Abstract

A mutually pumped phase-conjugate mirror based on a bidirectional ring oscillator in a single photorefractive crystal has been studied theoretically and experimentally. This system has a significantly increased operating range and a lower threshold coupling strength compared with other types of mutually pumped conjugators. High-quality mutual phase conjugation without cross talk has been demonstrated in experiments in a single barium titanate crystal. Both stable and unstable regimes of operation have been observed. A theoretical model of this conjugator based on a six-wave mixing process in the photorefractive material has been developed. Good agreement between theory and experiment has been achieved.

© 1994 Optical Society of America

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1989 (1)

D. Wang, Z. Zhang, Y. Zhu, S. Zhang, and P. Ye, Opt. Commun. 73, 495 (1989).
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1988 (3)

1987 (3)

1985 (4)

Ph. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, J. Appl. Phys. 58, 45 (1985); J. Kumar, G. Albanese, W. H. Steir, and M. Ziari, Opt. Lett. 12, 120 (1987).
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[Crossref]

P. Yeh, J. Opt. Soc. Am. B 2, 1924 (1985).
[Crossref]

H. Rajbenbach and J.-P. Huinard, Opt. Lett. 10, 137 (1985).
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1984 (1)

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984); Q. B. He, P. Yeh, C. Gu, and R. R. Neurgaonkar, J. Opt. Soc. Am. B 9, 114 (1992).
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1979 (1)

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

Caulfield, H. J.

Chang, T. Y.

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984); Q. B. He, P. Yeh, C. Gu, and R. R. Neurgaonkar, J. Opt. Soc. Am. B 9, 114 (1992).
[Crossref]

Eason, R. W.

Ewbank, M. D.

Feinberg, J.

Fischer, B.

S. Weiss, S. Sternklar, and B. Fischer, Opt. Lett. 12, 114 (1987).
[Crossref] [PubMed]

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984); Q. B. He, P. Yeh, C. Gu, and R. R. Neurgaonkar, J. Opt. Soc. Am. B 9, 114 (1992).
[Crossref]

Heaton, J. M.

J. M. Heaton and L. Solymar, Opt. Acta 32, 397 (1985); L. Soylmar and J. M. Heaton, Opt. Commun. 51, 76 (1984).
[Crossref]

Hendrickson, B. M.

Huignard, J.-P.

Ph. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, J. Appl. Phys. 58, 45 (1985); J. Kumar, G. Albanese, W. H. Steir, and M. Ziari, Opt. Lett. 12, 120 (1987).
[Crossref] [PubMed]

Huinard, J.-P.

Kukhtarev, N. V.

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

Markov, V. B.

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

Neurgoankar, R. R.

Odulov, S. G.

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

Rajbenbach, H.

Ph. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, J. Appl. Phys. 58, 45 (1985); J. Kumar, G. Albanese, W. H. Steir, and M. Ziari, Opt. Lett. 12, 120 (1987).
[Crossref] [PubMed]

H. Rajbenbach and J.-P. Huinard, Opt. Lett. 10, 137 (1985).
[Crossref] [PubMed]

Réfrégier, Ph.

Ph. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, J. Appl. Phys. 58, 45 (1985); J. Kumar, G. Albanese, W. H. Steir, and M. Ziari, Opt. Lett. 12, 120 (1987).
[Crossref] [PubMed]

Shamir, J.

Smout, A. M.

Solymar, L.

J. M. Heaton and L. Solymar, Opt. Acta 32, 397 (1985); L. Soylmar and J. M. Heaton, Opt. Commun. 51, 76 (1984).
[Crossref]

Ph. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, J. Appl. Phys. 58, 45 (1985); J. Kumar, G. Albanese, W. H. Steir, and M. Ziari, Opt. Lett. 12, 120 (1987).
[Crossref] [PubMed]

Soskin, M. S.

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

Sternklar, S.

Vazquez, R. A.

Vinetskii, V. L.

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

Wang, D.

Weiss, S.

White, J. O.

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984); Q. B. He, P. Yeh, C. Gu, and R. R. Neurgaonkar, J. Opt. Soc. Am. B 9, 114 (1992).
[Crossref]

Wu, X.

Yariv, A.

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984); Q. B. He, P. Yeh, C. Gu, and R. R. Neurgaonkar, J. Opt. Soc. Am. B 9, 114 (1992).
[Crossref]

Ye, P.

Yeh, P.

Zhang, S.

