Abstract

The temporal behavior of optical phase conjugation by single-grating anisotropic four-wave mixing in photorefractive crystals is studied. Numerical evidence for optical instabilities of the phase-conjugate wave amplitude is shown.

© 1989 Optical Society of America

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  1. P. Günter, Phys. Rep. 93, 199 (1982); IEEE J. Quantum Electron. QE-22(8) (1986), special issue on dynamic gratings and four-wave mixing; R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983).
    [Crossref]
  2. J. O. White, M. Cronin-Golomb, B. Fischer, and A. Yariv, Appl. Phys. Lett. 40, 450 (1962); J. Feinberg, Opt. Lett. 7, 486 (1982); K. R. McDonald and J. Feinberg, J. Opt. Soc. Am. 73, 548 (1983).
    [Crossref] [PubMed]
  3. P. Günter, E. Voit, M. Z. Zha, and J. Albers, Opt. Commun. 55, 210 (1985).
    [Crossref]
  4. A. M. C. Smout, R. W. Eason, and M. C. Gower, Opt. Commun. 59, 77 (1986).
    [Crossref]
  5. D. J. Gauthier, P. Narum, and R. W. Boyd, Phys. Rev. Lett. 58, 1640 (1987).
    [Crossref] [PubMed]
  6. Y. Silberberg and I. Bar Joseph, Phys. Rev. Lett. 48, 1541 (1982); J. Opt. Soc. Am. B 1, 662 (1984).
    [Crossref]
  7. S. I. Stepanov and M. P. Petrov, Opt. Commun. 53, 64 (1985); A. Błȩdowski and W. Królikowski, IEEE J. Quantum Electon. QE-24, 652 (1988); H. Kong, C. Lin, A. M. Biernacki, and M. Cronin-Golomb, Opt. Lett. 13, 324 (1988).
    [Crossref] [PubMed]
  8. N. V. Kukhtarev, V. Markov, and C. Odulov, Opt. Commun. 23, 338 (1977).
    [Crossref]
  9. R. R. Neurgaonkar and W. K. Cory, J. Opt. Soc. Am. B 3, 274 (1986).
    [Crossref]
  10. M. Cronin-Golomb, B. Fischer, J. White, and A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
    [Crossref]
  11. G. Costabile, S. Pagano, and R. D. Parmentier, Phys. Rev. B 25, 5225 (1987).
    [Crossref]
  12. Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, J. Appl. Phys. 58, 45 (1985). S. I. Stepanov and M. P. Petrov, Opt. Commun. 53, 292 (1985).
    [Crossref]
  13. B. Imbert, H. Rajbenbach, S. Mallick, J. P. Herriau, and J. P. Huignard, Opt. Lett. 13, 327 (1988).
    [Crossref] [PubMed]

1988 (1)

1987 (2)

G. Costabile, S. Pagano, and R. D. Parmentier, Phys. Rev. B 25, 5225 (1987).
[Crossref]

D. J. Gauthier, P. Narum, and R. W. Boyd, Phys. Rev. Lett. 58, 1640 (1987).
[Crossref] [PubMed]

1986 (2)

A. M. C. Smout, R. W. Eason, and M. C. Gower, Opt. Commun. 59, 77 (1986).
[Crossref]

R. R. Neurgaonkar and W. K. Cory, J. Opt. Soc. Am. B 3, 274 (1986).
[Crossref]

1985 (3)

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, J. Appl. Phys. 58, 45 (1985). S. I. Stepanov and M. P. Petrov, Opt. Commun. 53, 292 (1985).
[Crossref]

P. Günter, E. Voit, M. Z. Zha, and J. Albers, Opt. Commun. 55, 210 (1985).
[Crossref]

S. I. Stepanov and M. P. Petrov, Opt. Commun. 53, 64 (1985); A. Błȩdowski and W. Królikowski, IEEE J. Quantum Electon. QE-24, 652 (1988); H. Kong, C. Lin, A. M. Biernacki, and M. Cronin-Golomb, Opt. Lett. 13, 324 (1988).
[Crossref] [PubMed]

1984 (1)

M. Cronin-Golomb, B. Fischer, J. White, and A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[Crossref]

1982 (2)

