Abstract

We propose and demonstrate an interferometric method to measure the spatial-frequency response of photorefractive phase conjugators with Ce:BaTiO3. Two coherent beams are incident on a crystal and form an interference pattern inside the crystal. The two beams undergo stimulated photorefractive backscattering, which creates their corresponding phase conjugations. Then the four waves interact within the crystal. The spatial-frequency resolution of the phase conjugators is measured to be as high as 3750 line pairs/mm by use of the interferometric method. There are several factors that limit the measured spatial resolution when using a U.S. Air Force Resolution Chart. The output modulation deviates from the input modulation for high spatial frequencies. In the presence of a strong additional pump beam, the output modulation of the phase conjugators is almost the same as the input modulation for a wide range of input spatial frequencies. The phase conjugator exhibits a large dynamic range of intensity. We analyze theoretically the modulation transfer function of photorefractive phase conjugators with Ce:BaTiO3 for two mutually coherent beams. The theoretical analysis is in agreement with the experimental results within a small incident-angle region.

© 1998 Optical Society of America

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  17. A. D. Meigs, B. E. A. Saleh, “Spatial fidelity of photorefractive image correlators,” IEEE J. Quantum Electron. 30, 3025–3032 (1994).
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    [CrossRef]
  19. O. L. Lyubomudrov, V. V. Shkunov, “Threshold for conjugation of speckle beams by a double phase conjugate mirror,” Sov. J. Quantum Electron. 22, 1027–1031 (1992).
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  20. B. Q. He, P. Yeh, “Multigrating competition effects in photorefractive mutually pumped phase conjugation,” J. Opt. Soc. Am. B 9, 114–120 (1992).
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  21. A. V. Mamaev, V. V. Shkunov, “Self-conjugation of a speckle pump beam in a loop containing a photorefractive crystal,” Sov. J. Quantum Electron. 22, 1036–1040 (1992).
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  24. M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems, Vol. 59 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1991).
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    [CrossRef]
  26. P. E. Andersen, P. E. Petersen, P. Buchhave, “Nonlinear combinations of gratings in drift-dominated recording in Bi12SiO20,” J. Opt. Soc. Am. B 12, 2453–2462 (1995).
    [CrossRef]
  27. P. Yeh, “Two-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–519 (1989).
    [CrossRef]
  28. J. E. Millerd, E. M. Garmire, M. B. Klein, “Investigation of photorefractive self-pumped phase-conjugate mirrors in the presence of loss and high modulation depth,” J. Opt. Soc. Am. B 9, 1499–1506 (1992).
    [CrossRef]
  29. P. Réfrégier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with a moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
    [CrossRef]
  30. F. Vachss, L. Hesselink, “Nonlinear photorefractive response at high modulation depths,” J. Opt. Soc. Am. A 5, 690–701 (1988).
    [CrossRef]
  31. L. B. Au, L. Solymar, “Higher harmonic gratings in photorefractive materials at large modulation with moving fringes,” J. Opt. Soc. Am. A 7, 1554–1561 (1990).
    [CrossRef]
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    [CrossRef]
  34. C. Yang, Y. Zhang, X. Yi, P. Yeh, Y. Zhu, M. Hui, X. Wu, “Intensity-dependent absorption and photorefractive properties in cerium-doped BaTiO3 crystals,” J. Appl. Phys. 78, 4323–4330 (1995).
    [CrossRef]
  35. M. Cronin-Golomb, “Whole beam method for photorefractive nonlinear optics,” Opt. Commun. 89, 276–282 (1992).
    [CrossRef]
  36. A. A. Zozulya, M. Saffman, D. Z. Anderson, “Propagation of light beams in photorefractive media: fanning, self-bending, and formation of self-pumped four-wave-mixing phase conjugation geometries,” Phys. Rev. Lett. 73, 818–821 (1994).
    [CrossRef] [PubMed]
  37. A. A. Zozulya, M. Saffman, D. Z. Anderson, “Double phase-conjugate mirror: convection and diffraction,” J. Opt. Soc. Am. B 12, 255–264 (1995).
    [CrossRef]

1995 (8)

C. Yang, Y. Zhu, M. Hui, X. Niu, H. Liu, X. Wu, “High efficiency self-pumped phase conjugation at 633 nm in cerium-doped barium titanate crystals,” Opt. Commun. 109, 318–321 (1995).
[CrossRef]

A. A. Zozulya, G. Montemezzani, D. Z. Anderson, “Analysis of total-internal-reflection phase conjugation mirror,” Phys. Rev. A 52, 4167–4175 (1995).
[CrossRef] [PubMed]

S. X. Dou, H. Gao, J. Zhang, Y. Lian, H. Wang, Y. Zhu, X. Wu, C. Yang, P. Ye, “Studies on formation mechanisms of self-pumped phase conjugation in BaTiO3:Ce crystals at wavelengths from 570 to 680 nm,” J. Opt. Soc. Am. B 12, 1048–1055 (1995).
[CrossRef]

