Abstract

A band-conduction model for the photorefractive effect is derived in which simultaneous hole and electron conduction is taken into account. The anomalous behavior of nearly compensated BaTiO3 crystals in beam-coupling experiments is explained.

© 1986 Optical Society of America

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References

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  1. N. V. Kukhtarev, Sov. Tech. Phys. Lett. 2, 438 (1976).
  2. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
    [CrossRef]
  3. G. C. Valley, IEEE J. Quantum Electron. QE-19, 1637 (1983).
    [CrossRef]
  4. J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
    [CrossRef]
  5. R. Orlowski, E. Kratzig, Solid State Commun. 27, 1351 (1978).
    [CrossRef]
  6. M. B. Klein, G. C. Valley, J. Appl. Phys. 57, 4901 (1985).
    [CrossRef]
  7. S. Ducharme, J. Feinberg, J. Opt. Soc. Am. B 3, 283 (1986).
    [CrossRef]
  8. P. Gunther, Phys. Rep. 93, 200 (1983).
  9. S. H. Wemple, M. Didomenico, I. Camlibel, J. Phys. Chem. Solids 29, 1797 (1968).
    [CrossRef]

1986

1985

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

1983

P. Gunther, Phys. Rep. 93, 200 (1983).

G. C. Valley, IEEE J. Quantum Electron. QE-19, 1637 (1983).
[CrossRef]

1980

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

1979

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

1978

R. Orlowski, E. Kratzig, Solid State Commun. 27, 1351 (1978).
[CrossRef]

1976

N. V. Kukhtarev, Sov. Tech. Phys. Lett. 2, 438 (1976).

1968

S. H. Wemple, M. Didomenico, I. Camlibel, J. Phys. Chem. Solids 29, 1797 (1968).
[CrossRef]

Camlibel, I.

S. H. Wemple, M. Didomenico, I. Camlibel, J. Phys. Chem. Solids 29, 1797 (1968).
[CrossRef]

Didomenico, M.

S. H. Wemple, M. Didomenico, I. Camlibel, J. Phys. Chem. Solids 29, 1797 (1968).
[CrossRef]

Ducharme, S.

Feinberg, J.

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

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

Gunther, P.

P. Gunther, Phys. Rep. 93, 200 (1983).

Heiman, D.

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

Hellwarth, R. W.

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

Klein, M. B.

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

Kratzig, E.

R. Orlowski, E. Kratzig, Solid State Commun. 27, 1351 (1978).
[CrossRef]

Kukhtarev, N. V.

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

N. V. Kukhtarev, Sov. Tech. Phys. Lett. 2, 438 (1976).

Markov, V. B.

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

Odulov, S. G.

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

Orlowski, R.

R. Orlowski, E. Kratzig, Solid State Commun. 27, 1351 (1978).
[CrossRef]

Soskin, M. S.

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

Tanguay, A. R.

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

Valley, G. C.

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

G. C. Valley, IEEE J. Quantum Electron. QE-19, 1637 (1983).
[CrossRef]

Vinetskii, V. L.

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

Wemple, S. H.

S. H. Wemple, M. Didomenico, I. Camlibel, J. Phys. Chem. Solids 29, 1797 (1968).
[CrossRef]

Ferroelectrics

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

IEEE J. Quantum Electron.

G. C. Valley, IEEE J. Quantum Electron. QE-19, 1637 (1983).
[CrossRef]

J. Appl. Phys.

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

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

J. Opt. Soc. Am. B

J. Phys. Chem. Solids

S. H. Wemple, M. Didomenico, I. Camlibel, J. Phys. Chem. Solids 29, 1797 (1968).
[CrossRef]

Phys. Rep.

P. Gunther, Phys. Rep. 93, 200 (1983).

Solid State Commun.

R. Orlowski, E. Kratzig, Solid State Commun. 27, 1351 (1978).
[CrossRef]

Sov. Tech. Phys. Lett.

N. V. Kukhtarev, Sov. Tech. Phys. Lett. 2, 438 (1976).

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Figures (2)

Fig. 1
Fig. 1

Beam-coupling geometry for the anomalous BaTiO3 crystal GB5. θ is the half angle between signal and pump beams inside the crystal. The polarizations are parallel to the paper plane. The direction of the crystal axis is given as defined in Ref. 4.

Fig. 2
Fig. 2

The data for the anomalous crystal GB5 of Ref. 6 are given as circles. The solid curve is the prediction of Eq. (13) of the text with the parameter values given there for the best fit. The dotted and dashed curves are plots of Eq. (13) with extreme parameter values that are still consistent with the data, as discussed in the text. The prediction of Eq. (13) to higher grating wave vectors is shown at the top.

Equations (17)

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N D i / t = s e I ( N D - N D i ) - γ e n e N D i - s h I N D i + γ h n h ( N D - N D i ) ,
j e = e n e μ e E + μ e k B T n e ,
j h = e n h μ e E - μ h k B T n h ,
n e / t = j e / e + s e I ( N D - N D i ) - γ e n e N D i ,
n h / t = - j h / e + s h I N D i - γ h n h ( N D - N D i ) ,
E = - ( e / ) ( n e + N A - N D i - n h ) .
N D i ( t , z ) = N 0 ( t ) + Re [ N 1 I ( t ) exp ( i k z ) ] , n e ( t , z ) = n e 0 ( t ) + Re [ n e 1 ( t ) exp ( i k z ) ] , n h ( t , z ) = n h 0 ( t ) + Re [ n h 1 ( t ) exp ( i k z ) ] , j e ( t , z ) = j e 0 ( t ) + Re [ j e 1 ( t ) exp ( i k z ) ] , j h ( t , z ) = j h 0 ( t ) + Re [ j h 1 ( t ) exp ( i k z ) ] , E ( z , t ) = E 0 + Re [ E 1 ( t ) exp ( i k z ) ] ,
I 0 h ν k 2 k B T / τ α p e 2 ,
n e 0 = s e I 0 ( N D - N 0 ) γ e N 0 ,             n h 0 = s h I 0 N 0 γ h ( N D - N 0 ) ,
- d E 1 ( t ) d t = E 1 ( t ) [ n e 0 e μ e 1 + k ( k - i V ) / k 0 2 1 + k ( k - i V ) / K e 2 + n h 0 e μ h 1 + k ( k + i V ) / k 0 2 1 + k ( k + i V ) / K h 2 ] + i m k B T e [ n e 0 e μ e k - i V 1 + k ( k - i V ) / K e 2 - n h 0 e μ h k + i V 1 + k ( k + i V ) / K h 2 ] ,
K e - 2 k B T μ e e γ e N 0 ,             K h - 2 k B T μ h e γ h ( N D - N 0 ) ,
k 0 2 e 2 N 0 ( N D - N 0 ) k B T N D ,             V = e E 0 / k B T .
E S C = - i m k B T e k 1 + k 2 / k 0 2 ξ ( k ) ,
ξ ( k ) ( 1 - C ) / ( 1 + C ) ,
C s h N 0 ( k 2 + K e 2 ) s e ( N D - N 0 ) ( k 2 + K h 2 ) .
Γ = - 2 π λ r eff n i E s c m cos 2 θ ,
K h - 1 + k 0 - 1 = K c - 1 ,

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