Abstract

A coupled-mode theory is developed for photorefractive hologram sharing in mutually pumped phase conjugators. The theory shows that the spatial gain coefficients for the mutually conjugated beams are twice as large as those of other scattered beams.

© 1989 Optical Society of America

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References

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  1. S. Weiss, S. Sternklar, B. Fischer, “Double Phase-Conjugate Mirror: Analysis, Demonstration, and Applications,” Opt. Lett. 12, 114–116 (1987).
    [CrossRef] [PubMed]
  2. M. D. Ewbank, “Incoherent Beams Sharing Photorefractive Holograms,” in Technical Digest, Topical Meeting on Photorefractive Materials, Effects, and Devices, Vol. 17 (Optical Society of America, Washington DC, 1987), pp. 179–182.
  3. R. W. Eason, A. M. C. Smout, “Bistability and Noncommutative Behavior of Multiple-Beam Self-Pulsing and Self-Pumping in BaTiO3,” Opt. Lett. 12, 51–53 (1987); A. M. C. Smout, R. W. Eason, “Analysis of Mutually Incoherent Beam Coupling in BaTiO3,” Opt. Lett. 12, 498–500 (1987).
    [CrossRef] [PubMed]
  4. M. D. Ewbank, “Mechanism for Photorefractive Phase Conjugation Using Incoherent Beams,” Opt. Lett. 13, 47–49 (1988).
    [CrossRef] [PubMed]
  5. M. Cronin-Golomb, Ph.D. Dissertation (Caltech, 1983).
  6. M. D. Ewbank, J. Feinberg (Rockwell International) and (U. Southern California); private communication.
  7. P. Yeh, T. Y. Chang, M. D. Ewbank, “Model for Mutually Pumped Phase Conjugation,” J. Opt. Soc. Am. 5, 1743–1750 (1988).
    [CrossRef]
  8. B. Ya. Zeldovich, V. I. Popovichev, V. V. Ragulskii, F. S. Faizullov, “Connection Between the Wavefronts of the Reflect ed and Exciting in SBS,” Zh Ekap. Teor. Fiz. Pis. Red. 15, 160–163 (1972) [JETP Lett. 15, 109–112 (1972)].
  9. R. W. Hellwarth, “Theory of Phase Conjugation by Stimulated Scattering in a Waveguide,” J. Opt. Soc. Am. 68, 1050–1056 (1978).
    [CrossRef]
  10. B. Ya. Zeldovich, N. F. Pilipetskii, V. V. Shkunov, Optical Phase Conjugation (Academic, New York, 1983), pp. 135–167.
  11. F. Laeri, T. Tschudi, J. Albers, “Coherent cw Image Amplifiers and Oscillators Using Two-Wave Interaction in a BaTiO3 Crystal,” Opt. Comm. 47, 387–390 (1983).
    [CrossRef]
  12. See, for example, A. Yariv, P. Yeh, “Optical Waves in Crystals,” (Wiley, New York, 1984), p. 52.

1988

M. D. Ewbank, “Mechanism for Photorefractive Phase Conjugation Using Incoherent Beams,” Opt. Lett. 13, 47–49 (1988).
[CrossRef] [PubMed]

P. Yeh, T. Y. Chang, M. D. Ewbank, “Model for Mutually Pumped Phase Conjugation,” J. Opt. Soc. Am. 5, 1743–1750 (1988).
[CrossRef]

1987

1983

F. Laeri, T. Tschudi, J. Albers, “Coherent cw Image Amplifiers and Oscillators Using Two-Wave Interaction in a BaTiO3 Crystal,” Opt. Comm. 47, 387–390 (1983).
[CrossRef]

1978

1972

B. Ya. Zeldovich, V. I. Popovichev, V. V. Ragulskii, F. S. Faizullov, “Connection Between the Wavefronts of the Reflect ed and Exciting in SBS,” Zh Ekap. Teor. Fiz. Pis. Red. 15, 160–163 (1972) [JETP Lett. 15, 109–112 (1972)].

Albers, J.

F. Laeri, T. Tschudi, J. Albers, “Coherent cw Image Amplifiers and Oscillators Using Two-Wave Interaction in a BaTiO3 Crystal,” Opt. Comm. 47, 387–390 (1983).
[CrossRef]

Chang, T. Y.