S. X. Dou, J. Zhang, M. G. Wang, H. Gao, P. Ye, “Theoretical study on the effect of stimulated photorefractive backscattering in self-pumped phase conjugators,” J. Opt. Soc. Am. B 12, 1056–1064 (1995).
[CrossRef]

P. Buchhave, P. E. Andersen, P. M. Petersen, M. V. Vasnetsov, “Nonlinear grating interactions in photorefractive Bi12SiO20 crystals,” Appl. Phys. Lett. 66, 792–794 (1995).
[CrossRef]

P. E. Andersen, P. E. Petersen, P. Buchhave, “Nonlinear combinations of gratings in drift-dominated recording in Bi12SiO20,” J. Opt. Soc. Am. B 12, 2453–2462 (1995).
[CrossRef]

C. Yang, Y. Zhang, X. Yi, P. Yeh, Y. Zhu, M. Hui, X. Wu, “Intensity-dependent absorption and photorefractive properties in cerium-doped BaTiO3 crystals,” J. Appl. Phys. 78, 4323–4330 (1995).
[CrossRef]

A. A. Zozulya, M. Saffman, D. Z. Anderson, “Double phase-conjugate mirror: convection and diffraction,” J. Opt. Soc. Am. B 12, 255–264 (1995).
[CrossRef]

1994 (4)

A. A. Zozulya, M. Saffman, D. Z. Anderson, “Propagation of light beams in photorefractive media: fanning, self-bending, and formation of self-pumped four-wave-mixing phase conjugation geometries,” Phys. Rev. Lett. 73, 818–821 (1994).
[CrossRef] [PubMed]

S. Orlov, M. Segev, A. Yariv, G. C. Valley, “Conjugate fidelity and reflectivity in photorefractive double phase-conjugate mirrors,” Opt. Lett. 19, 578–580 (1994).
[CrossRef] [PubMed]

A. D. Meigs, B. E. A. Saleh, “Spatial fidelity of photorefractive image correlators,” IEEE J. Quantum Electron. 30, 3025–3032 (1994).
[CrossRef]

Y. Zhu, C. Yang, M. Hui, X. Niu, J. Zhang, T. Zhou, X. Wu, “Optical phase conjugation by stimulated backscattering in BaTiO3:Ce crystals,” Appl. Phys. Lett. 64, 2341–2343 (1994).
[CrossRef]

1993 (2)

1992 (8)

R. A. Mullen, D. J. Vickers, L. West, D. M. Pepper, “Phase conjugation by stimulated photorefractive scattering using a retroreflected seeding beam,” J. Opt. Soc. Am. B 9, 1726–1734 (1992).
[CrossRef]

J. E. Millerd, E. M. Garmire, M. B. Klein, “Investigation of photorefractive self-pumped phase-conjugate mirrors in the presence of loss and high modulation depth,” J. Opt. Soc. Am. B 9, 1499–1506 (1992).
[CrossRef]

M. Cronin-Golomb, “Whole beam method for photorefractive nonlinear optics,” Opt. Commun. 89, 276–282 (1992).
[CrossRef]

M. Carrascosa, “Photorefractive phase conjugation of an image field: fidelity analysis,” Opt. Commun. 91, 481–488 (1992);J. Ma, L. Liu, S. Wu, Z. Wang, L. Xu, B. Shu, “Multibeam coupling in photorefractive SBN:Ce,” Opt. Lett. 13, 1020–1022 (1988).
[CrossRef] [PubMed]

D. L. Naylor, P. W. Tam, R. W. Hellwarth, “Fidelity of optical phase conjugation by photorefractive degenerate four-wave mixing in barium titanate,” J. Appl. Phys. 72, 5840–5847 (1992);O. Ikeda, “Low-pass, high-pass, and bandpass spatial-filtering characteristics of a BaTiO3 phase conjugator,” J. Opt. Soc. Am. B 4, 1387–1391 (1987).
[CrossRef]

O. L. Lyubomudrov, V. V. Shkunov, “Threshold for conjugation of speckle beams by a double phase conjugate mirror,” Sov. J. Quantum Electron. 22, 1027–1031 (1992).
[CrossRef]

B. Q. He, P. Yeh, “Multigrating competition effects in photorefractive mutually pumped phase conjugation,” J. Opt. Soc. Am. B 9, 114–120 (1992).
[CrossRef]

A. V. Mamaev, V. V. Shkunov, “Self-conjugation of a speckle pump beam in a loop containing a photorefractive crystal,” Sov. J. Quantum Electron. 22, 1036–1040 (1992).
[CrossRef]

1990 (2)

H. Rajbenbach, “Digital optical processing with photorefractive materials: applications of a parallel half-adder circuit to algorithmic state machines,” J. Appl. Phys. 62, 4675–4681 (1990).
[CrossRef]

L. B. Au, L. Solymar, “Higher harmonic gratings in photorefractive materials at large modulation with moving fringes,” J. Opt. Soc. Am. A 7, 1554–1561 (1990).
[CrossRef]

1989 (2)

P. Yeh, “Two-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–519 (1989).
[CrossRef]

F. Vachss, P. Yeh, “Image-degradation mechanisms in photorefractive amplifiers,” J. Opt. Soc. Am. B 6, 1834–1844 (1989).
[CrossRef]

1988 (1)

1985 (2)

P. Réfrégier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with a moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

T. Y. Chang, R. W. Hellwarth, “Optical phase conjugation by backscattering in barium titanate,” Opt. Lett. 10, 408–430 (1985).
[CrossRef] [PubMed]

1984 (1)

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12–30 (1984).
[CrossRef]

1983 (1)

1982 (1)

1980 (1)

Andersen, P. E.