Y. Silberberg and I. Bar Joseph, Phys. Rev. Lett. 48, 1541 (1982); J. Opt. Soc. Am. B 1, 662 (1984).
[Crossref]

P. Günter, Phys. Rep. 93, 199 (1982); IEEE J. Quantum Electron. QE-22(8) (1986), special issue on dynamic gratings and four-wave mixing; R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983).
[Crossref]

1977 (1)

N. V. Kukhtarev, V. Markov, and C. Odulov, Opt. Commun. 23, 338 (1977).
[Crossref]

1962 (1)

J. O. White, M. Cronin-Golomb, B. Fischer, and A. Yariv, Appl. Phys. Lett. 40, 450 (1962); J. Feinberg, Opt. Lett. 7, 486 (1982); K. R. McDonald and J. Feinberg, J. Opt. Soc. Am. 73, 548 (1983).
[Crossref] [PubMed]

Albers, J.

P. Günter, E. Voit, M. Z. Zha, and J. Albers, Opt. Commun. 55, 210 (1985).
[Crossref]

Bar Joseph, I.

Y. Silberberg and I. Bar Joseph, Phys. Rev. Lett. 48, 1541 (1982); J. Opt. Soc. Am. B 1, 662 (1984).
[Crossref]

Boyd, R. W.

D. J. Gauthier, P. Narum, and R. W. Boyd, Phys. Rev. Lett. 58, 1640 (1987).
[Crossref] [PubMed]

Cory, W. K.

Costabile, G.

G. Costabile, S. Pagano, and R. D. Parmentier, Phys. Rev. B 25, 5225 (1987).
[Crossref]

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fischer, J. White, and A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[Crossref]

J. O. White, M. Cronin-Golomb, B. Fischer, and A. Yariv, Appl. Phys. Lett. 40, 450 (1962); J. Feinberg, Opt. Lett. 7, 486 (1982); K. R. McDonald and J. Feinberg, J. Opt. Soc. Am. 73, 548 (1983).
[Crossref] [PubMed]

Eason, R. W.

A. M. C. Smout, R. W. Eason, and M. C. Gower, Opt. Commun. 59, 77 (1986).
[Crossref]

Fischer, B.

M. Cronin-Golomb, B. Fischer, J. White, and A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[Crossref]

J. O. White, M. Cronin-Golomb, B. Fischer, and A. Yariv, Appl. Phys. Lett. 40, 450 (1962); J. Feinberg, Opt. Lett. 7, 486 (1982); K. R. McDonald and J. Feinberg, J. Opt. Soc. Am. 73, 548 (1983).
[Crossref] [PubMed]

Gauthier, D. J.

D. J. Gauthier, P. Narum, and R. W. Boyd, Phys. Rev. Lett. 58, 1640 (1987).
[Crossref] [PubMed]

Gower, M. C.

A. M. C. Smout, R. W. Eason, and M. C. Gower, Opt. Commun. 59, 77 (1986).
[Crossref]

Günter, P.

P. Günter, E. Voit, M. Z. Zha, and J. Albers, Opt. Commun. 55, 210 (1985).
[Crossref]

P. Günter, Phys. Rep. 93, 199 (1982); IEEE J. Quantum Electron. QE-22(8) (1986), special issue on dynamic gratings and four-wave mixing; R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983).
[Crossref]

Herriau, J. P.

Huignard, J. P.

B. Imbert, H. Rajbenbach, S. Mallick, J. P. Herriau, and J. P. Huignard, Opt. Lett. 13, 327 (1988).
[Crossref] [PubMed]

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, J. Appl. Phys. 58, 45 (1985). S. I. Stepanov and M. P. Petrov, Opt. Commun. 53, 292 (1985).
[Crossref]

Imbert, B.

Kukhtarev, N. V.

N. V. Kukhtarev, V. Markov, and C. Odulov, Opt. Commun. 23, 338 (1977).
[Crossref]

Mallick, S.

Markov, V.

N. V. Kukhtarev, V. Markov, and C. Odulov, Opt. Commun. 23, 338 (1977).
[Crossref]

Narum, P.

