Abstract

We present experimental data for BaTiO3 that exhibit an intensity dependence in the absorption coefficient and the two-beam coupling coefficient at intensities between 0.002 and 40 W/cm2. The effective empty-trap concentration was found to increase with intensity. We present a model, in the spirit of commonly used (photorefractive) theories, for photorefraction and optical absorption that explains these effects. The intensity dependence was attributed to the presence of secondary photorefractive centers.

© 1988 Optical Society of America

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References

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  1. J. Feinberg in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983).
  2. P. Yeh, J. Opt. Soc. Am. B 2, 1924 (1985).
    [Crossref]
  3. J. O. White, M. Cronin-Golomb, B. Fischer, and A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
    [Crossref]
  4. S. Ducharme and J. Feinberg, J. Opt. Soc. Am. B 3, 283 (1986).
    [Crossref]
  5. M. B. Klein and R. N. Schwartz, J. Opt. Soc. Am. B 3, 293 (1986).
    [Crossref]
  6. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
    [Crossref]
  7. J. Feinberg, D. Heiman, A. R. Tanguay, and R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
    [Crossref]
  8. G. Valley and M. Klein, Opt. Eng. 22, 704 (1983).
    [Crossref]
  9. M. B. Klein and G. Valley, J. Appl. Phys. 57, 4901 (1985).
    [Crossref]
  10. A. Motes and J. J. Kim, Opt. Lett. 12, 199 (1987).
    [Crossref] [PubMed]
  11. A. Motes and J. J. Kim, J. Opt. Soc. Am. B 4, 1379 (1987).
    [Crossref]
  12. P. Gunter, Phys. Rep. 93, 199 (1982).
    [Crossref]
  13. D. Staebler and J. Amodei, J. Appl. Phys. 43, 1042 (1972).
    [Crossref]
  14. A. Marrakchi and J. P. Huignard, Appl. Phys. 24, 131 (1981).
    [Crossref]
  15. J. P. Huignard and G. Rosen, in Nonlinear Optics: Materials and Devices, C. Flytzanis and J. L. Oudar, eds. (Springer-Verlag, Berlin, 1986).
  16. R. L. Townsend and J. T. LaMacchia, J. Appl. Phys. 41, 5188 (1970).
    [Crossref]
  17. D. Rak, I. Ledoux, and J. P. Huignard, Opt. Commun. 49, 302 (1984).
    [Crossref]
  18. C. Chen, D. M. Kim, and D. Von der Linde, IEEE J. Quantum Electron. QE-16, 126 (1980).The term secondary photorefractive center was used here to describe enhanced effects in LiNbO3 under pulsed illumination.
    [Crossref]
  19. A. Motes, G. Brost, J. Rotgé, and J. Kim, Opt. Lett. 13, 509 (1988).
    [Crossref] [PubMed]
  20. A. M. J. H. Seuter, Philips Res. Rep. Suppl.3, 1 (1974).
  21. S. Ducharme and J. Feinberg, J. Appl. Phys. 56, 839 (1984).
    [Crossref]
  22. E. Kratzig, F. Welz, R. Orlowski, V. Doorman, and M. Rosen-kranz, Solid State Commun. 34, 817 (1980).
    [Crossref]
  23. G. Valley, J. Appl. Phys. 59, 3363 (1986).
    [Crossref]
  24. F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, Opt. Lett. 11, 312 (1986).
    [Crossref]

1988 (1)

1987 (2)

1986 (4)

1985 (2)

P. Yeh, J. Opt. Soc. Am. B 2, 1924 (1985).
[Crossref]

M. B. Klein and G. Valley, J. Appl. Phys. 57, 4901 (1985).
[Crossref]

1984 (2)

D. Rak, I. Ledoux, and J. P. Huignard, Opt. Commun. 49, 302 (1984).
[Crossref]

S. Ducharme and J. Feinberg, J. Appl. Phys. 56, 839 (1984).
[Crossref]

1983 (1)

G. Valley and M. Klein, Opt. Eng. 22, 704 (1983).
[Crossref]

1982 (2)