P. Buchhave, P. E. Andersen, P. M. Petersen, M. V. Vasnetsov, “Nonlinear grating interactions in photorefractive Bi12SiO20 crystals,” Appl. Phys. Lett. 66, 792–794 (1995).
[CrossRef]

P. E. Andersen, P. E. Petersen, P. Buchhave, “Nonlinear combinations of gratings in drift-dominated recording in Bi12SiO20,” J. Opt. Soc. Am. B 12, 2453–2462 (1995).
[CrossRef]

Anderson, D. Z.

A. A. Zozulya, M. Saffman, D. Z. Anderson, “Double phase-conjugate mirror: convection and diffraction,” J. Opt. Soc. Am. B 12, 255–264 (1995).
[CrossRef]

A. A. Zozulya, G. Montemezzani, D. Z. Anderson, “Analysis of total-internal-reflection phase conjugation mirror,” Phys. Rev. A 52, 4167–4175 (1995).
[CrossRef] [PubMed]

A. A. Zozulya, M. Saffman, D. Z. Anderson, “Propagation of light beams in photorefractive media: fanning, self-bending, and formation of self-pumped four-wave-mixing phase conjugation geometries,” Phys. Rev. Lett. 73, 818–821 (1994).
[CrossRef] [PubMed]

Au, L. B.

Boutsikaris, L.

Buchhave, P.

P. Buchhave, P. E. Andersen, P. M. Petersen, M. V. Vasnetsov, “Nonlinear grating interactions in photorefractive Bi12SiO20 crystals,” Appl. Phys. Lett. 66, 792–794 (1995).
[CrossRef]

P. E. Andersen, P. E. Petersen, P. Buchhave, “Nonlinear combinations of gratings in drift-dominated recording in Bi12SiO20,” J. Opt. Soc. Am. B 12, 2453–2462 (1995).
[CrossRef]

Carrascosa, M.

M. Carrascosa, “Photorefractive phase conjugation of an image field: fidelity analysis,” Opt. Commun. 91, 481–488 (1992);J. Ma, L. Liu, S. Wu, Z. Wang, L. Xu, B. Shu, “Multibeam coupling in photorefractive SBN:Ce,” Opt. Lett. 13, 1020–1022 (1988).
[CrossRef] [PubMed]

Chang, T. Y.

Cronin-Golomb, M.

M. Cronin-Golomb, “Whole beam method for photorefractive nonlinear optics,” Opt. Commun. 89, 276–282 (1992).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12–30 (1984).
[CrossRef]

Davidson, F.

Dou, S. X.

Engin, D.

Feinberg, J.

Fischer, B.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12–30 (1984).
[CrossRef]

Gao, H.

Garmire, E. M.

Günter, P.

H. Rajbenbach, J.-P. Huignard, P. Günter, “Optical processing with nonlinear photorefractive crystals,” in Nonlinear Photonics, H. M. Gibbs, G. Khitrova, N. Peyghambarian, eds. (Springer-Verlag, Berlin, 1990), Vol. 30, pp. 151–183.
[CrossRef]

He, B. Q.

Hellwarth, R. W.

D. L. Naylor, P. W. Tam, R. W. Hellwarth, “Fidelity of optical phase conjugation by photorefractive degenerate four-wave mixing in barium titanate,” J. Appl. Phys. 72, 5840–5847 (1992);O. Ikeda, “Low-pass, high-pass, and bandpass spatial-filtering characteristics of a BaTiO3 phase conjugator,” J. Opt. Soc. Am. B 4, 1387–1391 (1987).
[CrossRef]

T. Y. Chang, R. W. Hellwarth, “Optical phase conjugation by backscattering in barium titanate,” Opt. Lett. 10, 408–430 (1985).
[CrossRef] [PubMed]

Hesselink, L.

Hui, M.

C. Yang, Y. Zhang, X. Yi, P. Yeh, Y. Zhu, M. Hui, X. Wu, “Intensity-dependent absorption and photorefractive properties in cerium-doped BaTiO3 crystals,” J. Appl. Phys. 78, 4323–4330 (1995).
[CrossRef]

C. Yang, Y. Zhu, M. Hui, X. Niu, H. Liu, X. Wu, “High efficiency self-pumped phase conjugation at 633 nm in cerium-doped barium titanate crystals,” Opt. Commun. 109, 318–321 (1995).
[CrossRef]

Y. Zhu, C. Yang, M. Hui, X. Niu, J. Zhang, T. Zhou, X. Wu, “Optical phase conjugation by stimulated backscattering in BaTiO3:Ce crystals,” Appl. Phys. Lett. 64, 2341–2343 (1994).
[CrossRef]

Huignard, J.-P.

