Abstract

We have used a 20-kHz ac square-wave electric field to enhance the beam-coupling gain and the degenerate four-wave mixing reflectivity of photorefractive GaAs at 1.06 μm. The largest measured four-wave mixing reflectivity in the steady state was 15% at a grating period of 9 μm and an applied voltage of 3.2 kV across 0.4 cm. Theoretical results predict substantially higher reflectivity values for a field of 8 kV/cm; the origin of this discrepancy is thought to be space-charge effects that prevent us from obtaining the full field inside the crystal. We have also measured a transient reflectivity of 510% during the switch on of the backward pump beam. Finally, we have determined the accuracy of wave-front reversal through measurements of piston-error correction and conjugation fidelity.

© 1988 Optical Society of America

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References

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  1. M. B. Klein, Opt. Lett. 9, 350 (1984).
    [Crossref] [PubMed]
  2. G. Albanese, J. Kumar, and W. H. Steir, Opt. Lett. 11, 650 (1986).
    [Crossref] [PubMed]
  3. J. Kumar, G. Albanese, W. H. Steier, and M. Ziari, Opt. Lett 12, 120 (1987).
    [Crossref] [PubMed]
  4. J. Kumar, G. Albanese, and W. H. Steier, Opt Commun. 63, 191 (1987).
    [Crossref]
  5. B. Imbert, H. Rajbenbach, S. Mallick, J. P. Herriau, and J. P. Huignard, Opt. Lett. 13, 327 (1988).
    [Crossref] [PubMed]
  6. A. M. Glass, A. M. Johnson, D. H. Olsen, W. Simpson, and A. A. Ballman, Appl. Phys. Lett. 44, 948 (1984).
    [Crossref]
  7. S. I. Stepanov and M. P. Petrov, Opt. Commun. 53, 292 (1985).
    [Crossref]
  8. S. I. Stepanov and M. P. Petrov, Sov. Tech. Phys. Lett. 10, 572 (1984).
  9. P. Dobrilla and J. S. Blakemore, J. Appl. Phys. 58, 208 (1985).
    [Crossref]
  10. M. Sugie and K. Tada, Jpn. J. Appl. Phys. 15, 421 (1976).
    [Crossref]
  11. D. T. F. Marple, J. Appl. Phys. 35, 1241 (1964).
    [Crossref]
  12. R. E. Neidert, Electron. Lett. 16, 244 (1980).
    [Crossref]
  13. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
    [Crossref]
  14. L.-J. Cheng and A. Partovi, Appl. Phys. Lett. 49, 1456 (1986).
    [Crossref]
  15. G. M. Martin and S. Makram-Ebeid, in Deep Centers in Semiconductors, a State-of-the-Art Approach, S. T. Pantelides, ed. (Gordon & Breach, New York, 1986), Chap. 6, pp. 399–487.
  16. M. Cronin-Golomb, J. O. White, B. Fisher, and A. Yariv, Opt. Lett. 7, 313 (1982).
    [Crossref] [PubMed]

1988 (1)

1987 (2)

J. Kumar, G. Albanese, W. H. Steier, and M. Ziari, Opt. Lett 12, 120 (1987).
[Crossref] [PubMed]

J. Kumar, G. Albanese, and W. H. Steier, Opt Commun. 63, 191 (1987).
[Crossref]

1986 (2)

G. Albanese, J. Kumar, and W. H. Steir, Opt. Lett. 11, 650 (1986).
[Crossref] [PubMed]

L.-J. Cheng and A. Partovi, Appl. Phys. Lett. 49, 1456 (1986).
[Crossref]

1985 (2)

P. Dobrilla and J. S. Blakemore, J. Appl. Phys. 58, 208 (1985).
[Crossref]

S. I. Stepanov and M. P. Petrov, Opt. Commun. 53, 292 (1985).
[Crossref]

1984 (3)

S. I. Stepanov and M. P. Petrov, Sov. Tech. Phys. Lett. 10, 572 (1984).

A. M. Glass, A. M. Johnson, D. H. Olsen, W. Simpson, and A. A. Ballman, Appl. Phys. Lett. 44, 948 (1984).
[Crossref]

M. B. Klein, Opt. Lett. 9, 350 (1984).
[Crossref] [PubMed]

1982 (1)

1980 (1)

R. E. Neidert, Electron. Lett. 16, 244 (1980).
[Crossref]

1979 (1)

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

1976 (1)

M. Sugie and K. Tada, Jpn. J. Appl. Phys. 15, 421 (1976).
[Crossref]

1964 (1)

D. T. F. Marple, J. Appl. Phys. 35, 1241 (1964).
[Crossref]

Albanese, G.