P. Yeh, T. Y. Chang, M. D. Ewbank, “Model for Mutually Pumped Phase Conjugation,” J. Opt. Soc. Am. 5, 1743–1750 (1988).
[CrossRef]

Cronin-Golomb, M.

M. Cronin-Golomb, Ph.D. Dissertation (Caltech, 1983).

Eason, R. W.

Ewbank, M. D.

P. Yeh, T. Y. Chang, M. D. Ewbank, “Model for Mutually Pumped Phase Conjugation,” J. Opt. Soc. Am. 5, 1743–1750 (1988).
[CrossRef]

M. D. Ewbank, “Mechanism for Photorefractive Phase Conjugation Using Incoherent Beams,” Opt. Lett. 13, 47–49 (1988).
[CrossRef] [PubMed]

M. D. Ewbank, J. Feinberg (Rockwell International) and (U. Southern California); private communication.

M. D. Ewbank, “Incoherent Beams Sharing Photorefractive Holograms,” in Technical Digest, Topical Meeting on Photorefractive Materials, Effects, and Devices, Vol. 17 (Optical Society of America, Washington DC, 1987), pp. 179–182.

Faizullov, F. S.

B. Ya. Zeldovich, V. I. Popovichev, V. V. Ragulskii, F. S. Faizullov, “Connection Between the Wavefronts of the Reflect ed and Exciting in SBS,” Zh Ekap. Teor. Fiz. Pis. Red. 15, 160–163 (1972) [JETP Lett. 15, 109–112 (1972)].

Feinberg, J.

M. D. Ewbank, J. Feinberg (Rockwell International) and (U. Southern California); private communication.

Fischer, B.

Hellwarth, R. W.

Laeri, F.

F. Laeri, T. Tschudi, J. Albers, “Coherent cw Image Amplifiers and Oscillators Using Two-Wave Interaction in a BaTiO3 Crystal,” Opt. Comm. 47, 387–390 (1983).
[CrossRef]

Pilipetskii, N. F.

B. Ya. Zeldovich, N. F. Pilipetskii, V. V. Shkunov, Optical Phase Conjugation (Academic, New York, 1983), pp. 135–167.

Popovichev, V. I.

B. Ya. Zeldovich, V. I. Popovichev, V. V. Ragulskii, F. S. Faizullov, “Connection Between the Wavefronts of the Reflect ed and Exciting in SBS,” Zh Ekap. Teor. Fiz. Pis. Red. 15, 160–163 (1972) [JETP Lett. 15, 109–112 (1972)].

Ragulskii, V. V.

B. Ya. Zeldovich, V. I. Popovichev, V. V. Ragulskii, F. S. Faizullov, “Connection Between the Wavefronts of the Reflect ed and Exciting in SBS,” Zh Ekap. Teor. Fiz. Pis. Red. 15, 160–163 (1972) [JETP Lett. 15, 109–112 (1972)].

Shkunov, V. V.

B. Ya. Zeldovich, N. F. Pilipetskii, V. V. Shkunov, Optical Phase Conjugation (Academic, New York, 1983), pp. 135–167.

Smout, A. M. C.

Sternklar, S.

Tschudi, T.

F. Laeri, T. Tschudi, J. Albers, “Coherent cw Image Amplifiers and Oscillators Using Two-Wave Interaction in a BaTiO3 Crystal,” Opt. Comm. 47, 387–390 (1983).
[CrossRef]

Weiss, S.

Yariv, A.

See, for example, A. Yariv, P. Yeh, “Optical Waves in Crystals,” (Wiley, New York, 1984), p. 52.

Yeh, P.

P. Yeh, T. Y. Chang, M. D. Ewbank, “Model for Mutually Pumped Phase Conjugation,” J. Opt. Soc. Am. 5, 1743–1750 (1988).
[CrossRef]

See, for example, A. Yariv, P. Yeh, “Optical Waves in Crystals,” (Wiley, New York, 1984), p. 52.

Zeldovich, B. Ya.

B. Ya. Zeldovich, V. I. Popovichev, V. V. Ragulskii, F. S. Faizullov, “Connection Between the Wavefronts of the Reflect ed and Exciting in SBS,” Zh Ekap. Teor. Fiz. Pis. Red. 15, 160–163 (1972) [JETP Lett. 15, 109–112 (1972)].