P. Réfrégier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with a moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

H. Rajbenbach, J.-P. Huignard, P. Günter, “Optical processing with nonlinear photorefractive crystals,” in Nonlinear Photonics, H. M. Gibbs, G. Khitrova, N. Peyghambarian, eds. (Springer-Verlag, Berlin, 1990), Vol. 30, pp. 151–183.
[CrossRef]

Khomenko, A. V.

M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems, Vol. 59 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1991).

Klein, M. B.

Lian, Y.

Liu, H.

C. Yang, Y. Zhu, M. Hui, X. Niu, H. Liu, X. Wu, “High efficiency self-pumped phase conjugation at 633 nm in cerium-doped barium titanate crystals,” Opt. Commun. 109, 318–321 (1995).
[CrossRef]

Lyubomudrov, O. L.

O. L. Lyubomudrov, V. V. Shkunov, “Threshold for conjugation of speckle beams by a double phase conjugate mirror,” Sov. J. Quantum Electron. 22, 1027–1031 (1992).
[CrossRef]

MacDonald, K. R.

Mamaev, A. V.

A. V. Mamaev, V. V. Shkunov, “Self-conjugation of a speckle pump beam in a loop containing a photorefractive crystal,” Sov. J. Quantum Electron. 22, 1036–1040 (1992).
[CrossRef]

Meigs, A. D.

A. D. Meigs, B. E. A. Saleh, “Spatial fidelity of photorefractive image correlators,” IEEE J. Quantum Electron. 30, 3025–3032 (1994).
[CrossRef]

Millerd, J. E.

Montemezzani, G.

A. A. Zozulya, G. Montemezzani, D. Z. Anderson, “Analysis of total-internal-reflection phase conjugation mirror,” Phys. Rev. A 52, 4167–4175 (1995).
[CrossRef] [PubMed]

Mullen, R. A.

Naylor, D. L.

D. L. Naylor, P. W. Tam, R. W. Hellwarth, “Fidelity of optical phase conjugation by photorefractive degenerate four-wave mixing in barium titanate,” J. Appl. Phys. 72, 5840–5847 (1992);O. Ikeda, “Low-pass, high-pass, and bandpass spatial-filtering characteristics of a BaTiO3 phase conjugator,” J. Opt. Soc. Am. B 4, 1387–1391 (1987).
[CrossRef]

Niu, X.

C. Yang, Y. Zhu, M. Hui, X. Niu, H. Liu, X. Wu, “High efficiency self-pumped phase conjugation at 633 nm in cerium-doped barium titanate crystals,” Opt. Commun. 109, 318–321 (1995).
[CrossRef]

Y. Zhu, C. Yang, M. Hui, X. Niu, J. Zhang, T. Zhou, X. Wu, “Optical phase conjugation by stimulated backscattering in BaTiO3:Ce crystals,” Appl. Phys. Lett. 64, 2341–2343 (1994).
[CrossRef]

Orlov, S.

Pepper, D. M.

Petersen, P. E.

Petersen, P. M.

P. Buchhave, P. E. Andersen, P. M. Petersen, M. V. Vasnetsov, “Nonlinear grating interactions in photorefractive Bi12SiO20 crystals,” Appl. Phys. Lett. 66, 792–794 (1995).
[CrossRef]

Petrov, M. P.

M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems, Vol. 59 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1991).

Rajbenbach, H.

H. Rajbenbach, “Digital optical processing with photorefractive materials: applications of a parallel half-adder circuit to algorithmic state machines,” J. Appl. Phys. 62, 4675–4681 (1990).
[CrossRef]

P. Réfrégier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with a moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

H. Rajbenbach, J.-P. Huignard, P. Günter, “Optical processing with nonlinear photorefractive crystals,” in Nonlinear Photonics, H. M. Gibbs, G. Khitrova, N. Peyghambarian, eds. (Springer-Verlag, Berlin, 1990), Vol. 30, pp. 151–183.
[CrossRef]

Réfrégier, P.

P. Réfrégier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with a moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Saffman, M.

A. A. Zozulya, M. Saffman, D. Z. Anderson, “Double phase-conjugate mirror: convection and diffraction,” J. Opt. Soc. Am. B 12, 255–264 (1995).
[CrossRef]

A. A. Zozulya, M. Saffman, D. Z. Anderson, “Propagation of light beams in photorefractive media: fanning, self-bending, and formation of self-pumped four-wave-mixing phase conjugation geometries,” Phys. Rev. Lett. 73, 818–821 (1994).
[CrossRef] [PubMed]

Saleh, B. E. A.

A. D. Meigs, B. E. A. Saleh, “Spatial fidelity of photorefractive image correlators,” IEEE J. Quantum Electron. 30, 3025–3032 (1994).
[CrossRef]

Segev, M.

Shkunov, V. V.

