Abstract

We present a method to separate the effects of trap gratings and electro-optic gratings in BaTiO3 crystals, and we determine the true spatial shift between the electro-optic grating and the optical intensity pattern. At small beam-crossing angles this spatial shift is strongly affected by a photogalvanic current in the crystal.

© 1992 Optical Society of America

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  1. A. V. Alekseev-Popov, A. V. Knyaz’kov, A. S. Saikin, Sov. Tech. Phys. Lett. 9, 475 (1983).
  2. R. B. Bylsma, D. H. Olson, A. M. Glass, Opt. Lett. 13, 853 (1988).
    [CrossRef] [PubMed]
  3. R. M. Pierce, R. S. Cudney, G. D. Bacher, J. Feinberg, Opt. Lett. 15, 414 (1990).
    [CrossRef] [PubMed]
  4. In this Letter, index of refraction and absorption mean the real and imaginary parts of the complex index of refraction, respectively.
  5. V. Kondilenko, V. Markov, S. Odulov, S. Soskin, Opt. Acta 26, 239 (1979).
    [CrossRef]
  6. Y. B. Afanas’ev, A. A. Petrov, M. P. Petrov, S. I. Stepanov, G. S. Trofimov, Sov. Tech. Phys. Lett. 13, 486 (1987).
  7. P. Magno García, L. Cescato, J. Frejlich, J. Appl. Phys. 66, 47 (1989).
    [CrossRef]
  8. P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications I: Fundamental Phenomena, Vol. 61 of Springer Series on Topics in Applied Physics (Springer-Verlag, New York, 1988), p. 54.
  9. R. S. Cudney, R. M. Pierce, G. D. Bacher, J. Feinberg, J. Opt. Soc. Am. B 8, 1326 (1991).
    [CrossRef]
  10. A. M. Glass, D. von der Linde, T. J. Negran, Appl. Phys. Lett. 25, 233 (1974).
    [CrossRef]
  11. R. S. Cudney, R. M. Pierce, G. D. Bacher, D. Mahgerefteh, J. Feinberg, “Photogalvanic effect in barium titanate,” submitted to J. Opt. Soc. Am. B.

1991 (1)

1990 (1)

1989 (1)

P. Magno García, L. Cescato, J. Frejlich, J. Appl. Phys. 66, 47 (1989).
[CrossRef]

1988 (1)

1987 (1)

Y. B. Afanas’ev, A. A. Petrov, M. P. Petrov, S. I. Stepanov, G. S. Trofimov, Sov. Tech. Phys. Lett. 13, 486 (1987).

1983 (1)

A. V. Alekseev-Popov, A. V. Knyaz’kov, A. S. Saikin, Sov. Tech. Phys. Lett. 9, 475 (1983).

1979 (1)

V. Kondilenko, V. Markov, S. Odulov, S. Soskin, Opt. Acta 26, 239 (1979).
[CrossRef]

1974 (1)

A. M. Glass, D. von der Linde, T. J. Negran, Appl. Phys. Lett. 25, 233 (1974).
[CrossRef]

Afanas’ev, Y. B.

Y. B. Afanas’ev, A. A. Petrov, M. P. Petrov, S. I. Stepanov, G. S. Trofimov, Sov. Tech. Phys. Lett. 13, 486 (1987).

Alekseev-Popov, A. V.

A. V. Alekseev-Popov, A. V. Knyaz’kov, A. S. Saikin, Sov. Tech. Phys. Lett. 9, 475 (1983).

Bacher, G. D.

R. S. Cudney, R. M. Pierce, G. D. Bacher, J. Feinberg, J. Opt. Soc. Am. B 8, 1326 (1991).
[CrossRef]

R. M. Pierce, R. S. Cudney, G. D. Bacher, J. Feinberg, Opt. Lett. 15, 414 (1990).
[CrossRef] [PubMed]

R. S. Cudney, R. M. Pierce, G. D. Bacher, D. Mahgerefteh, J. Feinberg, “Photogalvanic effect in barium titanate,” submitted to J. Opt. Soc. Am. B.

Bylsma, R. B.

Cescato, L.

P. Magno García, L. Cescato, J. Frejlich, J. Appl. Phys. 66, 47 (1989).
[CrossRef]

Cudney, R. S.

