Abstract

The effect of reflection and 2K gratings on the efficiency of photorefractive self-pumped phase-conjugate mirrors (SPPCM’s) was studied theoretically and experimentally. Semilinear SPPCM’s of BaTiO3 are used as an example. It is shown with numerical calculations that in normal experimental configurations all these gratings are helpful for the performance of the SPPCM’s. With a 45°-cut BaTiO3:Ce we determined experimentally the variation of reflectivity of a semilinear SPPCM when the crystal’s gain coefficients that correspond to the gratings were changed by variation of the cavity length of the semiresonator in the SPPCM. The experimental results verified the theoretical predications. The validity of our conclusions for SPPCM’s with other photorefractive crystals such as KTaxNb1-xO3 and (KyNa1-y)2Z(SrxBa1-x)1-ZNb2O6 is discussed.

© 1999 Optical Society of America

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References

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  1. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).
  2. M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984).
    [CrossRef]
  3. P. Yeh, “Photorefractive phase conjugator,” Proc. IEEE 80, 436–450 (1992).
    [CrossRef]
  4. N. Sonderer and P. Günter, “Near infrared nonlinear optical phase conjugation in photorefractive crystals and semiconductor materials part II: materials and applications,” Int. J. Nonlinear Opt. Phys. 3, 373–438 (1994).
    [CrossRef]
  5. J. Feinberg, “Self-pumped, continuous-wave phase conjugator using internal reflection,” Opt. Lett. 7, 486–488 (1982).
    [CrossRef] [PubMed]
  6. Y. Lian, H. Gao, P. Ye, Q. Guan, and J. Wang, “Self-pumped phase conjugation with a new mechanism in KTaxNb1−xO3 crystals,” Appl. Phys. Lett. 63, 1745–1747 (1993).
    [CrossRef]
  7. J. Zhang, Y. Lian, S. X. Dou, and P. Ye, “Theory of a ‘stimulated photorefractive backscattering and four-wave mixing’ self-pumped phase conjugator,” Opt. Commun. 110, 631–637 (1994).
    [CrossRef]
  8. S. X. Dou, J. Zhang, M. Wang, H. Gao, and P. Ye, “Theoretical studies on effects of stimulated photorefractive backscattering in self-pumped phase conjugators,” J. Opt. Soc. Am. B 12, 1056–1064 (1995).
    [CrossRef]
  9. S. H. Lin, Y. W. Lian, P. Yeh, K. Y. Hsu, and Y. Zhu, “2k-Grating-assisted self-pumped phase conjugation: the-oretical and experimental studies,” J. Opt. Soc. Am. B 13, 1772–1779 (1996).
    [CrossRef]
  10. M. Cronin-Golomb, J. Paslaski, and A. Yariv, “Vibration resistance, short coherence length operation, and mode-locked pumping in passive phase conjugate mirrors,” Appl. Phys. Lett. 47, 1131–1133 (1985).
    [CrossRef]
  11. K. Nakagawa, M. Zgonik, and P. Günter, “Reflection gratings in self-pumped phase-conjugate mirrors,” J. Opt. Soc. Am. B 14, 839–845 (1997).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  14. J. Zhang, H. Gao, Y. Zhu, and P. Ye, “Reduction of fanning influence in two-wave-mixing coefficient measurements in thick crystal,” Appl. Phys. Lett. 68, 2174–2176 (1996).
    [CrossRef]
  15. D. M. Pepper, “Hybrid phase conjugator/modulators using self-pumped 0°-cut and 45°-cut BaTiO3 crystals,” Appl. Phys. Lett. 49, 1001–1003 (1986), and Ref. 16 therein.
    [CrossRef]
  16. X. Mu, Z. Shao, X. Yue, J. Chen, Q. Guan, and J. Wang, “High reflectivity self-pumped phase conjugation in an unusually cut Fe-doped KTaxNb1−xO3 crystal,” Appl. Phys. Lett. 66, 1047–1049 (1995).
    [CrossRef]
  17. G. Salamo, M. J. Miller, W. W. Clark III, G. L. Wood, and E. J. Sharp, “Strontium barium niobate as a self-pumped phase conjugator,” Opt. Commun. 59, 417–422 (1986).
    [CrossRef]
  18. J. Rodriguez, A. Siahmakoun, G. Salamo, M. J. Miller, W. W. Clark III, G. L. Wood, E. J. Sharp, and R. R. Neurgaonkar, “BSKNN as a self-pumped phase conjugator,” Appl. Opt. 26, 1732–1736 (1987).
    [CrossRef] [PubMed]
  19. S. Bian, J. Zhang, X. Su, K. Xu, W. Sun, Q. Jiang, H. Chen, and D. Sun, “Self-pumped phase conjugation of a 18°-cut Ce-doped KNSBN crystal at 632.8 nm,” Opt. Lett. 18, 769–771 (1993).
    [CrossRef] [PubMed]
  20. X. Mu, L. Zhang, Z. Shao, and M. Jiang, “Characters of the contradirectional two-wave mixing in the tetragonal photorefractive crystals,” in Photorefractive Materials, R. R. Neurgaonkar, T. Shimura, and P. Ye, eds., Proc. SPIE 2896, 167–172 (1996).
    [CrossRef]

