Abstract

We have performed a detailed investigation of the readout decay of optically encoded second-harmonic generation in bulk lead-silicate glasses. The data show that over several decades of readout pulses, the relaxation is a stretched exponential in the pulse number. A new photoimpulsive dispersive transport model, in which the experimental data on the order of the optical process and the depth of the trap distribution below the mobility edge have been included, is used to explain the results.

© 1996 Optical Society of America

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Corrections

Jae H. Kyung and N. M. Lawandy, "Photoimpulsive dispersive relaxation of the effective χ(2) in binary lead-silicate glasses: errata," Opt. Lett. 21, 1795-1795 (1996)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-21-21-1795

References

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  1. M. E. Scharfe, Phys. Rev. B 2, 5025 (1970).
    [CrossRef]
  2. H. Scher, E. W. Montroll, Phys. Rev. B 12, 2455 (1975).
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    [CrossRef]
  6. W. H. Hamill, K. Funabashi, Phys. Rev. B 16, 5523 (1977).
    [CrossRef]
  7. M. F. Shlesinger, E. W. Montroll, Proc. Natl. Acad. Sci. USA 81, 1280 (1984).
    [CrossRef] [PubMed]
  8. Y. Nageno, J. H. Kyung, N. M. Lawandy, Opt. Lett. 20, 2180 (1995).
    [CrossRef] [PubMed]
  9. F. Ouellette, K. O. Hill, D. C. Johnson, Opt. Lett. 13, 515 (1988).
    [CrossRef] [PubMed]
  10. Y. Hibino, V. Mizrahi, G. I. Stegeman, S. Sudo, Appl. Phys. Lett. 57, 656 (1990).
    [CrossRef]
  11. T. Tiedje, A. Rose, Solid State Commun. 37, 49 (1980).
    [CrossRef]
  12. F. W. Schmidlin, Phys. Rev. B. 16, 2362 (1977).
    [CrossRef]
  13. M. Silver, L. Cohen, Phys. Rev. B 15, 3276 (1977).
    [CrossRef]
  14. M. Tachiya, Radiat. Phys. Chem. 17, 447 (1981).
  15. E. M. Rabinovich, J. Mater. Sci. 11, 925 (1976).
    [CrossRef]

1995 (1)

1994 (1)

J. C. Phillips, J. Non-Cryst. Solids 98, 172 (1994).

1990 (1)

Y. Hibino, V. Mizrahi, G. I. Stegeman, S. Sudo, Appl. Phys. Lett. 57, 656 (1990).
[CrossRef]

1988 (1)

1984 (1)

M. F. Shlesinger, E. W. Montroll, Proc. Natl. Acad. Sci. USA 81, 1280 (1984).
[CrossRef] [PubMed]

1981 (2)

M. Tachiya, Radiat. Phys. Chem. 17, 447 (1981).

M. H. Cohen, G. S. Grest, Phys. Rev. B 24, 4091 (1981).
[CrossRef]

1980 (1)

T. Tiedje, A. Rose, Solid State Commun. 37, 49 (1980).
[CrossRef]

1977 (3)

F. W. Schmidlin, Phys. Rev. B. 16, 2362 (1977).
[CrossRef]

M. Silver, L. Cohen, Phys. Rev. B 15, 3276 (1977).
[CrossRef]

W. H. Hamill, K. Funabashi, Phys. Rev. B 16, 5523 (1977).
[CrossRef]

1976 (1)

E. M. Rabinovich, J. Mater. Sci. 11, 925 (1976).
[CrossRef]

1975 (1)

H. Scher, E. W. Montroll, Phys. Rev. B 12, 2455 (1975).
[CrossRef]

1970 (1)

M. E. Scharfe, Phys. Rev. B 2, 5025 (1970).
[CrossRef]

1863 (1)

F. Kohlrausch, Pogg. Ann. Phys. 19, 352 (1863).

Cohen, L.

