Abstract

We describe the experimental measurement of phase-conjugate reflectivity versus various ratios of input-beam intensities in photorefractive barium titanate and strontium barium niobate crystals. The experimental results are compared with the theoretical prediction from the coupled-wave theory. Three different methods to measure the nonlinear coupling constant of the crystal are also presented and compared.

© 1985 Optical Society of America

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  1. M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
    [CrossRef]
  2. M. Cronin-Golomb, S. K. Kwong, A. Yariv, Appl. Phys. Lett. 44, 727 (1984).
    [CrossRef]
  3. K. R. MacDonald, J. Feinberg, J. Opt. Soc. Am. 73, 548 (1983).
    [CrossRef]
  4. J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
    [CrossRef]
  5. S. K. Kwong, A. Yariv, M. Cronin-Golomb, I. Ury (to be published).
  6. S. K. Kwong, M. Cronin-Golomb, A. Yariv, Appl. Phys. Lett. 45, 1016 (1984).
    [CrossRef]
  7. D. W. Vahey, J. Appl. Phys. 46, 3510 (1975).
    [CrossRef]
  8. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
    [CrossRef]
  9. J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
    [CrossRef]
  10. B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
    [CrossRef] [PubMed]
  11. M. Cronin-Golomb, J. O. White, B. Fischer, A. Yariv, Opt. Lett. 7, 313 (1982).
    [CrossRef] [PubMed]
  12. The theoretical curves were based on the solutions to the coupled-wave equations by M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984), where we approximated θ ≃ (θ1 + θ2)/2 in plotting these curves. This approximation will not give any significant changes in the curves since (θ1 − θ2) is only 10°.
    [CrossRef]
  13. J. O. White, Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1984, unpublished).
  14. The coupling constant γ˙l defined in this Letter does not include a geometrical factor cos θ, whereas this factor was included in the definition of the coupling constant in Refs. 10–12.
  15. The crystal absorption α was already taken into account in deriving this formula.
  16. V. V. Voronov, I. R. Dorosh, Yu. S. Kuz’minov, N. V. Tkachenko, Sov. J. Quantum Electron. 10, 1346 (1980).
    [CrossRef]
  17. J. Feinberg, J. Opt. Soc. Am. 72, 46 (1982).
    [CrossRef]
  18. In the undepleted pump approximation, we can theoretically calculate the exact amount of reflectivity lowered by the presence of crystal absorption; see Ref. 12.

1984

S. K. Kwong, M. Cronin-Golomb, A. Yariv, Appl. Phys. Lett. 45, 1016 (1984).
[CrossRef]

M. Cronin-Golomb, S. K. Kwong, A. Yariv, Appl. Phys. Lett. 44, 727 (1984).
[CrossRef]

The theoretical curves were based on the solutions to the coupled-wave equations by M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984), where we approximated θ ≃ (θ1 + θ2)/2 in plotting these curves. This approximation will not give any significant changes in the curves since (θ1 − θ2) is only 10°.
[CrossRef]

1983

1982

M. Cronin-Golomb, J. O. White, B. Fischer, A. Yariv, Opt. Lett. 7, 313 (1982).
[CrossRef] [PubMed]

J. Feinberg, J. Opt. Soc. Am. 72, 46 (1982).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

1981

1980

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

V. V. Voronov, I. R. Dorosh, Yu. S. Kuz’minov, N. V. Tkachenko, Sov. J. Quantum Electron. 10, 1346 (1980).
[CrossRef]

1979

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

1975

D. W. Vahey, J. Appl. Phys. 46, 3510 (1975).
[CrossRef]

Cronin-Golomb, M.

M. Cronin-Golomb, S. K. Kwong, A. Yariv, Appl. Phys. Lett. 44, 727 (1984).
[CrossRef]

S. K. Kwong, M. Cronin-Golomb, A. Yariv, Appl. Phys. Lett. 45, 1016 (1984).
[CrossRef]

The theoretical curves were based on the solutions to the coupled-wave equations by M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984), where we approximated θ ≃ (θ1 + θ2)/2 in plotting these curves. This approximation will not give any significant changes in the curves since (θ1 − θ2) is only 10°.
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

M. Cronin-Golomb, J. O. White, B. Fischer, A. Yariv, Opt. Lett. 7, 313 (1982).
[CrossRef] [PubMed]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
[CrossRef] [PubMed]

S. K. Kwong, A. Yariv, M. Cronin-Golomb, I. Ury (to be published).

Dorosh, I. R.

V. V. Voronov, I. R. Dorosh, Yu. S. Kuz’minov, N. V. Tkachenko, Sov. J. Quantum Electron. 10, 1346 (1980).
[CrossRef]

Feinberg, J.

Fischer, B.

The theoretical curves were based on the solutions to the coupled-wave equations by M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984), where we approximated θ ≃ (θ1 + θ2)/2 in plotting these curves. This approximation will not give any significant changes in the curves since (θ1 − θ2) is only 10°.
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

M. Cronin-Golomb, J. O. White, B. Fischer, A. Yariv, Opt. Lett. 7, 313 (1982).
[CrossRef] [PubMed]

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
[CrossRef] [PubMed]

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]

Kukhtarev, N. V.

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

Kuz’minov, Yu. S.

V. V. Voronov, I. R. Dorosh, Yu. S. Kuz’minov, N. V. Tkachenko, Sov. J. Quantum Electron. 10, 1346 (1980).
[CrossRef]

Kwong, S. K.

