Abstract

A numerical model of photorefraction in barium titanate with simultaneous hole and electron photoconductivity and combined deep and secondary photorefractive centers is compared with experimental observations of both continuous-wave (10 mW/cm2–20 W/cm2) and pulsed high-peak-intensity (1–40 MW/cm2) laser illumination. Between 10 mW/cm2 and 20 W/cm2 (continuous wave) and below ~10 MW/cm2 (pulsed) the sample is hole dominated and has a sublinear intensity-dependent response time, whereas above ~12 MW/cm2 (pulsed) the crystal displays dominant electron conductivity and has a superlinear intensity-dependent response time.

© 1994 Optical Society of America

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  1. F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole–electron competition in photorefractive gratings,” Opt. Lett. 11, 312 (1986).
    [Crossref]
  2. G. C. Valley, “Simultaneous electron/hole transport in photorefractive materials,” J. Appl. Phys. 59, 3363 (1986).
    [Crossref]
  3. M. B. Klein and R. N. Schwartz, “Photorefractive effect in BaTiO3: microscopic origins,” J. Opt. Soc. Am. B 3, 293 (1986).
    [Crossref]
  4. G. A. Brost, R. A. Motes, and J. R. Rotge, “Intensity-dependent absorption and photorefractive effects in barium titanate,” J. Opt. Soc. Am. B 5, 1879 (1988).
    [Crossref]
  5. D. Mahgerefteh and J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195 (1990).
    [Crossref] [PubMed]
  6. P. Tayebati and D. Mahgerefteh, “Theory of the photorefractive effect for Bi12SiO20and BaTiO3with shallow traps,” J. Opt. Soc. Am. B 8, 1053 (1991).
    [Crossref]
  7. P. Tayebati, “Effect of shallow traps on electron–hole competition in semi-insulating photorefractive materials,” J. Opt. Soc. Am. B 9, 415 (1992).
    [Crossref]
  8. L. K. Lam, T. Y. Chang, J. Feinberg, and R. W. Hellwarth, “Photorefractive-index gratings formed by nanosecond optical pulses in BaTiO3,” Opt. Lett. 6, 475 (1981).
    [Crossref] [PubMed]
  9. C. P. Tzou, T. Y. Chang, and R. W. Hellwarth, “Photorefractive measurement of anisotropy of the mobility of photoexcited holes in BaTiO3,” in Nonlinear Optics and Applications, P. Yeh, ed., Proc. Soc. Photo-Opt. Instrum. Eng.613, 58 (1986).
    [Crossref]
  10. N. Barry and M. J. Damzen, “Two-beam coupling and response-time measurements in barium titanate using high-intensity laser pulses,” J. Opt. Soc. Am. B 9, 1488 (1992).
    [Crossref]
  11. A. L. Smirl, G. C. Valley, R. A. Mullen, K. Bohnert, C. D. Mire, and T. F. Boggess, “Picosecond photorefractive effects in BaTiO3,” Opt. Lett. 12, 501 (1987).
    [Crossref] [PubMed]
  12. A. L. Smirl, K. Bohnert, G. C. Valley, R. A. Mullen, and T. F. Boggess, “Formation, decay, and erasure of photorefractive gratings written in barium titanate by picosecond pulses,” J. Opt. Soc. Am. B 6, 606 (1989).
    [Crossref]
  13. M. J. Damzen and N. Barry, “Intensity-dependent hole–electron competition and photorefractive saturation in BaTiO3when using intense laser pulses,” J. Opt. Soc. Am. B 10, 600 (1993).
    [Crossref]
  14. G. A. Brost and R. A. Motes, “Origin of the sublinear photorefractive response time in BaTiO3,” Opt. Lett. 15, 1194 (1990).
    [Crossref] [PubMed]
  15. I. Camlibel, M. Didomenico, and S. H. Wemple, “Dielectric properties of single-domain melt-grown BaTiO3,” J. Phys. Chem. Solids 31, 1417 (1970).
    [Crossref]
  16. G. A. Brost and R. A. Motes, “Photoinduced absorption in photorefractive barium titanate,” Opt. Lett. 15, 538 (1990).
    [Crossref] [PubMed]
  17. S. H. Wemple, M. Didomenico, and I. Camlibel, “Dielectric and optical properties of melt-grown BaTiO3,” J. Phys. Chem. Solids 29, 1797 (1968).
    [Crossref]
  18. G. C. Valley and M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704 (1983).
    [Crossref]
  19. S. Ducharme, J. Feinberg, and R. R. Neurgaonkar, “Electrooptic and piezoelectric measurements in photorefractive barium titanate and strontium barium niobate,” IEEE J. Quantum Electron. QE-23, 2116 (1987).
    [Crossref]
  20. M. B. Klein, in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Heidelberg, 1987), Chap. 7, p. 222, Eq. 7.50.
  21. G. C. Valley, “Short-pulse grating formation in photorefractive materials,” IEEE J. Quantum Electron. QE-19, 1637 (1983).
    [Crossref]
  22. L. Benguigui, “Space charge limited currents in BaTiO3single crystals,” Solid State Commun. 7, 1245 (1969).
    [Crossref]