M. Silver, L. Cohen, Phys. Rev. B 15, 3276 (1977).
[CrossRef]

Cohen, M. H.

M. H. Cohen, G. S. Grest, Phys. Rev. B 24, 4091 (1981).
[CrossRef]

Funabashi, K.

W. H. Hamill, K. Funabashi, Phys. Rev. B 16, 5523 (1977).
[CrossRef]

Grest, G. S.

M. H. Cohen, G. S. Grest, Phys. Rev. B 24, 4091 (1981).
[CrossRef]

Hamill, W. H.

W. H. Hamill, K. Funabashi, Phys. Rev. B 16, 5523 (1977).
[CrossRef]

Hibino, Y.

Y. Hibino, V. Mizrahi, G. I. Stegeman, S. Sudo, Appl. Phys. Lett. 57, 656 (1990).
[CrossRef]

Hill, K. O.

Johnson, D. C.

Kohlrausch, F.

F. Kohlrausch, Pogg. Ann. Phys. 19, 352 (1863).

Kyung, J. H.

Lawandy, N. M.

Mizrahi, V.

Y. Hibino, V. Mizrahi, G. I. Stegeman, S. Sudo, Appl. Phys. Lett. 57, 656 (1990).
[CrossRef]

Montroll, E. W.

M. F. Shlesinger, E. W. Montroll, Proc. Natl. Acad. Sci. USA 81, 1280 (1984).
[CrossRef] [PubMed]

H. Scher, E. W. Montroll, Phys. Rev. B 12, 2455 (1975).
[CrossRef]

Nageno, Y.

Ouellette, F.

Phillips, J. C.

J. C. Phillips, J. Non-Cryst. Solids 98, 172 (1994).

Rabinovich, E. M.

E. M. Rabinovich, J. Mater. Sci. 11, 925 (1976).
[CrossRef]

Rose, A.

T. Tiedje, A. Rose, Solid State Commun. 37, 49 (1980).
[CrossRef]

Scharfe, M. E.

M. E. Scharfe, Phys. Rev. B 2, 5025 (1970).
[CrossRef]

Scher, H.

H. Scher, E. W. Montroll, Phys. Rev. B 12, 2455 (1975).
[CrossRef]

Schmidlin, F. W.

F. W. Schmidlin, Phys. Rev. B. 16, 2362 (1977).
[CrossRef]

Shlesinger, M. F.

M. F. Shlesinger, E. W. Montroll, Proc. Natl. Acad. Sci. USA 81, 1280 (1984).
[CrossRef] [PubMed]

Silver, M.

M. Silver, L. Cohen, Phys. Rev. B 15, 3276 (1977).
[CrossRef]

Stegeman, G. I.

Y. Hibino, V. Mizrahi, G. I. Stegeman, S. Sudo, Appl. Phys. Lett. 57, 656 (1990).
[CrossRef]

Sudo, S.

Y. Hibino, V. Mizrahi, G. I. Stegeman, S. Sudo, Appl. Phys. Lett. 57, 656 (1990).
[CrossRef]

Tachiya, M.

M. Tachiya, Radiat. Phys. Chem. 17, 447 (1981).

Tiedje, T.

T. Tiedje, A. Rose, Solid State Commun. 37, 49 (1980).
[CrossRef]

Appl. Phys. Lett. (1)

Y. Hibino, V. Mizrahi, G. I. Stegeman, S. Sudo, Appl. Phys. Lett. 57, 656 (1990).
[CrossRef]

J. Mater. Sci. (1)

E. M. Rabinovich, J. Mater. Sci. 11, 925 (1976).
[CrossRef]

J. Non-Cryst. Solids (1)

J. C. Phillips, J. Non-Cryst. Solids 98, 172 (1994).

Opt. Lett. (2)

Phys. Rev. B (5)

