−1, and χ1 = 8 × 10−46 C cm3.

Fig. 3
Fig. 3

Effect of average light intensity I0 on (a) recording and (b) dark erasure. For recording the product, It is used in the abscissa axis to scale the data. Photoactive donor and acceptor concentrations are N 1 0 = 10 17 cm 3 and N 1 + 0 = 10 18 cm 3. The thermal ionization rate for the donors is βT = 10−4 s−1, the photoionization cross section is σ1 = 10−19 cm2, the trapping coefficient is γ1 = γ2 = 10−9 cm−3, the mobility μ = 10−1 cm2 V−1 s−1, and χ1 = 8 × 10−46 C cm3.

Equations (49)

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E 1 = C + exp [ i ( ω t + K x x k z z ) ] e 1 , E 2 = C exp [ i ( ω t K x x k z z ) ] e 2 ,
I = I 0 { 1 + [ M + exp ( iqx ) + c . c . ] }
I 0 = | C + | 2 + | C | 2 , q = 2 k x = 2 π Λ , M + = C + C × I 0 e 1 e 2 .
ρ = e [ n + i ( N i N i 0 ) ] ,
E x = ρ s ,
ρ t + t x = 0 ,
N i t = ( σ i I + β i ) N i γ i n N i + ,
E x = e s k ( N k N k 0 ) ,
k N k t = 1 e j x ,
N k t = ( σ k I + β k ) N k γ k n N k + ,
j = | e | μ n E e D n x + j ph ,
N k = I d k ( I ) exp ( iqIx ) ,
N k + = I a k ( I ) exp ( iqIx ) ,
E = I E ( I ) exp ( iqIx ) ,
n = I n ( I ) exp ( iqIx ) .
d k ( 0 ) t = ξ k d k ( 0 ) γ k n ( 0 ) [ N k d k ( 0 ) ] ,
t k d k ( 0 ) = 0 .
d k ( 0 ) t = ξ k d k ( 0 ) + γ k [ N k d k ( 0 ) ] p ξ p d p ( 0 ) γ N p γ p d p ( 0 ) ,
γ N = k γ k N k , N = k N k .
s E ( 0 ) t + | e | μ n ( 0 ) E ( 0 ) = J I 0 k χ k d k ( 0 ) ,
i q E ( 1 ) = e s k d k ( 1 ) .
d k ( 1 ) t = ξ k η k M + d k ( 0 ) γ k n ( 1 ) a k ( 0 ) + ξ k d k ( 1 ) γ k n ( 0 ) a k ( 1 ) ,
η k = ( 1 + β k σ k I 0 ) 1 .
d k ( 1 ) t = [ ξ k η k d k ( 0 ) γ k a k ( 0 ) A ( t ) ] M + + [ ξ k + γ k n ( 0 ) ] d k ( 1 ) γ k a k ( 0 ) p b p ( t ) d p ( 1 ) ,
A ( t ) = 1 G p ( ξ p η p i q I 0 χ k e ) d k ( 0 ) ,
b k ( t ) = [ ξ k + γ k n ( 0 ) | e | μ s n ( 0 ) i q I 0 χ k e ] ,
G = D q 2 + p γ p a p ( 0 ) + i q μ E ( 0 ) .
N D = d 1 ( 0 ) + d 2 ( 0 ) = N 1 0 + N 2 0 ,
[ α 1 + α 2 d 1 ( 0 ) ] d 1 ( 0 ) t = α 3 + α 4 d 1 ( 0 ) + α 5 [ d 1 ( 0 ) ] 2 ,
α 1 = γ N γ 2 N D γ 1 ,
α 2 = γ 2 γ 1 γ 1 ,
α 3 = ξ 2 N 1 N D ,
α 4 = ξ 2 N D + ( ξ 1 ξ 2 ) N 1 ξ 1 ( γ N γ 2 N D γ 1 ) ,
α 5 = ( ξ 2 ξ 1 ) ξ 1 ( γ 2 γ 1 γ 1 ) .
α 2 = 0 ,
α 4 2 4 α 3 α 5 0 ,
Δ = ( α 4 2 4 α 3 α 5 ) 1 / 2 ,
d 1 ( 0 ) ( t ) = α 4 2 α 5 + d 1 ( 0 ) ( 0 ) + α 4 2 | α 5 | Δ 2 | α 5 | tanh ( Δ α 5 2 α 1 | α 5 | t ) 1 2 | α 5 | Δ [ d 1 ( 0 ) ( 0 ) + α 4 2 α 5 ] tanh ( Δ α 5 2 α 1 | α 5 | t ) .
τ | 2 a 1 Δ | .
d k ( 1 ) t = δ k ( t ) + q α k q ( t ) d q ( 1 ) ,
δ k ( t ) = [ ξ k η k d k ( 0 ) ( t ) γ k a k ( 0 ) ( t ) A ( t ) ] M + ,
α k k ( t ) = ξ k + γ k n ( 0 ) ( t ) γ k a k ( 0 ) ( t ) b k ( t ) ,
α k q ( t ) = γ k a k ( 0 ) ( t ) b q ( t ) , q k .
d k ( 1 ) t = 0 ,
δ k ( ) = q α k q ( ) d q ( 1 ) ( ) ,
d k ( 1 ) t = q α k q ( ) d q ( 1 ) .
d k ( 1 ) ( t ) = ρ V ( λ ρ ) k exp ( λ ρ t ) ,
q [ α k q ( ) λ δ k q ] V ( λ ) q = 0 .
E ( 1 ) ( t ) = i e q s ρ exp ( λ ρ t ) [ k V ( λ ρ ) k ] .

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