J. Kumar, G. Albanese, W. H. Steier, and M. Ziari, Opt. Lett 12, 120 (1987).
[Crossref] [PubMed]

J. Kumar, G. Albanese, and W. H. Steier, Opt Commun. 63, 191 (1987).
[Crossref]

G. Albanese, J. Kumar, and W. H. Steir, Opt. Lett. 11, 650 (1986).
[Crossref] [PubMed]

Ballman, A. A.

A. M. Glass, A. M. Johnson, D. H. Olsen, W. Simpson, and A. A. Ballman, Appl. Phys. Lett. 44, 948 (1984).
[Crossref]

Blakemore, J. S.

P. Dobrilla and J. S. Blakemore, J. Appl. Phys. 58, 208 (1985).
[Crossref]

Cheng, L.-J.

L.-J. Cheng and A. Partovi, Appl. Phys. Lett. 49, 1456 (1986).
[Crossref]

Cronin-Golomb, M.

Dobrilla, P.

P. Dobrilla and J. S. Blakemore, J. Appl. Phys. 58, 208 (1985).
[Crossref]

Fisher, B.

Glass, A. M.

A. M. Glass, A. M. Johnson, D. H. Olsen, W. Simpson, and A. A. Ballman, Appl. Phys. Lett. 44, 948 (1984).
[Crossref]

Herriau, J. P.

Huignard, J. P.

Imbert, B.

Johnson, A. M.

A. M. Glass, A. M. Johnson, D. H. Olsen, W. Simpson, and A. A. Ballman, Appl. Phys. Lett. 44, 948 (1984).
[Crossref]

Klein, M. B.

Kukhtarev, N. V.

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

Kumar, J.

J. Kumar, G. Albanese, W. H. Steier, and M. Ziari, Opt. Lett 12, 120 (1987).
[Crossref] [PubMed]

J. Kumar, G. Albanese, and W. H. Steier, Opt Commun. 63, 191 (1987).
[Crossref]

G. Albanese, J. Kumar, and W. H. Steir, Opt. Lett. 11, 650 (1986).
[Crossref] [PubMed]

Makram-Ebeid, S.

G. M. Martin and S. Makram-Ebeid, in Deep Centers in Semiconductors, a State-of-the-Art Approach, S. T. Pantelides, ed. (Gordon & Breach, New York, 1986), Chap. 6, pp. 399–487.

Mallick, S.

Markov, V. B.

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

Marple, D. T. F.

D. T. F. Marple, J. Appl. Phys. 35, 1241 (1964).
[Crossref]

Martin, G. M.

G. M. Martin and S. Makram-Ebeid, in Deep Centers in Semiconductors, a State-of-the-Art Approach, S. T. Pantelides, ed. (Gordon & Breach, New York, 1986), Chap. 6, pp. 399–487.

Neidert, R. E.

R. E. Neidert, Electron. Lett. 16, 244 (1980).
[Crossref]

Odulov, S. G.

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

Olsen, D. H.

A. M. Glass, A. M. Johnson, D. H. Olsen, W. Simpson, and A. A. Ballman, Appl. Phys. Lett. 44, 948 (1984).
[Crossref]

Partovi, A.

L.-J. Cheng and A. Partovi, Appl. Phys. Lett. 49, 1456 (1986).
[Crossref]

Petrov, M. P.

S. I. Stepanov and M. P. Petrov, Opt. Commun. 53, 292 (1985).
[Crossref]

S. I. Stepanov and M. P. Petrov, Sov. Tech. Phys. Lett. 10, 572 (1984).

Rajbenbach, H.

Simpson, W.

A. M. Glass, A. M. Johnson, D. H. Olsen, W. Simpson, and A. A. Ballman, Appl. Phys. Lett. 44, 948 (1984).
[Crossref]

Soskin, M. S.

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

Steier, W. H.

J. Kumar, G. Albanese, W. H. Steier, and M. Ziari, Opt. Lett 12, 120 (1987).
[Crossref] [PubMed]

J. Kumar, G. Albanese, and W. H. Steier, Opt Commun. 63, 191 (1987).
[Crossref]

Steir, W. H.

Stepanov, S. I.

S. I. Stepanov and M. P. Petrov, Opt. Commun. 53, 292 (1985).
[Crossref]

S. I. Stepanov and M. P. Petrov, Sov. Tech. Phys. Lett. 10, 572 (1984).

Sugie, M.

M. Sugie and K. Tada, Jpn. J. Appl. Phys. 15, 421 (1976).
[Crossref]

Tada, K.

M. Sugie and K. Tada, Jpn. J. Appl. Phys. 15, 421 (1976).
[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]

White, J. O.

Yariv, A.

Ziari, M.