1993 (1)

1992 (2)

1991 (1)

1990 (3)

1989 (1)

1988 (1)

1987 (2)

A. L. Smirl, G. C. Valley, R. A. Mullen, K. Bohnert, C. D. Mire, and T. F. Boggess, “Picosecond photorefractive effects in BaTiO3,” Opt. Lett. 12, 501 (1987).
[Crossref] [PubMed]

S. Ducharme, J. Feinberg, and R. R. Neurgaonkar, “Electrooptic and piezoelectric measurements in photorefractive barium titanate and strontium barium niobate,” IEEE J. Quantum Electron. QE-23, 2116 (1987).
[Crossref]

1986 (3)

1983 (2)

G. C. Valley, “Short-pulse grating formation in photorefractive materials,” IEEE J. Quantum Electron. QE-19, 1637 (1983).
[Crossref]

G. C. Valley and M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704 (1983).
[Crossref]

1981 (1)

1970 (1)

I. Camlibel, M. Didomenico, and S. H. Wemple, “Dielectric properties of single-domain melt-grown BaTiO3,” J. Phys. Chem. Solids 31, 1417 (1970).
[Crossref]

1969 (1)

L. Benguigui, “Space charge limited currents in BaTiO3single crystals,” Solid State Commun. 7, 1245 (1969).
[Crossref]

1968 (1)

S. H. Wemple, M. Didomenico, and I. Camlibel, “Dielectric and optical properties of melt-grown BaTiO3,” J. Phys. Chem. Solids 29, 1797 (1968).
[Crossref]

Barry, N.

Benguigui, L.

L. Benguigui, “Space charge limited currents in BaTiO3single crystals,” Solid State Commun. 7, 1245 (1969).
[Crossref]

Boggess, T. F.

Bohnert, K.

Brost, G. A.

Camlibel, I.

I. Camlibel, M. Didomenico, and S. H. Wemple, “Dielectric properties of single-domain melt-grown BaTiO3,” J. Phys. Chem. Solids 31, 1417 (1970).
[Crossref]

S. H. Wemple, M. Didomenico, and I. Camlibel, “Dielectric and optical properties of melt-grown BaTiO3,” J. Phys. Chem. Solids 29, 1797 (1968).
[Crossref]

Chang, T. Y.

L. K. Lam, T. Y. Chang, J. Feinberg, and R. W. Hellwarth, “Photorefractive-index gratings formed by nanosecond optical pulses in BaTiO3,” Opt. Lett. 6, 475 (1981).
[Crossref] [PubMed]

C. P. Tzou, T. Y. Chang, and R. W. Hellwarth, “Photorefractive measurement of anisotropy of the mobility of photoexcited holes in BaTiO3,” in Nonlinear Optics and Applications, P. Yeh, ed., Proc. Soc. Photo-Opt. Instrum. Eng.613, 58 (1986).
[Crossref]

Damzen, M. J.

Didomenico, M.