A. V. Mamaev, V. V. Shkunov, “Self-conjugation of a speckle pump beam in a loop containing a photorefractive crystal,” Sov. J. Quantum Electron. 22, 1036–1040 (1992).
[CrossRef]

O. L. Lyubomudrov, V. V. Shkunov, “Threshold for conjugation of speckle beams by a double phase conjugate mirror,” Sov. J. Quantum Electron. 22, 1027–1031 (1992).
[CrossRef]

Solymar, L.

L. B. Au, L. Solymar, “Higher harmonic gratings in photorefractive materials at large modulation with moving fringes,” J. Opt. Soc. Am. A 7, 1554–1561 (1990).
[CrossRef]

P. Réfrégier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with a moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Stepanov, S. I.

M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems, Vol. 59 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1991).

Tam, P. W.

D. L. Naylor, P. W. Tam, R. W. Hellwarth, “Fidelity of optical phase conjugation by photorefractive degenerate four-wave mixing in barium titanate,” J. Appl. Phys. 72, 5840–5847 (1992);O. Ikeda, “Low-pass, high-pass, and bandpass spatial-filtering characteristics of a BaTiO3 phase conjugator,” J. Opt. Soc. Am. B 4, 1387–1391 (1987).
[CrossRef]

Vachss, F.

Valley, G. C.

Vasnetsov, M. V.

P. Buchhave, P. E. Andersen, P. M. Petersen, M. V. Vasnetsov, “Nonlinear grating interactions in photorefractive Bi12SiO20 crystals,” Appl. Phys. Lett. 66, 792–794 (1995).
[CrossRef]

Vickers, D. J.

Wang, H.

Wang, M. G.

West, L.

White, J. O.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12–30 (1984).
[CrossRef]

Wu, X.

C. Yang, Y. Zhang, X. Yi, P. Yeh, Y. Zhu, M. Hui, X. Wu, “Intensity-dependent absorption and photorefractive properties in cerium-doped BaTiO3 crystals,” J. Appl. Phys. 78, 4323–4330 (1995).
[CrossRef]

S. X. Dou, H. Gao, J. Zhang, Y. Lian, H. Wang, Y. Zhu, X. Wu, C. Yang, P. Ye, “Studies on formation mechanisms of self-pumped phase conjugation in BaTiO3:Ce crystals at wavelengths from 570 to 680 nm,” J. Opt. Soc. Am. B 12, 1048–1055 (1995).
[CrossRef]

C. Yang, Y. Zhu, M. Hui, X. Niu, H. Liu, X. Wu, “High efficiency self-pumped phase conjugation at 633 nm in cerium-doped barium titanate crystals,” Opt. Commun. 109, 318–321 (1995).
[CrossRef]

Y. Zhu, C. Yang, M. Hui, X. Niu, J. Zhang, T. Zhou, X. Wu, “Optical phase conjugation by stimulated backscattering in BaTiO3:Ce crystals,” Appl. Phys. Lett. 64, 2341–2343 (1994).
[CrossRef]

Yang, C.

C. Yang, Y. Zhu, M. Hui, X. Niu, H. Liu, X. Wu, “High efficiency self-pumped phase conjugation at 633 nm in cerium-doped barium titanate crystals,” Opt. Commun. 109, 318–321 (1995).
[CrossRef]

S. X. Dou, H. Gao, J. Zhang, Y. Lian, H. Wang, Y. Zhu, X. Wu, C. Yang, P. Ye, “Studies on formation mechanisms of self-pumped phase conjugation in BaTiO3:Ce crystals at wavelengths from 570 to 680 nm,” J. Opt. Soc. Am. B 12, 1048–1055 (1995).
[CrossRef]

C. Yang, Y. Zhang, X. Yi, P. Yeh, Y. Zhu, M. Hui, X. Wu, “Intensity-dependent absorption and photorefractive properties in cerium-doped BaTiO3 crystals,” J. Appl. Phys. 78, 4323–4330 (1995).
[CrossRef]

Y. Zhu, C. Yang, M. Hui, X. Niu, J. Zhang, T. Zhou, X. Wu, “Optical phase conjugation by stimulated backscattering in BaTiO3:Ce crystals,” Appl. Phys. Lett. 64, 2341–2343 (1994).
[CrossRef]

Yariv, A.

Ye, P.

Yeh, P.

C. Yang, Y. Zhang, X. Yi, P. Yeh, Y. Zhu, M. Hui, X. Wu, “Intensity-dependent absorption and photorefractive properties in cerium-doped BaTiO3 crystals,” J. Appl. Phys. 78, 4323–4330 (1995).
[CrossRef]

B. Q. He, P. Yeh, “Multigrating competition effects in photorefractive mutually pumped phase conjugation,” J. Opt. Soc. Am. B 9, 114–120 (1992).
[CrossRef]

F. Vachss, P. Yeh, “Image-degradation mechanisms in photorefractive amplifiers,” J. Opt. Soc. Am. B 6, 1834–1844 (1989).
[CrossRef]

P. Yeh, “Two-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–519 (1989).
[CrossRef]

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993), Chap. 4.