1997 (1)

1996 (4)

X. Yi, S. H. Lin, P. Yeh, and K. Y. Hsu, “Contradirectional two-wave mixing with partially coherent waves in photorefractive crystals,” Opt. Lett. 21, 1123–1125 (1996).
[CrossRef] [PubMed]

J. Zhang, H. Gao, Y. Zhu, and P. Ye, “Reduction of fanning influence in two-wave-mixing coefficient measurements in thick crystal,” Appl. Phys. Lett. 68, 2174–2176 (1996).
[CrossRef]

S. H. Lin, Y. W. Lian, P. Yeh, K. Y. Hsu, and Y. Zhu, “2k-Grating-assisted self-pumped phase conjugation: the-oretical and experimental studies,” J. Opt. Soc. Am. B 13, 1772–1779 (1996).
[CrossRef]

X. Mu, L. Zhang, Z. Shao, and M. Jiang, “Characters of the contradirectional two-wave mixing in the tetragonal photorefractive crystals,” in Photorefractive Materials, R. R. Neurgaonkar, T. Shimura, and P. Ye, eds., Proc. SPIE 2896, 167–172 (1996).
[CrossRef]

1995 (2)

X. Mu, Z. Shao, X. Yue, J. Chen, Q. Guan, and J. Wang, “High reflectivity self-pumped phase conjugation in an unusually cut Fe-doped KTaxNb1−xO3 crystal,” Appl. Phys. Lett. 66, 1047–1049 (1995).
[CrossRef]

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

1994 (2)

J. Zhang, Y. Lian, S. X. Dou, and P. Ye, “Theory of a ‘stimulated photorefractive backscattering and four-wave mixing’ self-pumped phase conjugator,” Opt. Commun. 110, 631–637 (1994).
[CrossRef]

N. Sonderer and P. Günter, “Near infrared nonlinear optical phase conjugation in photorefractive crystals and semiconductor materials part II: materials and applications,” Int. J. Nonlinear Opt. Phys. 3, 373–438 (1994).
[CrossRef]

1993 (2)

Y. Lian, H. Gao, P. Ye, Q. Guan, and J. Wang, “Self-pumped phase conjugation with a new mechanism in KTaxNb1−xO3 crystals,” Appl. Phys. Lett. 63, 1745–1747 (1993).
[CrossRef]

S. Bian, J. Zhang, X. Su, K. Xu, W. Sun, Q. Jiang, H. Chen, and D. Sun, “Self-pumped phase conjugation of a 18°-cut Ce-doped KNSBN crystal at 632.8 nm,” Opt. Lett. 18, 769–771 (1993).
[CrossRef] [PubMed]

1992 (1)

P. Yeh, “Photorefractive phase conjugator,” Proc. IEEE 80, 436–450 (1992).
[CrossRef]

1987 (1)

1986 (2)

G. Salamo, M. J. Miller, W. W. Clark III, G. L. Wood, and E. J. Sharp, “Strontium barium niobate as a self-pumped phase conjugator,” Opt. Commun. 59, 417–422 (1986).
[CrossRef]

D. M. Pepper, “Hybrid phase conjugator/modulators using self-pumped 0°-cut and 45°-cut BaTiO3 crystals,” Appl. Phys. Lett. 49, 1001–1003 (1986), and Ref. 16 therein.
[CrossRef]

1985 (1)

M. Cronin-Golomb, J. Paslaski, and A. Yariv, “Vibration resistance, short coherence length operation, and mode-locked pumping in passive phase conjugate mirrors,” Appl. Phys. Lett. 47, 1131–1133 (1985).
[CrossRef]

1984 (1)

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

1982 (2)

Bian, S.