J. O. White, M. Cronin-Golomb, B. Fischer, and A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[Crossref]

P. Gunter, Phys. Rep. 93, 199 (1982).
[Crossref]

1981 (1)

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

1980 (3)

J. Feinberg, D. Heiman, A. R. Tanguay, and R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[Crossref]

E. Kratzig, F. Welz, R. Orlowski, V. Doorman, and M. Rosen-kranz, Solid State Commun. 34, 817 (1980).
[Crossref]

C. Chen, D. M. Kim, and D. Von der Linde, IEEE J. Quantum Electron. QE-16, 126 (1980).The term secondary photorefractive center was used here to describe enhanced effects in LiNbO3 under pulsed illumination.
[Crossref]

1979 (1)

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

1972 (1)

D. Staebler and J. Amodei, J. Appl. Phys. 43, 1042 (1972).
[Crossref]

1970 (1)

R. L. Townsend and J. T. LaMacchia, J. Appl. Phys. 41, 5188 (1970).
[Crossref]

Amodei, J.

D. Staebler and J. Amodei, J. Appl. Phys. 43, 1042 (1972).
[Crossref]

Brost, G.

Chen, C.

C. Chen, D. M. Kim, and D. Von der Linde, IEEE J. Quantum Electron. QE-16, 126 (1980).The term secondary photorefractive center was used here to describe enhanced effects in LiNbO3 under pulsed illumination.
[Crossref]

Cronin-Golomb, M.

J. O. White, M. Cronin-Golomb, B. Fischer, and A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[Crossref]

Doorman, V.

E. Kratzig, F. Welz, R. Orlowski, V. Doorman, and M. Rosen-kranz, Solid State Commun. 34, 817 (1980).
[Crossref]

Ducharme, S.

S. Ducharme and J. Feinberg, J. Opt. Soc. Am. B 3, 283 (1986).
[Crossref]

S. Ducharme and J. Feinberg, J. Appl. Phys. 56, 839 (1984).
[Crossref]

Feinberg, J.

S. Ducharme and J. Feinberg, J. Opt. Soc. Am. B 3, 283 (1986).
[Crossref]

S. Ducharme and J. Feinberg, J. Appl. Phys. 56, 839 (1984).
[Crossref]

J. Feinberg, D. Heiman, A. R. Tanguay, and R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[Crossref]

J. Feinberg in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983).

Fischer, B.

J. O. White, M. Cronin-Golomb, B. Fischer, and A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[Crossref]

Gunter, P.

P. Gunter, Phys. Rep. 93, 199 (1982).
[Crossref]

Heiman, D.

J. Feinberg, D. Heiman, A. R. Tanguay, and R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[Crossref]

Hellwarth, R. W.

F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, Opt. Lett. 11, 312 (1986).
[Crossref]

J. Feinberg, D. Heiman, A. R. Tanguay, and R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[Crossref]

Huignard, J. P.

D. Rak, I. Ledoux, and J. P. Huignard, Opt. Commun. 49, 302 (1984).
[Crossref]

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

J. P. Huignard and G. Rosen, in Nonlinear Optics: Materials and Devices, C. Flytzanis and J. L. Oudar, eds. (Springer-Verlag, Berlin, 1986).

Jonathan, J. M. C.

Kim, D. M.

C. Chen, D. M. Kim, and D. Von der Linde, IEEE J. Quantum Electron. QE-16, 126 (1980).The term secondary photorefractive center was used here to describe enhanced effects in LiNbO3 under pulsed illumination.
[Crossref]

Kim, J.

Kim, J. J.

Klein, M.

G. Valley and M. Klein, Opt. Eng. 22, 704 (1983).
[Crossref]

Klein, M. B.

M. B. Klein and R. N. Schwartz, J. Opt. Soc. Am. B 3, 293 (1986).
[Crossref]

M. B. Klein and G. Valley, J. Appl. Phys. 57, 4901 (1985).
[Crossref]

Kratzig, E.