R. S. Cudney, R. M. Pierce, G. D. Bacher, J. Feinberg, J. Opt. Soc. Am. B 8, 1326 (1991).
[CrossRef]

R. M. Pierce, R. S. Cudney, G. D. Bacher, J. Feinberg, Opt. Lett. 15, 414 (1990).
[CrossRef] [PubMed]

R. S. Cudney, R. M. Pierce, G. D. Bacher, D. Mahgerefteh, J. Feinberg, “Photogalvanic effect in barium titanate,” submitted to J. Opt. Soc. Am. B.

Feinberg, J.

R. S. Cudney, R. M. Pierce, G. D. Bacher, J. Feinberg, J. Opt. Soc. Am. B 8, 1326 (1991).
[CrossRef]

R. M. Pierce, R. S. Cudney, G. D. Bacher, J. Feinberg, Opt. Lett. 15, 414 (1990).
[CrossRef] [PubMed]

R. S. Cudney, R. M. Pierce, G. D. Bacher, D. Mahgerefteh, J. Feinberg, “Photogalvanic effect in barium titanate,” submitted to J. Opt. Soc. Am. B.

Frejlich, J.

P. Magno García, L. Cescato, J. Frejlich, J. Appl. Phys. 66, 47 (1989).
[CrossRef]

Glass, A. M.

R. B. Bylsma, D. H. Olson, A. M. Glass, Opt. Lett. 13, 853 (1988).
[CrossRef] [PubMed]

A. M. Glass, D. von der Linde, T. J. Negran, Appl. Phys. Lett. 25, 233 (1974).
[CrossRef]

Günter, P.

P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications I: Fundamental Phenomena, Vol. 61 of Springer Series on Topics in Applied Physics (Springer-Verlag, New York, 1988), p. 54.

Huignard, J.-P.

P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications I: Fundamental Phenomena, Vol. 61 of Springer Series on Topics in Applied Physics (Springer-Verlag, New York, 1988), p. 54.

Knyaz’kov, A. V.

A. V. Alekseev-Popov, A. V. Knyaz’kov, A. S. Saikin, Sov. Tech. Phys. Lett. 9, 475 (1983).

Kondilenko, V.

V. Kondilenko, V. Markov, S. Odulov, S. Soskin, Opt. Acta 26, 239 (1979).
[CrossRef]

Magno García, P.

P. Magno García, L. Cescato, J. Frejlich, J. Appl. Phys. 66, 47 (1989).
[CrossRef]

Mahgerefteh, D.

R. S. Cudney, R. M. Pierce, G. D. Bacher, D. Mahgerefteh, J. Feinberg, “Photogalvanic effect in barium titanate,” submitted to J. Opt. Soc. Am. B.

Markov, V.

V. Kondilenko, V. Markov, S. Odulov, S. Soskin, Opt. Acta 26, 239 (1979).
[CrossRef]

Negran, T. J.

A. M. Glass, D. von der Linde, T. J. Negran, Appl. Phys. Lett. 25, 233 (1974).
[CrossRef]

Odulov, S.

V. Kondilenko, V. Markov, S. Odulov, S. Soskin, Opt. Acta 26, 239 (1979).
[CrossRef]

Olson, D. H.

Petrov, A. A.

Y. B. Afanas’ev, A. A. Petrov, M. P. Petrov, S. I. Stepanov, G. S. Trofimov, Sov. Tech. Phys. Lett. 13, 486 (1987).

Petrov, M. P.

Y. B. Afanas’ev, A. A. Petrov, M. P. Petrov, S. I. Stepanov, G. S. Trofimov, Sov. Tech. Phys. Lett. 13, 486 (1987).

Pierce, R. M.

R. S. Cudney, R. M. Pierce, G. D. Bacher, J. Feinberg, J. Opt. Soc. Am. B 8, 1326 (1991).
[CrossRef]

R. M. Pierce, R. S. Cudney, G. D. Bacher, J. Feinberg, Opt. Lett. 15, 414 (1990).
[CrossRef] [PubMed]

R. S. Cudney, R. M. Pierce, G. D. Bacher, D. Mahgerefteh, J. Feinberg, “Photogalvanic effect in barium titanate,” submitted to J. Opt. Soc. Am. B.

Saikin, A. S.

A. V. Alekseev-Popov, A. V. Knyaz’kov, A. S. Saikin, Sov. Tech. Phys. Lett. 9, 475 (1983).

Soskin, S.

V. Kondilenko, V. Markov, S. Odulov, S. Soskin, Opt. Acta 26, 239 (1979).
[CrossRef]

Stepanov, S. I.