Chen, H.

Chen, J.

X. Mu, Z. Shao, X. Yue, J. Chen, Q. Guan, and J. Wang, “High reflectivity self-pumped phase conjugation in an unusually cut Fe-doped KTaxNb1−xO3 crystal,” Appl. Phys. Lett. 66, 1047–1049 (1995).
[CrossRef]

Clark III, W. W.

J. Rodriguez, A. Siahmakoun, G. Salamo, M. J. Miller, W. W. Clark III, G. L. Wood, E. J. Sharp, and R. R. Neurgaonkar, “BSKNN as a self-pumped phase conjugator,” Appl. Opt. 26, 1732–1736 (1987).
[CrossRef] [PubMed]

G. Salamo, M. J. Miller, W. W. Clark III, G. L. Wood, and E. J. Sharp, “Strontium barium niobate as a self-pumped phase conjugator,” Opt. Commun. 59, 417–422 (1986).
[CrossRef]

Cronin-Golomb, M.

M. Cronin-Golomb, J. Paslaski, and A. Yariv, “Vibration resistance, short coherence length operation, and mode-locked pumping in passive phase conjugate mirrors,” Appl. Phys. Lett. 47, 1131–1133 (1985).
[CrossRef]

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

Dou, S. X.

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

J. Zhang, Y. Lian, S. X. Dou, and P. Ye, “Theory of a ‘stimulated photorefractive backscattering and four-wave mixing’ self-pumped phase conjugator,” Opt. Commun. 110, 631–637 (1994).
[CrossRef]

Feinberg, J.

Fischer, B.

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

Gao, H.

J. Zhang, H. Gao, Y. Zhu, and P. Ye, “Reduction of fanning influence in two-wave-mixing coefficient measurements in thick crystal,” Appl. Phys. Lett. 68, 2174–2176 (1996).
[CrossRef]

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

Y. Lian, H. Gao, P. Ye, Q. Guan, and J. Wang, “Self-pumped phase conjugation with a new mechanism in KTaxNb1−xO3 crystals,” Appl. Phys. Lett. 63, 1745–1747 (1993).
[CrossRef]

Guan, Q.

X. Mu, Z. Shao, X. Yue, J. Chen, Q. Guan, and J. Wang, “High reflectivity self-pumped phase conjugation in an unusually cut Fe-doped KTaxNb1−xO3 crystal,” Appl. Phys. Lett. 66, 1047–1049 (1995).
[CrossRef]

Y. Lian, H. Gao, P. Ye, Q. Guan, and J. Wang, “Self-pumped phase conjugation with a new mechanism in KTaxNb1−xO3 crystals,” Appl. Phys. Lett. 63, 1745–1747 (1993).
[CrossRef]

Günter, P.

K. Nakagawa, M. Zgonik, and P. Günter, “Reflection gratings in self-pumped phase-conjugate mirrors,” J. Opt. Soc. Am. B 14, 839–845 (1997).
[CrossRef]

N. Sonderer and P. Günter, “Near infrared nonlinear optical phase conjugation in photorefractive crystals and semiconductor materials part II: materials and applications,” Int. J. Nonlinear Opt. Phys. 3, 373–438 (1994).
[CrossRef]

Hsu, K. Y.

Jiang, M.

X. Mu, L. Zhang, Z. Shao, and M. Jiang, “Characters of the contradirectional two-wave mixing in the tetragonal photorefractive crystals,” in Photorefractive Materials, R. R. Neurgaonkar, T. Shimura, and P. Ye, eds., Proc. SPIE 2896, 167–172 (1996).
[CrossRef]

Jiang, Q.

Lian, Y.