S. K. Kwong, M. Cronin-Golomb, A. Yariv, Appl. Phys. Lett. 45, 1016 (1984).
[CrossRef]

M. Cronin-Golomb, S. K. Kwong, A. Yariv, Appl. Phys. Lett. 44, 727 (1984).
[CrossRef]

S. K. Kwong, A. Yariv, M. Cronin-Golomb, I. Ury (to be published).

MacDonald, K. R.

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]

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]

Tkachenko, N. V.

V. V. Voronov, I. R. Dorosh, Yu. S. Kuz’minov, N. V. Tkachenko, Sov. J. Quantum Electron. 10, 1346 (1980).
[CrossRef]

Ury, I.

S. K. Kwong, A. Yariv, M. Cronin-Golomb, I. Ury (to be published).

Vahey, D. W.

D. W. Vahey, J. Appl. Phys. 46, 3510 (1975).
[CrossRef]

Vinetskii, V. L.

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

Voronov, V. V.

V. V. Voronov, I. R. Dorosh, Yu. S. Kuz’minov, N. V. Tkachenko, Sov. J. Quantum Electron. 10, 1346 (1980).
[CrossRef]

White, J. O.

The theoretical curves were based on the solutions to the coupled-wave equations by M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984), where we approximated θ ≃ (θ1 + θ2)/2 in plotting these curves. This approximation will not give any significant changes in the curves since (θ1 − θ2) is only 10°.
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

M. Cronin-Golomb, J. O. White, B. Fischer, A. Yariv, Opt. Lett. 7, 313 (1982).
[CrossRef] [PubMed]

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
[CrossRef] [PubMed]

J. O. White, Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1984, unpublished).

Yariv, A.

S. K. Kwong, M. Cronin-Golomb, A. Yariv, Appl. Phys. Lett. 45, 1016 (1984).
[CrossRef]

The theoretical curves were based on the solutions to the coupled-wave equations by M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984), where we approximated θ ≃ (θ1 + θ2)/2 in plotting these curves. This approximation will not give any significant changes in the curves since (θ1 − θ2) is only 10°.
[CrossRef]

M. Cronin-Golomb, S. K. Kwong, A. Yariv, Appl. Phys. Lett. 44, 727 (1984).
[CrossRef]

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

M. Cronin-Golomb, J. O. White, B. Fischer, A. Yariv, Opt. Lett. 7, 313 (1982).
[CrossRef] [PubMed]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
[CrossRef] [PubMed]

S. K. Kwong, A. Yariv, M. Cronin-Golomb, I. Ury (to be published).

Appl. Phys. Lett.

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

S. K. Kwong, M. Cronin-Golomb, A. Yariv, Appl. Phys. Lett. 45, 1016 (1984).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 689 (1982).
[CrossRef]

M. Cronin-Golomb, S. K. Kwong, A. Yariv, Appl. Phys. Lett. 44, 727 (1984).
[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.

The theoretical curves were based on the solutions to the coupled-wave equations by M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984), where we approximated θ ≃ (θ1 + θ2)/2 in plotting these curves. This approximation will not give any significant changes in the curves since (θ1 − θ2) is only 10°.
[CrossRef]

J. Appl. Phys.

D. W. Vahey, J. Appl. Phys. 46, 3510 (1975).
[CrossRef]

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

J. Opt. Soc. Am.

Opt. Lett.

Sov. J. Quantum Electron.

V. V. Voronov, I. R. Dorosh, Yu. S. Kuz’minov, N. V. Tkachenko, Sov. J. Quantum Electron. 10, 1346 (1980).
[CrossRef]

Other

In the undepleted pump approximation, we can theoretically calculate the exact amount of reflectivity lowered by the presence of crystal absorption; see Ref. 12.

S. K. Kwong, A. Yariv, M. Cronin-Golomb, I. Ury (to be published).

J. O. White, Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1984, unpublished).

The coupling constant γ˙l defined in this Letter does not include a geometrical factor cos θ, whereas this factor was included in the definition of the coupling constant in Refs. 10–12.

The crystal absorption α was already taken into account in deriving this formula.

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Figures (7)

Fig. 1
Fig. 1

Experimental configuration for measuring phase-conjugate reflectivity versus various beam ratios. The elements are a 10× objective, a pinhole, and a lens; λ/2, half-wave plate; PBS’s, polarizing beam splitters; P’s, polarizers; BS, beam splitter; C, crystal; M1–M6, mirrors; D1–D4, detectors.

Fig. 2
Fig. 2

The orientation of the BaTiO3 and the SBN crystals with respect to the input beams.

Fig. 3
Fig. 3

Experimental and theoretical curves of phase-conjugate reflectivity in BaTiO3 versus probe ratio at natural-log pump ratio: (a) 4.2, 2.0, −0.1, (b) −1.0, −2.0, −3.0, −4.1.

Fig. 4
Fig. 4

Experimental and theoretical curves of phase-conjugate reflectivity in SBN versus probe ratio at natural-log pump ratio: 2.0, 0.0, −2.0.

Fig. 5
Fig. 5

Experimental and theoretical curves of phase-conjugate reflectivity versus pump ratio in undepleted pump region for BaTiO3.

Fig. 6
Fig. 6

Experimental and theoretical curves of phase-conjugate reflectivity versus pump ratio in undepleted pump region for SBN.

Fig. 7
Fig. 7

Two-beam-coupling constant versus ratio of the intensities of the two input beams.

Equations (3)

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

R = | sinh ( γ ˙ l 2 cos θ 2 ) cosh ( γ ˙ l 2 cos θ 2 + ln r 2 ) | 2 .
γ ˙ l = - cos θ 2 ln r .
γ ˙ l = - 1 2 [ cos θ 1 ln I 1 ( l ) I 1 ( 0 ) + cos θ 2 ln I 4 ( 0 ) I 4 ( l ) ] .

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