D. J. Gauthier, P. Narum, and R. W. Boyd, Phys. Rev. Lett. 58, 1640 (1987).
[Crossref] [PubMed]

Neurgaonkar, R. R.

Odulov, C.

N. V. Kukhtarev, V. Markov, and C. Odulov, Opt. Commun. 23, 338 (1977).
[Crossref]

Pagano, S.

G. Costabile, S. Pagano, and R. D. Parmentier, Phys. Rev. B 25, 5225 (1987).
[Crossref]

Parmentier, R. D.

G. Costabile, S. Pagano, and R. D. Parmentier, Phys. Rev. B 25, 5225 (1987).
[Crossref]

Petrov, M. P.

S. I. Stepanov and M. P. Petrov, Opt. Commun. 53, 64 (1985); A. Błȩdowski and W. Królikowski, IEEE J. Quantum Electon. QE-24, 652 (1988); H. Kong, C. Lin, A. M. Biernacki, and M. Cronin-Golomb, Opt. Lett. 13, 324 (1988).
[Crossref] [PubMed]

Rajbenbach, H.

B. Imbert, H. Rajbenbach, S. Mallick, J. P. Herriau, and J. P. Huignard, Opt. Lett. 13, 327 (1988).
[Crossref] [PubMed]

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, J. Appl. Phys. 58, 45 (1985). S. I. Stepanov and M. P. Petrov, Opt. Commun. 53, 292 (1985).
[Crossref]

Refregier, Ph.

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, J. Appl. Phys. 58, 45 (1985). S. I. Stepanov and M. P. Petrov, Opt. Commun. 53, 292 (1985).
[Crossref]

Silberberg, Y.

Y. Silberberg and I. Bar Joseph, Phys. Rev. Lett. 48, 1541 (1982); J. Opt. Soc. Am. B 1, 662 (1984).
[Crossref]

Smout, A. M. C.

A. M. C. Smout, R. W. Eason, and M. C. Gower, Opt. Commun. 59, 77 (1986).
[Crossref]

Solymar, L.

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, J. Appl. Phys. 58, 45 (1985). S. I. Stepanov and M. P. Petrov, Opt. Commun. 53, 292 (1985).
[Crossref]

Stepanov, S. I.

S. I. Stepanov and M. P. Petrov, Opt. Commun. 53, 64 (1985); A. Błȩdowski and W. Królikowski, IEEE J. Quantum Electon. QE-24, 652 (1988); H. Kong, C. Lin, A. M. Biernacki, and M. Cronin-Golomb, Opt. Lett. 13, 324 (1988).
[Crossref] [PubMed]

Voit, E.

P. Günter, E. Voit, M. Z. Zha, and J. Albers, Opt. Commun. 55, 210 (1985).
[Crossref]

White, J.

M. Cronin-Golomb, B. Fischer, J. White, and A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[Crossref]

White, J. O.

J. O. White, M. Cronin-Golomb, B. Fischer, and A. Yariv, Appl. Phys. Lett. 40, 450 (1962); J. Feinberg, Opt. Lett. 7, 486 (1982); K. R. McDonald and J. Feinberg, J. Opt. Soc. Am. 73, 548 (1983).
[Crossref] [PubMed]

Yariv, A.

M. Cronin-Golomb, B. Fischer, J. White, and A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[Crossref]

J. O. White, M. Cronin-Golomb, B. Fischer, and A. Yariv, Appl. Phys. Lett. 40, 450 (1962); J. Feinberg, Opt. Lett. 7, 486 (1982); K. R. McDonald and J. Feinberg, J. Opt. Soc. Am. 73, 548 (1983).
[Crossref] [PubMed]

Zha, M. Z.

