Abstract

We present results of high-intensity measurements of the two-beam coupling gain coefficient and the photorefractive grating response time in barium titanate (BaTiO3). For hole-dominated BaTiO3 the gain coefficient is observed to decrease with intensity in the megawatt-per-square-centimeter range, because of intensity-dependent photocarrier competition, and is also seen to reverse signs above a critical intensity determined by the crystal doping. Significant two-beam coupling is observed to develop transiently during a single pulse of 15-ns duration. An analytical theory, valid at high intensity, is developed that includes the effects of simultaneous electron and hole photoconductivities and carrier saturation. The analysis predicts the experimentally observed strong intensity dependence in the two-beam coupling gain coefficient, including its reversal in sign.

© 1992 Optical Society of America

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References

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  1. M. J. Damzen and N. Barry, “Intensity-dependent hole–electron competition and photocarrier saturation in BaTiO3 using intense laser pulses,” submitted to J. Opt. Soc. Am. B.
  2. M. J. Damzen, N. Barry, and M. Buttinger, “High-intensity effects in self-pumped photorefractive phase conjugation using nanosecond pulses,” submitted to IEEE J. Quantum Electron.
  3. M. B. Klein, “Photorefractive properties of BaTiO3,” in Photorefractive Materials and Their Applications I, P. Günter and J. P. Huignard, eds. (Springer-Verlag, Berlin, 1989), Chap. 7.
  4. F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole–electron competition in photorefractive gratings,” Opt. Lett. 18, 312 (1987).
  5. G. C. Valley, “Short-pulse grating formation in photorefractive materials,” IEEE J. Quantum Electron. QE-19, 1637 (1983).
    [Crossref]
  6. M. B. Klein and R. N. Schwartz, “Photorefractive effect in BaTiO3: microscopic origins,” J. Opt. Soc. Am. B 3, 293 (1986).
    [Crossref]
  7. 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]
  8. G. C. Valley and J. F. Lam, “Theory of photorefractive effects in electro-optic crystals,” in Photorefractive Materials and Their Applications I, P. Günter and J. P. Huignard, eds. (Springer-Verlag, Berlin, 1989), Chap. 3.
  9. P. Tayebati and D. Mahgerefteh, “Theory of the photorefractive effect for Bi12SiO20 and BaTiO3 with shallow traps,” J. Opt. Soc. Am. B 8, 1053 (1991).
    [Crossref]
  10. D. Mahgerefteh and J. Feinberg, “Explanation of the apparent sublinear photoconductivity of photorefractive barium titanate,” Phys. Rev. Lett. 64, 2195 (1990).
    [Crossref] [PubMed]

1991 (1)

1990 (1)

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

1988 (1)

1987 (1)

F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole–electron competition in photorefractive gratings,” Opt. Lett. 18, 312 (1987).

1986 (1)

1983 (1)

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

Barry, N.

M. J. Damzen, N. Barry, and M. Buttinger, “High-intensity effects in self-pumped photorefractive phase conjugation using nanosecond pulses,” submitted to IEEE J. Quantum Electron.

M. J. Damzen and N. Barry, “Intensity-dependent hole–electron competition and photocarrier saturation in BaTiO3 using intense laser pulses,” submitted to J. Opt. Soc. Am. B.

Brost, G. A.

Buttinger, M.

M. J. Damzen, N. Barry, and M. Buttinger, “High-intensity effects in self-pumped photorefractive phase conjugation using nanosecond pulses,” submitted to IEEE J. Quantum Electron.

Damzen, M. J.

M. J. Damzen, N. Barry, and M. Buttinger, “High-intensity effects in self-pumped photorefractive phase conjugation using nanosecond pulses,” submitted to IEEE J. Quantum Electron.

M. J. Damzen and N. Barry, “Intensity-dependent hole–electron competition and photocarrier saturation in BaTiO3 using intense laser pulses,” submitted to J. Opt. Soc. Am. B.

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]

Hellwarth, R. W.

F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole–electron competition in photorefractive gratings,” Opt. Lett. 18, 312 (1987).

Jonathan, J. M. C.

F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole–electron competition in photorefractive gratings,” Opt. Lett. 18, 312 (1987).

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]

M. B. Klein, “Photorefractive properties of BaTiO3,” in Photorefractive Materials and Their Applications I, P. Günter and J. P. Huignard, eds. (Springer-Verlag, Berlin, 1989), Chap. 7.

Lam, J. F.

G. C. Valley and J. F. Lam, “Theory of photorefractive effects in electro-optic crystals,” in Photorefractive Materials and Their Applications I, P. Günter and J. P. Huignard, eds. (Springer-Verlag, Berlin, 1989), Chap. 3.

Mahgerefteh, D.

P. Tayebati and D. Mahgerefteh, “Theory of the photorefractive effect for Bi12SiO20 and BaTiO3 with 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]

Motes, R. A.

Rotge, J. R.

Schwartz, R. N.