E. Kratzig, F. Welz, R. Orlowski, V. Doorman, and M. Rosen-kranz, Solid State Commun. 34, 817 (1980).
[Crossref]

Kukhtarev, N. V.

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

LaMacchia, J. T.

R. L. Townsend and J. T. LaMacchia, J. Appl. Phys. 41, 5188 (1970).
[Crossref]

Ledoux, I.

D. Rak, I. Ledoux, and J. P. Huignard, Opt. Commun. 49, 302 (1984).
[Crossref]

Markov, V. B.

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

Marrakchi, A.

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

Motes, A.

Odulov, S. G.

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

Orlowski, R.

E. Kratzig, F. Welz, R. Orlowski, V. Doorman, and M. Rosen-kranz, Solid State Commun. 34, 817 (1980).
[Crossref]

Rak, D.

D. Rak, I. Ledoux, and J. P. Huignard, Opt. Commun. 49, 302 (1984).
[Crossref]

Rosen, G.

J. P. Huignard and G. Rosen, in Nonlinear Optics: Materials and Devices, C. Flytzanis and J. L. Oudar, eds. (Springer-Verlag, Berlin, 1986).

Rosen-kranz, M.

E. Kratzig, F. Welz, R. Orlowski, V. Doorman, and M. Rosen-kranz, Solid State Commun. 34, 817 (1980).
[Crossref]

Rotgé, J.

Schwartz, R. N.

Seuter, A. M. J. H.

A. M. J. H. Seuter, Philips Res. Rep. Suppl.3, 1 (1974).

Soskin, M. S.

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

Staebler, D.

D. Staebler and J. Amodei, J. Appl. Phys. 43, 1042 (1972).
[Crossref]

Strohkendl, F. P.

Tanguay, A. R.

J. Feinberg, D. Heiman, A. R. Tanguay, and R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[Crossref]

Townsend, R. L.

R. L. Townsend and J. T. LaMacchia, J. Appl. Phys. 41, 5188 (1970).
[Crossref]

Valley, G.

G. Valley, J. Appl. Phys. 59, 3363 (1986).
[Crossref]

M. B. Klein and G. Valley, J. Appl. Phys. 57, 4901 (1985).
[Crossref]

G. Valley and M. Klein, Opt. Eng. 22, 704 (1983).
[Crossref]

Vinetskii, V. L.

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

Von der Linde, D.

C. Chen, D. M. Kim, and D. Von der Linde, IEEE J. Quantum Electron. QE-16, 126 (1980).The term secondary photorefractive center was used here to describe enhanced effects in LiNbO3 under pulsed illumination.
[Crossref]

Welz, F.

E. Kratzig, F. Welz, R. Orlowski, V. Doorman, and M. Rosen-kranz, Solid State Commun. 34, 817 (1980).
[Crossref]

White, J. O.

J. O. White, M. Cronin-Golomb, B. Fischer, and A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[Crossref]

Yariv, A.

J. O. White, M. Cronin-Golomb, B. Fischer, and A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[Crossref]

Yeh, P.

Appl. Phys. (1)

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

Appl. Phys. Lett. (1)

J. O. White, M. Cronin-Golomb, B. Fischer, and A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[Crossref]

Ferroelectrics (1)

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

IEEE J. Quantum Electron. (1)

C. Chen, D. M. Kim, and D. Von der Linde, IEEE J. Quantum Electron. QE-16, 126 (1980).The term secondary photorefractive center was used here to describe enhanced effects in LiNbO3 under pulsed illumination.
[Crossref]

J. Appl. Phys. (6)

S. Ducharme and J. Feinberg, J. Appl. Phys. 56, 839 (1984).
[Crossref]

R. L. Townsend and J. T. LaMacchia, J. Appl. Phys. 41, 5188 (1970).
[Crossref]

J. Feinberg, D. Heiman, A. R. Tanguay, and R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[Crossref]

M. B. Klein and G. Valley, J. Appl. Phys. 57, 4901 (1985).
[Crossref]

D. Staebler and J. Amodei, J. Appl. Phys. 43, 1042 (1972).
[Crossref]

G. Valley, J. Appl. Phys. 59, 3363 (1986).
[Crossref]

J. Opt. Soc. Am. B (4)

Opt. Commun. (1)