Yi, X.

C. Yang, Y. Zhang, X. Yi, P. Yeh, Y. Zhu, M. Hui, X. Wu, “Intensity-dependent absorption and photorefractive properties in cerium-doped BaTiO3 crystals,” J. Appl. Phys. 78, 4323–4330 (1995).
[CrossRef]

Zhang, J.

Zhang, Y.

C. Yang, Y. Zhang, X. Yi, P. Yeh, Y. Zhu, M. Hui, X. Wu, “Intensity-dependent absorption and photorefractive properties in cerium-doped BaTiO3 crystals,” J. Appl. Phys. 78, 4323–4330 (1995).
[CrossRef]

Zhou, T.

Y. Zhu, C. Yang, M. Hui, X. Niu, J. Zhang, T. Zhou, X. Wu, “Optical phase conjugation by stimulated backscattering in BaTiO3:Ce crystals,” Appl. Phys. Lett. 64, 2341–2343 (1994).
[CrossRef]

Zhu, Y.

C. Yang, Y. Zhu, M. Hui, X. Niu, H. Liu, X. Wu, “High efficiency self-pumped phase conjugation at 633 nm in cerium-doped barium titanate crystals,” Opt. Commun. 109, 318–321 (1995).
[CrossRef]

S. X. Dou, H. Gao, J. Zhang, Y. Lian, H. Wang, Y. Zhu, X. Wu, C. Yang, P. Ye, “Studies on formation mechanisms of self-pumped phase conjugation in BaTiO3:Ce crystals at wavelengths from 570 to 680 nm,” J. Opt. Soc. Am. B 12, 1048–1055 (1995).
[CrossRef]

C. Yang, Y. Zhang, X. Yi, P. Yeh, Y. Zhu, M. Hui, X. Wu, “Intensity-dependent absorption and photorefractive properties in cerium-doped BaTiO3 crystals,” J. Appl. Phys. 78, 4323–4330 (1995).
[CrossRef]

Y. Zhu, C. Yang, M. Hui, X. Niu, J. Zhang, T. Zhou, X. Wu, “Optical phase conjugation by stimulated backscattering in BaTiO3:Ce crystals,” Appl. Phys. Lett. 64, 2341–2343 (1994).
[CrossRef]

Zozulya, A. A.

A. A. Zozulya, G. Montemezzani, D. Z. Anderson, “Analysis of total-internal-reflection phase conjugation mirror,” Phys. Rev. A 52, 4167–4175 (1995).
[CrossRef] [PubMed]

A. A. Zozulya, M. Saffman, D. Z. Anderson, “Double phase-conjugate mirror: convection and diffraction,” J. Opt. Soc. Am. B 12, 255–264 (1995).
[CrossRef]

A. A. Zozulya, M. Saffman, D. Z. Anderson, “Propagation of light beams in photorefractive media: fanning, self-bending, and formation of self-pumped four-wave-mixing phase conjugation geometries,” Phys. Rev. Lett. 73, 818–821 (1994).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

Y. Zhu, C. Yang, M. Hui, X. Niu, J. Zhang, T. Zhou, X. Wu, “Optical phase conjugation by stimulated backscattering in BaTiO3:Ce crystals,” Appl. Phys. Lett. 64, 2341–2343 (1994).
[CrossRef]

P. Buchhave, P. E. Andersen, P. M. Petersen, M. V. Vasnetsov, “Nonlinear grating interactions in photorefractive Bi12SiO20 crystals,” Appl. Phys. Lett. 66, 792–794 (1995).
[CrossRef]

IEEE J. Quantum Electron. (3)

P. Yeh, “Two-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–519 (1989).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. 20, 12–30 (1984).
[CrossRef]

A. D. Meigs, B. E. A. Saleh, “Spatial fidelity of photorefractive image correlators,” IEEE J. Quantum Electron. 30, 3025–3032 (1994).
[CrossRef]

J. Appl. Phys. (4)

D. L. Naylor, P. W. Tam, R. W. Hellwarth, “Fidelity of optical phase conjugation by photorefractive degenerate four-wave mixing in barium titanate,” J. Appl. Phys. 72, 5840–5847 (1992);O. Ikeda, “Low-pass, high-pass, and bandpass spatial-filtering characteristics of a BaTiO3 phase conjugator,” J. Opt. Soc. Am. B 4, 1387–1391 (1987).
[CrossRef]

H. Rajbenbach, “Digital optical processing with photorefractive materials: applications of a parallel half-adder circuit to algorithmic state machines,” J. Appl. Phys. 62, 4675–4681 (1990).
[CrossRef]

C. Yang, Y. Zhang, X. Yi, P. Yeh, Y. Zhu, M. Hui, X. Wu, “Intensity-dependent absorption and photorefractive properties in cerium-doped BaTiO3 crystals,” J. Appl. Phys. 78, 4323–4330 (1995).
[CrossRef]

P. Réfrégier, L. Solymar, H. Rajbenbach, J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with a moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (8)