I. Camlibel, M. Didomenico, and S. H. Wemple, “Dielectric properties of single-domain melt-grown BaTiO3,” J. Phys. Chem. Solids 31, 1417 (1970).
[Crossref]

S. H. Wemple, M. Didomenico, and I. Camlibel, “Dielectric and optical properties of melt-grown BaTiO3,” J. Phys. Chem. Solids 29, 1797 (1968).
[Crossref]

Ducharme, S.

S. Ducharme, J. Feinberg, and R. R. Neurgaonkar, “Electrooptic and piezoelectric measurements in photorefractive barium titanate and strontium barium niobate,” IEEE J. Quantum Electron. QE-23, 2116 (1987).
[Crossref]

Feinberg, J.

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

S. Ducharme, J. Feinberg, and R. R. Neurgaonkar, “Electrooptic and piezoelectric measurements in photorefractive barium titanate and strontium barium niobate,” IEEE J. Quantum Electron. QE-23, 2116 (1987).
[Crossref]

L. K. Lam, T. Y. Chang, J. Feinberg, and R. W. Hellwarth, “Photorefractive-index gratings formed by nanosecond optical pulses in BaTiO3,” Opt. Lett. 6, 475 (1981).
[Crossref] [PubMed]

Hellwarth, R. W.

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

L. K. Lam, T. Y. Chang, J. Feinberg, and R. W. Hellwarth, “Photorefractive-index gratings formed by nanosecond optical pulses in BaTiO3,” Opt. Lett. 6, 475 (1981).
[Crossref] [PubMed]

C. P. Tzou, T. Y. Chang, and R. W. Hellwarth, “Photorefractive measurement of anisotropy of the mobility of photoexcited holes in BaTiO3,” in Nonlinear Optics and Applications, P. Yeh, ed., Proc. Soc. Photo-Opt. Instrum. Eng.613, 58 (1986).
[Crossref]

Jonathan, J. M. C.

Klein, M. B.

M. B. Klein and R. N. Schwartz, “Photorefractive effect in BaTiO3: microscopic origins,” J. Opt. Soc. Am. B 3, 293 (1986).
[Crossref]

G. C. Valley and M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704 (1983).
[Crossref]

M. B. Klein, in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Heidelberg, 1987), Chap. 7, p. 222, Eq. 7.50.

Lam, L. K.

Mahgerefteh, D.

P. Tayebati and D. Mahgerefteh, “Theory of the photorefractive effect for Bi12SiO20and BaTiO3with shallow traps,” J. Opt. Soc. Am. B 8, 1053 (1991).
[Crossref]

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

Mire, C. D.

Motes, R. A.

Mullen, R. A.

Neurgaonkar, R. R.

S. Ducharme, J. Feinberg, and R. R. Neurgaonkar, “Electrooptic and piezoelectric measurements in photorefractive barium titanate and strontium barium niobate,” IEEE J. Quantum Electron. QE-23, 2116 (1987).
[Crossref]

Rotge, J. R.

Schwartz, R. N.

Smirl, A. L.

Strohkendl, F. P.

Tayebati, P.

Tzou, C. P.

C. P. Tzou, T. Y. Chang, and R. W. Hellwarth, “Photorefractive measurement of anisotropy of the mobility of photoexcited holes in BaTiO3,” in Nonlinear Optics and Applications, P. Yeh, ed., Proc. Soc. Photo-Opt. Instrum. Eng.613, 58 (1986).
[Crossref]

Valley, G. C.

A. L. Smirl, K. Bohnert, G. C. Valley, R. A. Mullen, and T. F. Boggess, “Formation, decay, and erasure of photorefractive gratings written in barium titanate by picosecond pulses,” J. Opt. Soc. Am. B 6, 606 (1989).
[Crossref]

A. L. Smirl, G. C. Valley, R. A. Mullen, K. Bohnert, C. D. Mire, and T. F. Boggess, “Picosecond photorefractive effects in BaTiO3,” Opt. Lett. 12, 501 (1987).
[Crossref] [PubMed]

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

G. C. Valley, “Short-pulse grating formation in photorefractive materials,” IEEE J. Quantum Electron. QE-19, 1637 (1983).
[Crossref]

G. C. Valley and M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704 (1983).
[Crossref]

Wemple, S. H.