B. Ya. Zeldovich, N. F. Pilipetskii, V. V. Shkunov, Optical Phase Conjugation (Academic, New York, 1983), pp. 135–167.

J. Opt. Soc. Am.

P. Yeh, T. Y. Chang, M. D. Ewbank, “Model for Mutually Pumped Phase Conjugation,” J. Opt. Soc. Am. 5, 1743–1750 (1988).
[CrossRef]

R. W. Hellwarth, “Theory of Phase Conjugation by Stimulated Scattering in a Waveguide,” J. Opt. Soc. Am. 68, 1050–1056 (1978).
[CrossRef]

Opt. Comm.

F. Laeri, T. Tschudi, J. Albers, “Coherent cw Image Amplifiers and Oscillators Using Two-Wave Interaction in a BaTiO3 Crystal,” Opt. Comm. 47, 387–390 (1983).
[CrossRef]

Opt. Lett.

Zh Ekap. Teor. Fiz. Pis. Red.

B. Ya. Zeldovich, V. I. Popovichev, V. V. Ragulskii, F. S. Faizullov, “Connection Between the Wavefronts of the Reflect ed and Exciting in SBS,” Zh Ekap. Teor. Fiz. Pis. Red. 15, 160–163 (1972) [JETP Lett. 15, 109–112 (1972)].

Other

M. D. Ewbank, “Incoherent Beams Sharing Photorefractive Holograms,” in Technical Digest, Topical Meeting on Photorefractive Materials, Effects, and Devices, Vol. 17 (Optical Society of America, Washington DC, 1987), pp. 179–182.

M. Cronin-Golomb, Ph.D. Dissertation (Caltech, 1983).

M. D. Ewbank, J. Feinberg (Rockwell International) and (U. Southern California); private communication.

See, for example, A. Yariv, P. Yeh, “Optical Waves in Crystals,” (Wiley, New York, 1984), p. 52.

B. Ya. Zeldovich, N. F. Pilipetskii, V. V. Shkunov, Optical Phase Conjugation (Academic, New York, 1983), pp. 135–167.

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Figures (1)

Fig. 1
Fig. 1

Hologram sharing in photorefractive crystals.

Equations (12)

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E = j = 1 4 A j exp [ i ( w j t k j · r ) ] ,
ω 1 = ω 2 ω 3 = ω 4 .
Δ n = 1 2 n 1 exp ( i ϕ ) A 1 * A 2 exp ( i K 21 · r ) + A 3 * A 4 exp ( i K 43 · r ) I 0 + c . c .
I 0 = | A 1 | 2 + | A 2 | 2 + | A 3 | 2 + | A 4 | 2 ,
K 21 = k 2 k 1 , K 43 = k 4 k 3 ,
d d z A 1 = 1 2 γ 21 | A 2 | 2 A 1 / I 0 , d d z A 2 = 1 2 γ 21 | A 1 | 2 A 2 / I 0 , d d z A 3 = 1 2 γ 43 | A 4 | 2 A 3 / I 0 , d d z A 4 = 1 2 γ 43 | A 3 | 2 A 4 / I 0 ,
K 21 = K 43 .
d d z A 1 = 1 2 γ [ A 2 * A 1 + A 4 * A 3 ] A 2 / I 0 , d d z A 2 = 1 2 γ [ A 1 * A 2 + A 3 * A 4 ] A 1 / I 0 , d d z A 3 = 1 2 γ [ A 4 * A 3 + A 2 * A 1 ] A 4 / I 0 , d d z A 4 = 1 2 γ [ A 3 * A 3 + A 1 * A 1 ] A 3 / I 0 ,
A 4 = ρ A 1 * , A 2 = ρ A 3 * ,
d d z A 1 = γ | A 2 | 2 A 1 / I 0 , d d z A 3 = γ | A 4 | 2 A 3 / I 0 , d d z A 2 = γ | A 1 | 2 A 2 / I 0 , d d z A 4 = γ | A 3 | 2 A 4 / I 0 .
2 A + 2 i ( k · ) A = 0 .
A 2 ( 0 ) = ρ A 3 * ( 0 ) + A 2 ( 0 ) , A 4 ( L ) = ρ A 1 * ( L ) + A 4 ( L ) ,

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