Strohkendl, F. P.

F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole–electron competition in photorefractive gratings,” Opt. Lett. 18, 312 (1987).

Tayebati, P.

Valley, G. C.

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

G. C. Valley and J. F. Lam, “Theory of photorefractive effects in electro-optic crystals,” in Photorefractive Materials and Their Applications I, P. Günter and J. P. Huignard, eds. (Springer-Verlag, Berlin, 1989), Chap. 3.

IEEE J. Quantum Electron. (1)

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

J. Opt. Soc. Am. B (3)

Opt. Lett. (1)

F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole–electron competition in photorefractive gratings,” Opt. Lett. 18, 312 (1987).

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]

Other (4)

M. J. Damzen and N. Barry, “Intensity-dependent hole–electron competition and photocarrier saturation in BaTiO3 using intense laser pulses,” submitted to J. Opt. Soc. Am. B.

M. J. Damzen, N. Barry, and M. Buttinger, “High-intensity effects in self-pumped photorefractive phase conjugation using nanosecond pulses,” submitted to IEEE J. Quantum Electron.

M. B. Klein, “Photorefractive properties of BaTiO3,” in Photorefractive Materials and Their Applications I, P. Günter and J. P. Huignard, eds. (Springer-Verlag, Berlin, 1989), Chap. 7.

G. C. Valley and J. F. Lam, “Theory of photorefractive effects in electro-optic crystals,” in Photorefractive Materials and Their Applications I, P. Günter and J. P. Huignard, eds. (Springer-Verlag, Berlin, 1989), Chap. 3.

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Figures (5)

Fig. 1
Fig. 1

Model of a photorefractive material with simultaneous photoconductivity of electrons and holes from a common pair of photorefractive centers N and N+.

Fig. 2
Fig. 2

Theoretical intensity dependence of the space-charge field (proportional to the two-beam coupling gain coefficient) in BaTiO3 for various ratios of the number densities of the photorefractive centers r = N0+/N0. The space-charge field is normalized to the single-carrier (hole) low-intensity limit of the space-charge field. Positive values of ESC correspond to hole-dominated conductivity and negative values to electron-dominated conductivity.

Fig. 3
Fig. 3

Intensity dependence of the response time of the two-beam coupling grating decay. Solid curves are theoretical, from Eq. (10), for various values of hole mobility. Experimental data are shown for crystal 1(open data points) and for crystal 2 (filled data points).

Fig. 4
Fig. 4

Experimentally measured intensity dependence of the two-beam coupling gain coefficient for crystal 1 (open circles) and crystal 2 (open triangles).

Fig. 5
Fig. 5

Temporal form of the signal pulse transmitted by the BaTiO3 crystal with and without a two-beam coupling pump pulse, from which the temporal development of the two-beam coupling gain coefficient is deduced. (Peak pulse intensity I0 = 34 MWcm2, corresponding to a negative coefficient and signal attenuation.)

Equations (11)

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E SC = i m ( k B T k g / e ) 1 + ( k g 2 / k I 2 ) + ( n e + n h ) N D / N N + σ ( k g , I 0 ) ,
σ ( k g , I 0 ) = ( σ e / σ h ) [ 1 + ( k g 2 / k h 2 ) + ( 2 n h N D / N N + ) ] [ 1 + ( k g 2 / k e 2 ) + ( 2 n e N D / N N + ) ] ( σ e / σ h ) [ 1 + ( k g 2 / k h 2 ) ] + [ 1 + ( k g 2 / k e 2 ) ] ,
σ e σ h = ( s e μ e γ h s h μ h γ e ) ( N N + ) 2 = R ( N N + ) 2 ,
E SC = i m ( k B T k g / e ) 1 + ( k g 2 / k I 2 ) n h N D / N N + σ ( k g , I 0 ) ,
σ ( k g , I 0 ) = ( σ e / σ h ) [ 1 + ( 2 n h N D / N N + ) ] 1 ( σ e / σ h ) + 1 ,
σ e / σ h = R ( N / N + ) 2 ,
n h = ½ N 0 { ( 1 + f h ) + [ ( 1 + f h ) 2 + 4 f h r ] 1 / 2 } ,
Γ = ( 2 π / λ ) n 3 r eff E SC / i m ,
τ 1 = [ τ dih 1 1 + ( k g 2 / k h 2 ) + τ die 1 1 + ( k g 2 / k e 2 ) ] × 1 + ( k g 2 / k I 2 ) + ( n h + n e ) ( N D / N N + ) 1 + ( n h N D / N N + ) [ 1 + ( k g 2 / k h 2 ) ] 1 + ( n e N D / N N + ) [ 1 + ( k g 2 / k e 2 ) ] 1 ,
τ 1 = ( e μ h n h 0 ) ( 1 + σ e σ h ) { 1 + k g 2 k I 2 [ 1 + ( n h N D / N N + ) ] } .
g = ( 1 + β ) e Γ L β + e Γ L ,

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