J. E. Millerd, E. M. Garmire, M. B. Klein, “Investigation of photorefractive self-pumped phase-conjugate mirrors in the presence of loss and high modulation depth,” J. Opt. Soc. Am. B 9, 1499–1506 (1992).
[CrossRef]

P. E. Andersen, P. E. Petersen, P. Buchhave, “Nonlinear combinations of gratings in drift-dominated recording in Bi12SiO20,” J. Opt. Soc. Am. B 12, 2453–2462 (1995).
[CrossRef]

B. Q. He, P. Yeh, “Multigrating competition effects in photorefractive mutually pumped phase conjugation,” J. Opt. Soc. Am. B 9, 114–120 (1992).
[CrossRef]

R. A. Mullen, D. J. Vickers, L. West, D. M. Pepper, “Phase conjugation by stimulated photorefractive scattering using a retroreflected seeding beam,” J. Opt. Soc. Am. B 9, 1726–1734 (1992).
[CrossRef]

S. X. Dou, H. Gao, J. Zhang, Y. Lian, H. Wang, Y. Zhu, X. Wu, C. Yang, P. Ye, “Studies on formation mechanisms of self-pumped phase conjugation in BaTiO3:Ce crystals at wavelengths from 570 to 680 nm,” J. Opt. Soc. Am. B 12, 1048–1055 (1995).
[CrossRef]

S. X. Dou, J. Zhang, M. G. Wang, H. Gao, P. Ye, “Theoretical study on the effect of stimulated photorefractive backscattering in self-pumped phase conjugators,” J. Opt. Soc. Am. B 12, 1056–1064 (1995).
[CrossRef]

F. Vachss, P. Yeh, “Image-degradation mechanisms in photorefractive amplifiers,” J. Opt. Soc. Am. B 6, 1834–1844 (1989).
[CrossRef]

A. A. Zozulya, M. Saffman, D. Z. Anderson, “Double phase-conjugate mirror: convection and diffraction,” J. Opt. Soc. Am. B 12, 255–264 (1995).
[CrossRef]

Opt. Commun. (3)

M. Carrascosa, “Photorefractive phase conjugation of an image field: fidelity analysis,” Opt. Commun. 91, 481–488 (1992);J. Ma, L. Liu, S. Wu, Z. Wang, L. Xu, B. Shu, “Multibeam coupling in photorefractive SBN:Ce,” Opt. Lett. 13, 1020–1022 (1988).
[CrossRef] [PubMed]

C. Yang, Y. Zhu, M. Hui, X. Niu, H. Liu, X. Wu, “High efficiency self-pumped phase conjugation at 633 nm in cerium-doped barium titanate crystals,” Opt. Commun. 109, 318–321 (1995).
[CrossRef]

M. Cronin-Golomb, “Whole beam method for photorefractive nonlinear optics,” Opt. Commun. 89, 276–282 (1992).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. A (1)

A. A. Zozulya, G. Montemezzani, D. Z. Anderson, “Analysis of total-internal-reflection phase conjugation mirror,” Phys. Rev. A 52, 4167–4175 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

A. A. Zozulya, M. Saffman, D. Z. Anderson, “Propagation of light beams in photorefractive media: fanning, self-bending, and formation of self-pumped four-wave-mixing phase conjugation geometries,” Phys. Rev. Lett. 73, 818–821 (1994).
[CrossRef] [PubMed]

Sov. J. Quantum Electron. (2)

A. V. Mamaev, V. V. Shkunov, “Self-conjugation of a speckle pump beam in a loop containing a photorefractive crystal,” Sov. J. Quantum Electron. 22, 1036–1040 (1992).
[CrossRef]

O. L. Lyubomudrov, V. V. Shkunov, “Threshold for conjugation of speckle beams by a double phase conjugate mirror,” Sov. J. Quantum Electron. 22, 1027–1031 (1992).
[CrossRef]

Other (4)

See, for example, P. Günter, J.-P. Huignard, eds., Photorefractive Materials and Their Applications I Vol. 61 of Springer Series in Topics in Applied Physics (Springer-Verlag, Berlin, 1988); Photorefractive Materials and Their Applications II, Vol. 62 of Springer Series in Topics in Applied Physics (Springer-Verlag, Berlin, 1989).

H. Rajbenbach, J.-P. Huignard, P. Günter, “Optical processing with nonlinear photorefractive crystals,” in Nonlinear Photonics, H. M. Gibbs, G. Khitrova, N. Peyghambarian, eds. (Springer-Verlag, Berlin, 1990), Vol. 30, pp. 151–183.
[CrossRef]

M. P. Petrov, S. I. Stepanov, A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems, Vol. 59 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1991).

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993), Chap. 4.

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Figures (8)

Fig. 1
Fig. 1

Phase-conjugate images from a self-pumped phase conjugator with Ce:BaTiO3. (a) AFRC. (b) Roll pattern. The measured resolutions are 315 and 1200 lp/mm for an AFRC and a roll pattern, respectively.