I. Camlibel, M. Didomenico, and S. H. Wemple, “Dielectric properties of single-domain melt-grown BaTiO3,” J. Phys. Chem. Solids 31, 1417 (1970).
[Crossref]

S. H. Wemple, M. Didomenico, and I. Camlibel, “Dielectric and optical properties of melt-grown BaTiO3,” J. Phys. Chem. Solids 29, 1797 (1968).
[Crossref]

IEEE J. Quantum Electron. (2)

S. Ducharme, J. Feinberg, and R. R. Neurgaonkar, “Electrooptic and piezoelectric measurements in photorefractive barium titanate and strontium barium niobate,” IEEE J. Quantum Electron. QE-23, 2116 (1987).
[Crossref]

G. C. Valley, “Short-pulse grating formation in photorefractive materials,” IEEE J. Quantum Electron. QE-19, 1637 (1983).
[Crossref]

J. Appl. Phys. (1)

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

J. Opt. Soc. Am. B (7)

J. Phys. Chem. Solids (2)

I. Camlibel, M. Didomenico, and S. H. Wemple, “Dielectric properties of single-domain melt-grown BaTiO3,” J. Phys. Chem. Solids 31, 1417 (1970).
[Crossref]

S. H. Wemple, M. Didomenico, and I. Camlibel, “Dielectric and optical properties of melt-grown BaTiO3,” J. Phys. Chem. Solids 29, 1797 (1968).
[Crossref]

Opt. Eng. (1)

G. C. Valley and M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704 (1983).
[Crossref]

Opt. Lett. (5)

Phys. Rev. Lett. (1)

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

Solid State Commun. (1)

L. Benguigui, “Space charge limited currents in BaTiO3single crystals,” Solid State Commun. 7, 1245 (1969).
[Crossref]

Other (2)

M. B. Klein, in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Heidelberg, 1987), Chap. 7, p. 222, Eq. 7.50.

C. P. Tzou, T. Y. Chang, and R. W. Hellwarth, “Photorefractive measurement of anisotropy of the mobility of photoexcited holes in BaTiO3,” in Nonlinear Optics and Applications, P. Yeh, ed., Proc. Soc. Photo-Opt. Instrum. Eng.613, 58 (1986).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1

Model diagram of photorefractive barium titanate with deep and secondary (shallow) centers and simultaneous hole and electron conductivity.

Fig. 2
Fig. 2

Experimental intensity-dependent grating response time of barium titanate for continuous-wave illumination. The curve is theoretical, based on the numerical model and on either the initial or the final parameter values given in Table 1.

Fig. 3
Fig. 3

Experimental intensity dependence of the induced change in the absorption coefficient of barium titanate under continuous-wave illumination. The curve is theoretical, based on either the initial or the final model-parameter values given in Table 1.

Fig. 4
Fig. 4

Experimental asymptotic steady-state two-beam coupling gain coefficient after multiple-nanosecond-pulse illumination. The dashed curve is theoretical, based on the initial model-parameter values, and the solid curve is based on the final parameter values given in Table 1.

Fig. 5
Fig. 5

Experimental grating erasure response time with nanosecond-pulse-train erasure beam. The solid curve is theoretical, based on either the initial or the final parameter values given in Table 1. The dashed lines indicate the regions of linear fits to the experimental data above and below the compensation intensity.

Fig. 6
Fig. 6

Examples of temporal buildup of photorefractive gratings by use of 10-Hz-repetition-rate pulse trains with different pulse peak intensity (I). The intensity dependence of the buildup time and the asymptotic two-beam coupling gain coefficient are illustrated.

Tables (1)

Tables Icon

Table 1 Crystal Parameters Used in the Numerical Simulations

Equations (3)

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Δ α ( I ) = ( h c / λ ) ( S s - S h + S e ) M 0 + ( I ) ,
M 0 + t = - β s M 0 + 1 + γ s M / γ h N ,
τ - 1 = ( τ dih - 1 + τ die - 1 ) [ 1 + ( k 2 / k 0 2 ) ] = e μ h S h N + I ɛ 0 ɛ r γ h N [ 1 + R ( N / N + ) 2 ] [ 1 + ( k 2 / k 0 2 ) ] ,

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