D. Rak, I. Ledoux, and J. P. Huignard, Opt. Commun. 49, 302 (1984).
[Crossref]

Opt. Eng. (1)

G. Valley and M. Klein, Opt. Eng. 22, 704 (1983).
[Crossref]

Opt. Lett. (3)

Phys. Rep. (1)

P. Gunter, Phys. Rep. 93, 199 (1982).
[Crossref]

Solid State Commun. (1)

E. Kratzig, F. Welz, R. Orlowski, V. Doorman, and M. Rosen-kranz, Solid State Commun. 34, 817 (1980).
[Crossref]

Other (3)

A. M. J. H. Seuter, Philips Res. Rep. Suppl.3, 1 (1974).

J. P. Huignard and G. Rosen, in Nonlinear Optics: Materials and Devices, C. Flytzanis and J. L. Oudar, eds. (Springer-Verlag, Berlin, 1986).

J. Feinberg in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983).

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Figures (8)

Fig. 1
Fig. 1

Energy-level diagram of band model for photorefraction in BaTiO3. Holes are photoionized from level X and recombine at X′.

Fig. 2
Fig. 2

Crystal orientation and beam notation for two-beam coupling in BaTiO3.

Fig. 3
Fig. 3

Experimental arrangement for intensity-dependent measurements in BaTiO3: BE, beam expander; BS, beam splitter; DET, detector; M’s, mirrors. For absorption measurements, the path difference between IP and IS was made much greater than the coherence length.

Fig. 4
Fig. 4

Experimental values of intensity-dependent absorption coefficienta α1 versus laser intensity in BaTiO3.

Fig. 5
Fig. 5

Measured two-beam coupling coefficient (Γ) corrected for absorption versus grating period for different laser intensities.

Fig. 6
Fig. 6

Schematic diagram of the secondary-center model for BaTiO3. N1 and N1′ are primary photorefractive centers, and N2 is the secondary photorefractive center. CB, conduction band; VB, valence band.

Fig. 7
Fig. 7

Calculated intensity-dependent absorption coefficient versus laser intensity.

Fig. 8
Fig. 8

Calculated space-charge field (ESC) versus grating period for different intensities.

Tables (1)

Tables Icon

Table 1 Parameter Values Used in the Calculationsa

Equations (21)

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I ( z ) = I 0 [ 1 + m exp ( iKz ) ] ,
E SC = R [ ( m k B T / q ) { K / [ 1 + ( K / K 0 ) 2 ] } ,
K 0 2 = q 2 N E / ( 0 k B T ) ,
N E = N X ( 1 N X / N X ) ,
R = σ p / ( σ p + σ d ) .
n 1 = ( 1 / 2 ) n 3 r eff E SC ,
γ 0 = I S ( with I P on ) I S ( with I P off ) .
γ 0 = ( 1 + β 0 ) exp ( Γ d ) 1 + β 0 exp ( Γ d ) ,
Γ = k n 3 r eff E SC / m ,
I S ( with I P on ) I S ( with I P off ) = exp ( α 1 d ) ,
d N 1 / d t = ( S 1 I + β 1 ) N 1 + γ 1 ( N 1 T N 1 ) N h ,
d N 2 / d t = ( S 2 I + β 2 ) N 2 + γ 2 ( N 2 T N 2 ) N h ,
N h / t = d N 1 / d t d N 2 / d t j ,
j = N h μ E μ k B T q N h ,
E = ( N h + N 1 + N 2 N A ) q / 0 ,
α I = S 1 [ N 1 N 1 ( 0 ) ] + S 2 [ N 2 N 2 ( 0 ) ] .
N 1 = N 10 + N 11 exp ( i K z ) ,
N 2 = N 20 + N 21 exp ( i K z ) ,
N h = N h 0 + N h 1 exp ( i K z ) ,
E = E 0 + E SC exp ( i K z ) ,
j = j 0 + j 1 exp ( i K z ) .

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