M. Silver, L. Cohen, Phys. Rev. B 15, 3276 (1977).
[CrossRef]

M. H. Cohen, G. S. Grest, Phys. Rev. B 24, 4091 (1981).
[CrossRef]

W. H. Hamill, K. Funabashi, Phys. Rev. B 16, 5523 (1977).
[CrossRef]

M. E. Scharfe, Phys. Rev. B 2, 5025 (1970).
[CrossRef]

H. Scher, E. W. Montroll, Phys. Rev. B 12, 2455 (1975).
[CrossRef]

Phys. Rev. B. (1)

F. W. Schmidlin, Phys. Rev. B. 16, 2362 (1977).
[CrossRef]

Pogg. Ann. Phys. (1)

F. Kohlrausch, Pogg. Ann. Phys. 19, 352 (1863).

Proc. Natl. Acad. Sci. USA (1)

M. F. Shlesinger, E. W. Montroll, Proc. Natl. Acad. Sci. USA 81, 1280 (1984).
[CrossRef] [PubMed]

Radiat. Phys. Chem. (1)

M. Tachiya, Radiat. Phys. Chem. 17, 447 (1981).

Solid State Commun. (1)

T. Tiedje, A. Rose, Solid State Commun. 37, 49 (1980).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Relaxation curve of the second-harmonic light after subsequent laser pulse excitation of encoded 40- mol. % PbO–60-mol. % SiO2 glass at an average readout IR (1.064 μm) power of 300 mW (3 GW/cm2 peak intensity) fit to Eq. (2) with the following fit parameters: Φ0 = 18.81 ± 0.22 (arbitrary units), t0 = 5.32 ± 0.01 × 105 IR pulses, and α = 0.301 ± 0.01.

Fig. 2
Fig. 2

Pictorial representation of the photoimpulsive dispersive relaxation process in binary lead-silicate glass systems.

Fig. 3
Fig. 3

Relaxation constant (ξl −1) versus peak readout IR (1.064-μm) intensity curve for the 30-mol. % PbO–70- mol. % SiO2 glass sample prepared for SHG.

Equations (13)

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ψ ( t ) t - ( 1 + α )
Φ α ( t ) = Φ 0 exp [ - ( t / t 0 ) α ] .
ρ t ( ) = ρ 0 exp ( / k T c ) ,
ν e = P tailstate ν 0 exp ( - / k T ) ,
d N / d t = β N 0 I 2 ( t ) ,
I 2 ( t ) = i n j = 1 10 I 0 2 exp { - [ ( t - τ Q / 2 ) - i T 0 τ Q ] 2 } × ( Θ [ t - ( i - 1 ) ( T 0 + τ Q ) ] - Θ { t - [ ( i - 1 ) T 0 + i τ Q ] } ) × ( Θ [ t - ( j - 1 ) ( τ 0 + τ p ) ] - Θ { t - [ ( j - 1 ) τ 0 + j τ p ] } ) ,
P tailstate ( n l ) = N T / N 0 10 - 2 β I 0 2 τ Q n l ,
t = t 0 β 0 I 0 2 τ Q n l exp ( k T ) ,
N l = ν 0 - 1 β 0 I 0 2 τ Q T 0 exp ( k T ) = η 0 exp ( k T ) ,
ψ ( N l ) = ρ t ( ) k T c ρ 0 d d N l = α η 0 ( N l η 0 ) - ( 1 + α )
φ ( N l ) = s 1 = 1 ν s n = 1 ν i = 1 n [ 1 - 0 N l F ( s , N l ) d N l ] × u ( s 1 , s 2 , s n ) ,
χ eff ( 2 ) ( N l ) = χ 0 ( 2 ) exp [ - ( N l / ξ l ) α ] ,
ξ l = [ Γ ( 1 - α ) Γ ( α ) α n / ν ( 0.659 ) ] - 1 ( ν 0 - 1 τ Q ) 1 β 0 T 0 I 2 .

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