D. Wang, Z. Zhang, Y. Zhu, S. Zhang, and P. Ye, Opt. Commun. 73, 495 (1989).
[Crossref]

Zhang, Z.

Zhu, Y.

D. Wang, Z. Zhang, Y. Zhu, S. Zhang, and P. Ye, Opt. Commun. 73, 495 (1989).
[Crossref]

Appl. Opt. (1)

Ferroelectrics (1)

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

IEEE J. Quantum Electron. (1)

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984); Q. B. He, P. Yeh, C. Gu, and R. R. Neurgaonkar, J. Opt. Soc. Am. B 9, 114 (1992).
[Crossref]

J. Appl. Phys. (1)

Ph. Réfrégier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, J. Appl. Phys. 58, 45 (1985); J. Kumar, G. Albanese, W. H. Steir, and M. Ziari, Opt. Lett. 12, 120 (1987).
[Crossref] [PubMed]

J. Opt. Soc. Am. B (4)

Opt. Acta (1)

J. M. Heaton and L. Solymar, Opt. Acta 32, 397 (1985); L. Soylmar and J. M. Heaton, Opt. Commun. 51, 76 (1984).
[Crossref]

Opt. Commun. (1)

D. Wang, Z. Zhang, Y. Zhu, S. Zhang, and P. Ye, Opt. Commun. 73, 495 (1989).
[Crossref]

Opt. Lett. (5)

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of the mutual phase conjugator with a bidirectional ring resonator geometry.

Fig. 2
Fig. 2

Phase conjugate reflectivity versus coupling strength for several values of the cavity reflectivity and absorption.

Fig. 3
Fig. 3

Phase-conjugate reflectivities as a function of the input pump ratio for several values of the cavity reflectivity.

Fig. 4
Fig. 4

Comparison of the phase-conjugate reflectivity of the ring phase conjugator and the DPCM.

Fig. 5
Fig. 5

Theoretically predicted temporal instabilities of the phase-conjugate signal in the case of asymmetric coupling and nonzero phase shift: γ1 = 2.7, γ2 = 2.5, γ3 = 1.66, ϕ = 52°.

Fig. 6
Fig. 6

Experimental setup. L1–L4, lenses; M1–M5, mirrors; BS, beam splitter; T1, T2, image-bearing transparencies; PZT, piezoelectric transducer.

Fig. 7
Fig. 7

Results of the phase-conjugate reflectivity measurements as a function of the incident pump ratio (Ip1/Ip2).

Fig. 8
Fig. 8

Experimental verification of the fidelity of the phase-conjugation process: (a), (b) two input signals; (c), (d) two output phase-conjugate signals.

Fig. 9
Fig. 9

Experimentally recorded temporal instabilities of the phase-conjugate intensity. Asymmetric coupling case: θ = 105°, θ1 = θ2 = 45°.

Equations (11)

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A osc 1 z = Q 1 A p 1 - Q 3 * A pc 2 - α A osc 1 ,
A p 1 * z = - Q 1 A osc 1 * - Q 2 A pc 2 * - α A p 1 * ,
A pc 2 z = Q 2 A p 1 + Q 3 A osc 1 - α A pc 2 ,
A osc 2 z = - Q 3 A p 2 + Q 1 * A pc 1 + α A osc 2 ,
A p 2 * z = Q 3 A osc 2 * + Q 2 A pc 1 * + α A p 2 * ,
A pc 1 z = - Q 2 A p 2 - Q 1 A osc 2 + α A pc 1 ,
Q 1 t + Q 1 τ = γ 1 A osc 1 A p 1 * + A osc 2 * A pc 1 I 0 τ ,
Q 2 t + Q 2 τ = γ 2 A pc 2 A p 1 * + A pc 1 A p 2 * I 0 τ ,
Q 3 t + Q 3 τ = γ 3 A pc 2 A osc 1 * + A osc 2 A p 2 * I 0 τ ,
I 0 = A p 1 2 + A p 2 2 + A osc 1 2 + A osc 2 2 + A pc 1 2 + A pc 1 2 ,
A p 1 ( 0 ) = A p 10 , A p 2 ( L ) = A p 20 , A pc 2 ( 0 ) = 0 , A pc 1 ( L ) = 0 , A osc 1 ( 0 ) = A osc 1 ( L ) R exp ( i ϕ ) , A osc 2 ( L ) = A osc 2 ( 0 ) R exp ( i ϕ ) ,

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