Fig. 2
Fig. 2

Experimental setup: D, detector; BS, beam splitter; M, mirror. Laser beams are from the 514.5-nm line of an argon-ion laser. I 1 and I 2 are two coherent input beams; I 3 and I 4 are phase conjugations. θ is the half-angle between the two input beams in air.

Fig. 3
Fig. 3

Interaction of four waves in one photorefractive crystal. A 1 and A 2 are the input beams, and A 3 and A 4 are the phase conjugations. Γ is the amplitude coupling constant in the FWM region (0 ≤ zl), and γ1 and γ2 are the intensity coupling constants in the two SPB regions (lz ≤ L). K is the transmission-grating wave vector in the FWM; 2θ is the crossing angle between the two input beams; α is the angle between the c axis and the transmission-grating wave vector K.

Fig. 4
Fig. 4

Intensity ratio of phase conjugations as a function of the input intensity ratio. The crossing angles of the two input beams are θ = 8° (squares) and θ = 45° (triangles). The curves depict the theoretical simulations. The solid curve represents θ = 8°, and the dashed–dotted curve represents θ = 45°. I 1 = 440 mW/cm2.

Fig. 5
Fig. 5

Modulation of the phase-conjugate interference pattern as a function of the input spatial frequency for various input modulations M in: (a) I 1 < I 2. (b) I 1 > I 2.

Fig. 6
Fig. 6

Output modulation as a function of the input modulation. The squares represent θ = 8°, and the triangles represent θ = 45°. The curves depict the theoretical simulations. The solid curve represents θ = 8°, and the dashed curve represents θ = 45°.

Fig. 7
Fig. 7

Output modulation as a function of the input spatial frequency for various input modulations M in in the presence of a strong pump beam I o . The inset shows I o , the strong pump beam, and I 1 and I 2, two weak signal beams.

Fig. 8
Fig. 8

Output modulation as a function of the backscattering coefficient of the crystal. M in is the input modulation; β is the input intensity ratio I 2/I 1.

Equations (19)

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

D = 10   log I max I min ,
d I 1 d z 1 = - γ 1 I 1 I 4 I 1 + I 4 , d I 4 d z 1 = - γ 1 I 1 I 4 I 1 + I 4 ,
d I 2 d z 2 = - γ 2 I 2 I 3 I 2 + I 3 , d I 3 d z 2 = - γ 2 I 2 I 3 I 2 + I 3 ,
I 1 L = I 4 L , I 2 L = I 3 L ,
I 1 z = I 1 L ( 1 - / 2 + 1 - 2 / 4 + × exp - γ 1 z 1 - L 1 / 2 ) , I 4 z = I 1 L ( - 1 - / 2 + 1 - 2 / 4 + × exp - γ 1 z 1 - L 1 / 2 ) ,
I 2 z = I 2 L ( 1 - / 2 + 1 - 2 / 4 + × exp - γ 2 z 2 - L 1 / 2 ) , I 3 z = I 2 L ( - 1 - / 2 + 1 - 2 / 4 + × exp - γ 2 z 2 - L 1 / 2 ) .
d A 1 d z = - 1 2   Γ A 1 A 2 * + A 3 A 4 * A 2 I 0 , d A 2 d z = 1 2   Γ * A 1 * A 2 + A 3 * A 4 A 1 I 0 , d A 3 d z = 1 2   Γ A 1 A 2 * + A 3 A 4 * A 4 I 0 , d A 4 d z = - 1 2   Γ * A 1 * A 2 + A 3 * A 4 A 3 I 0 ,
tanh - 1 2 c * u - σ s = s Γ * 4 I 0   z + D ,
tanh - 1 2 c * v + σ s = - s Γ * 4 I 0 + D ,
σ = A 1 2 0 1 - v 2 0 + β 2 1 - 1 / u 2 0 ,
c = A 1 2 0 v 0 + β 2 / u 0 ,
s = A 1 2 0 ( 1 - v 2 0 + β 2 1 - 1 / u 2 0 + 4 v 0 + β 2 / u 0 2 ) 1 / 2 ,
β = A 2 0 / A 1 0 .
u 0 = A 2 0 A 3 * 0 ,
v 0 = A 4 0 A 1 * 0 ,
u l = A 2 l A 3 * l = ( 1 - / 2 + 1 - 2 / 4 +   exp - γ 2 l - L 1 / 2 ) 1 / 2 ( - 1 - / 2 + 1 - 2 / 4 +   exp - γ 2 l - L 1 / 2 ) 1 / 2 ,
v l = A 4 l A 1 * l = ( - 1 - / 2 + 1 - 2 / 4 +   exp - γ 2 l - L 1 / 2 ) 1 / 2 ( 1 - / 2 + 1 - 2 / 4 +   exp - γ 2 l - L 1 / 2 ) 1 / 2 .
s u l - u 0 = 2 c + σ u l + σ - 2 c * u l u 0 tanh   κ l , s v l - v 0 = - 2 c + σ v l + σ + 2 c * v l v 0 tanh   κ l ,
m out = 2 β u 0 v 0 β 2 + u 2 0 v 2 0 .

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