J. Kumar, G. Albanese, W. H. Steier, and M. Ziari, Opt. Lett 12, 120 (1987).
[Crossref] [PubMed]

Appl. Phys. Lett. (2)

A. M. Glass, A. M. Johnson, D. H. Olsen, W. Simpson, and A. A. Ballman, Appl. Phys. Lett. 44, 948 (1984).
[Crossref]

L.-J. Cheng and A. Partovi, Appl. Phys. Lett. 49, 1456 (1986).
[Crossref]

Electron. Lett. (1)

R. E. Neidert, Electron. Lett. 16, 244 (1980).
[Crossref]

Ferroelectrics (1)

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

J. Appl. Phys. (2)

D. T. F. Marple, J. Appl. Phys. 35, 1241 (1964).
[Crossref]

P. Dobrilla and J. S. Blakemore, J. Appl. Phys. 58, 208 (1985).
[Crossref]

Jpn. J. Appl. Phys. (1)

M. Sugie and K. Tada, Jpn. J. Appl. Phys. 15, 421 (1976).
[Crossref]

Opt Commun. (1)

J. Kumar, G. Albanese, and W. H. Steier, Opt Commun. 63, 191 (1987).
[Crossref]

Opt. Commun. (1)

S. I. Stepanov and M. P. Petrov, Opt. Commun. 53, 292 (1985).
[Crossref]

Opt. Lett (1)

J. Kumar, G. Albanese, W. H. Steier, and M. Ziari, Opt. Lett 12, 120 (1987).
[Crossref] [PubMed]

Opt. Lett. (4)

Sov. Tech. Phys. Lett. (1)

S. I. Stepanov and M. P. Petrov, Sov. Tech. Phys. Lett. 10, 572 (1984).

Other (1)

G. M. Martin and S. Makram-Ebeid, in Deep Centers in Semiconductors, a State-of-the-Art Approach, S. T. Pantelides, ed. (Gordon & Breach, New York, 1986), Chap. 6, pp. 399–487.

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Figures (8)

Fig. 1
Fig. 1

Gain coefficient versus grating period in our sample of GaAs:EL2 at 1.06 μm, with zero applied field. The circles are measured values. The curve is a theoretical plot using Eqs. (4) and (6).

Fig. 2
Fig. 2

Measured values of gain coefficient versus intensity (at the center of the sample) in GaAs:Cr (Ref. 14) and our sample of un-doped GaAs. The curves are fits to the data using Eq. (9).

Fig. 3
Fig. 3

Calculated gain coefficient versus grating period in our sample of GaAs:EL2 at 1.06 μm for several values of ac-field amplitude.

Fig. 4
Fig. 4

Measured values of intensity gain coefficient versus grating period for four values of applied ac voltage.

Fig. 5
Fig. 5

Depleted pump solutions for the DFWM reflectivity, using the approach of Cronin-Golomb et al,16 The intensities of the backward pump and probe beams are Ib = 1 and Ip = 0.1, respectively. The solutions are essentially independent of Ip for Ip ≲ 0.1. Because Ib = 1, the horizontal axis represents the pump ratio If/Ib as well as If.

Fig. 6
Fig. 6

Measured values of DFWM reflectivity versus intensity gain coefficient–length product ΓL for If/Ib = 2.75 and Ip/Ib = 0.1. The solid curve is a theoretical curve from the model of Cronin-Golomb et al.16 modified for absorption by the factor exp(−αL) = 0.42.

Fig. 7
Fig. 7

Experimental arrangement for measurements of piston-error correction: M’s, mirrors; BS’s, beam splitters; F, filters; BE, beam-expanding telescope; V, high-voltage square-wave generator.

Fig. 8
Fig. 8

Interference patterns of input probe beam and conjugate return beam for two values of relative phase delay.

Equations (11)

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τ T τ R .
E ¯ sc = i m E D ( 1 + τ R τ D ) + E 0 ( τ R τ E ) ( E D + E q ) ( 1 + τ R τ D ) + E 0 ( τ R τ E ) E q ,
E D = ( k T / e ) ( 2 π / Λ g ) , E q = e N E Λ g / ( 2 π 0 ) , τ D = e Λ g 2 / ( 4 π 2 μ e k T ) ,
τ E = Λ g / ( 2 π μ e E 0 ) ,
E ¯ sc = i m E D 2 + E 0 2 ( E D + E q ) E D + E 0 2 E q .
E ¯ sc = i m E D E q E D + E q .
E ¯ sc = i m E q ,
Γ = ( 2 π n 3 r 41 / m λ ) Im ( E ¯ sc ) ,
N E = N N + / ( N + N + ) .
Γ = Γ 0 / ( 1 + σ d / σ p ) ,
Γ = Γ 0 / ( 1 + I d / I ) ,

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