P. Günter, E. Voit, M. Z. Zha, and J. Albers, Opt. Commun. 55, 210 (1985).
[Crossref]

Appl. Phys. Lett. (1)

J. O. White, M. Cronin-Golomb, B. Fischer, and A. Yariv, Appl. Phys. Lett. 40, 450 (1962); J. Feinberg, Opt. Lett. 7, 486 (1982); K. R. McDonald and J. Feinberg, J. Opt. Soc. Am. 73, 548 (1983).
[Crossref] [PubMed]

IEEE J. Quantum Electron. (1)

M. Cronin-Golomb, B. Fischer, J. White, and A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[Crossref]

J. Appl. Phys. (1)

Ph. Refregier, L. Solymar, H. Rajbenbach, and J. P. Huignard, J. Appl. Phys. 58, 45 (1985). S. I. Stepanov and M. P. Petrov, Opt. Commun. 53, 292 (1985).
[Crossref]

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

Opt. Commun. (4)

S. I. Stepanov and M. P. Petrov, Opt. Commun. 53, 64 (1985); A. Błȩdowski and W. Królikowski, IEEE J. Quantum Electon. QE-24, 652 (1988); H. Kong, C. Lin, A. M. Biernacki, and M. Cronin-Golomb, Opt. Lett. 13, 324 (1988).
[Crossref] [PubMed]

N. V. Kukhtarev, V. Markov, and C. Odulov, Opt. Commun. 23, 338 (1977).
[Crossref]

P. Günter, E. Voit, M. Z. Zha, and J. Albers, Opt. Commun. 55, 210 (1985).
[Crossref]

A. M. C. Smout, R. W. Eason, and M. C. Gower, Opt. Commun. 59, 77 (1986).
[Crossref]

Opt. Lett. (1)

Phys. Rep. (1)

P. Günter, Phys. Rep. 93, 199 (1982); IEEE J. Quantum Electron. QE-22(8) (1986), special issue on dynamic gratings and four-wave mixing; R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983).
[Crossref]

Phys. Rev. B (1)

G. Costabile, S. Pagano, and R. D. Parmentier, Phys. Rev. B 25, 5225 (1987).
[Crossref]

Phys. Rev. Lett. (2)

D. J. Gauthier, P. Narum, and R. W. Boyd, Phys. Rev. Lett. 58, 1640 (1987).
[Crossref] [PubMed]

Y. Silberberg and I. Bar Joseph, Phys. Rev. Lett. 48, 1541 (1982); J. Opt. Soc. Am. B 1, 662 (1984).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1

Geometry of the 4WM interaction.

Fig. 2
Fig. 2

Possible crystal orientation for anisotropic 4WM (point symmetry group 23 or 43 ¯ m). Waves A1 and A2 are polarized along the aa axis, and A2 and A3 along the bb axis.

Fig. 3
Fig. 3

Steady-state phase-conjugate intensity I3 versus incident intensity I40.

Fig. 4
Fig. 4

Temporal behavior of the phase-conjugate amplitude after step input of intensity I40: (a) I40 = 2.4, (b) I40 = 2.85, (c) I40 = 3.0, (d) I40 = 3.23, (e) I40 = 3.242, (f) I40 =3.246. Coupling strength, γL = 10; pump ratio, I2L/I10 = 30. Time is normalized to the time constant τ.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

z A 1 = Q A 4 ,
z A 2 * = - Q A 3 * ,
z A 3 = Q A 2 ,
z A 4 * = - Q A 1 * ,
τ t Q + Q = ( γ / I 0 ) ( A 1 A 4 * + A 2 * A 3 ) ,
Q ( z , t ) = q ( z , t ) exp ( i ) ,             = φ 10 - φ 40 ,
A 1 ( z , t ) = A 10 cos θ + A 40 sin θ ,
A 2 ( z , t ) = A 2 L cos ( θ L - θ ) ,
A 3 ( z , t ) = - A 2 L sin ( θ L - θ ) ,
A 4 ( z , t ) = - A 10 sin θ + A 40 cos θ ,
θ ( z , t ) = 0 z q ( z , t ) d z ,             θ L = θ ( L , t ) .
τ t z 2 2 θ + z 2 θ = C sin ( 2 θ + β ) .
C = ( γ / I 0 ) { ( I 10 + I 40 ) 2 + I 2 L 2 + 2 I 2 L [ ( I 40 - I 10 ) cos 2 θ L - 2 ( I 10 I 40 ) 1 / 2 sin 2 θ L ] } 1 / 2 ,
tan β = 2 ( I 10 I 40 ) 1 / 2 - I 2 L sin 2 θ L I 40 - I 10 + I 2 L cos 2 θ L ,

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