Y. B. Afanas’ev, A. A. Petrov, M. P. Petrov, S. I. Stepanov, G. S. Trofimov, Sov. Tech. Phys. Lett. 13, 486 (1987).

Trofimov, G. S.

Y. B. Afanas’ev, A. A. Petrov, M. P. Petrov, S. I. Stepanov, G. S. Trofimov, Sov. Tech. Phys. Lett. 13, 486 (1987).

von der Linde, D.

A. M. Glass, D. von der Linde, T. J. Negran, Appl. Phys. Lett. 25, 233 (1974).
[CrossRef]

Appl. Phys. Lett. (1)

A. M. Glass, D. von der Linde, T. J. Negran, Appl. Phys. Lett. 25, 233 (1974).
[CrossRef]

J. Appl. Phys. (1)

P. Magno García, L. Cescato, J. Frejlich, J. Appl. Phys. 66, 47 (1989).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Acta (1)

V. Kondilenko, V. Markov, S. Odulov, S. Soskin, Opt. Acta 26, 239 (1979).
[CrossRef]

Opt. Lett. (2)

Sov. Tech. Phys. Lett. (2)

Y. B. Afanas’ev, A. A. Petrov, M. P. Petrov, S. I. Stepanov, G. S. Trofimov, Sov. Tech. Phys. Lett. 13, 486 (1987).

A. V. Alekseev-Popov, A. V. Knyaz’kov, A. S. Saikin, Sov. Tech. Phys. Lett. 9, 475 (1983).

Other (3)

In this Letter, index of refraction and absorption mean the real and imaginary parts of the complex index of refraction, respectively.

R. S. Cudney, R. M. Pierce, G. D. Bacher, D. Mahgerefteh, J. Feinberg, “Photogalvanic effect in barium titanate,” submitted to J. Opt. Soc. Am. B.

P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications I: Fundamental Phenomena, Vol. 61 of Springer Series on Topics in Applied Physics (Springer-Verlag, New York, 1988), p. 54.

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Figures (3)

Fig. 1
Fig. 1

Phase of the coupling coefficient gtraps versus kg at three different optical intensities in a BaTiO3 crystal (“Free” crystal). 0° and 90° correspond to pure absorption and pure index-of-refraction gratings, respectively. The solid curves are fits to Eq. (10). T = 20.0°C and λ = 488 nm.

Fig. 2
Fig. 2

Real and imaginary parts of the coupling parameter g versus intensity in a BaTiO3 crystal (“Free” crystal). (a) Trap coupling measured with ĉkg. The internai beam half-crossing angle was kept fixed at 0.3° so one could observe only the nondiffusive contribution to the coupling. (b), (c) The real and imaginary parts of the coupling obtained with ĉ || kg. The trap coupling shown in (a) has been subtracted from the total coupling to obtain the purely electro-optic coupling. T = 17.7°C, λ = 488 nm, and θint = 0.3°.

Fig. 3
Fig. 3

Phase ϕg = tan−1(gI/gR) of the total coupling and the purely electro-optic coupling versus intensity, with ĉ || kg. To find the spatial shift between the interference pattern and the electro-optic grating, add 90°.

Equations (10)

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d E 1 ( z , t ) d z g m ( z , t ) T E 2 ( z , t ) = 0 ,
E 1 ( z , t ) = E 1 ( 0 , t ) + E 1 ( 0 , t ) T [ exp ( g z ) 1 ] .
E 1 ( l ) = E 1 ( 0 ) exp ( g l ) .
I 1 ( 0 ) = I 1 0 exp ( 2 g R l ) ,
I 1 ( Ω ) = 2 μ I 1 0 exp ( g R l ) sin ( g I l ) ,
I 1 ( 2 Ω ) = ( μ 2 / 2 ) I 1 0 [ exp ( g R l ) cos ( g I l ) 1 ] ,
tan ϕ g μ 4 I 1 ( Ω ) I 1 ( 2 Ω ) .
g = g eo + g traps .
g traps ( k g , I ) = A ( I ) k g 2 / k 0 2 ( I ) + B ( I ) 1 + k g 2 / k 0 2 ( I ) | e ˆ 1 * e ˆ 2 | 2 .
ϕ g traps ( k g , I ) = tan 1 { Im [ A ( I ) ] k g 2 / k 0 2 ( I ) + Im [ B ( I ) ] Re [ A ( I ) ] k g 2 / k 0 2 ( I ) + Re [ B ( I ) ] } .

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