J. Zhang, Y. Lian, S. X. Dou, and P. Ye, “Theory of a ‘stimulated photorefractive backscattering and four-wave mixing’ self-pumped phase conjugator,” Opt. Commun. 110, 631–637 (1994).
[CrossRef]

Y. Lian, H. Gao, P. Ye, Q. Guan, and J. Wang, “Self-pumped phase conjugation with a new mechanism in KTaxNb1−xO3 crystals,” Appl. Phys. Lett. 63, 1745–1747 (1993).
[CrossRef]

Lian, Y. W.

Lin, S. H.

Miller, M. J.

J. Rodriguez, A. Siahmakoun, G. Salamo, M. J. Miller, W. W. Clark III, G. L. Wood, E. J. Sharp, and R. R. Neurgaonkar, “BSKNN as a self-pumped phase conjugator,” Appl. Opt. 26, 1732–1736 (1987).
[CrossRef] [PubMed]

G. Salamo, M. J. Miller, W. W. Clark III, G. L. Wood, and E. J. Sharp, “Strontium barium niobate as a self-pumped phase conjugator,” Opt. Commun. 59, 417–422 (1986).
[CrossRef]

Mu, X.

X. Mu, L. Zhang, Z. Shao, and M. Jiang, “Characters of the contradirectional two-wave mixing in the tetragonal photorefractive crystals,” in Photorefractive Materials, R. R. Neurgaonkar, T. Shimura, and P. Ye, eds., Proc. SPIE 2896, 167–172 (1996).
[CrossRef]

X. Mu, Z. Shao, X. Yue, J. Chen, Q. Guan, and J. Wang, “High reflectivity self-pumped phase conjugation in an unusually cut Fe-doped KTaxNb1−xO3 crystal,” Appl. Phys. Lett. 66, 1047–1049 (1995).
[CrossRef]

Nakagawa, K.

Neurgaonkar, R. R.

Paslaski, J.

M. Cronin-Golomb, J. Paslaski, and A. Yariv, “Vibration resistance, short coherence length operation, and mode-locked pumping in passive phase conjugate mirrors,” Appl. Phys. Lett. 47, 1131–1133 (1985).
[CrossRef]

Pepper, D. M.

D. M. Pepper, “Hybrid phase conjugator/modulators using self-pumped 0°-cut and 45°-cut BaTiO3 crystals,” Appl. Phys. Lett. 49, 1001–1003 (1986), and Ref. 16 therein.
[CrossRef]

Rodriguez, J.

Salamo, G.

J. Rodriguez, A. Siahmakoun, G. Salamo, M. J. Miller, W. W. Clark III, G. L. Wood, E. J. Sharp, and R. R. Neurgaonkar, “BSKNN as a self-pumped phase conjugator,” Appl. Opt. 26, 1732–1736 (1987).
[CrossRef] [PubMed]

G. Salamo, M. J. Miller, W. W. Clark III, G. L. Wood, and E. J. Sharp, “Strontium barium niobate as a self-pumped phase conjugator,” Opt. Commun. 59, 417–422 (1986).
[CrossRef]

Shao, Z.

X. Mu, L. Zhang, Z. Shao, and M. Jiang, “Characters of the contradirectional two-wave mixing in the tetragonal photorefractive crystals,” in Photorefractive Materials, R. R. Neurgaonkar, T. Shimura, and P. Ye, eds., Proc. SPIE 2896, 167–172 (1996).
[CrossRef]

X. Mu, Z. Shao, X. Yue, J. Chen, Q. Guan, and J. Wang, “High reflectivity self-pumped phase conjugation in an unusually cut Fe-doped KTaxNb1−xO3 crystal,” Appl. Phys. Lett. 66, 1047–1049 (1995).
[CrossRef]

Sharp, E. J.

J. Rodriguez, A. Siahmakoun, G. Salamo, M. J. Miller, W. W. Clark III, G. L. Wood, E. J. Sharp, and R. R. Neurgaonkar, “BSKNN as a self-pumped phase conjugator,” Appl. Opt. 26, 1732–1736 (1987).
[CrossRef] [PubMed]

G. Salamo, M. J. Miller, W. W. Clark III, G. L. Wood, and E. J. Sharp, “Strontium barium niobate as a self-pumped phase conjugator,” Opt. Commun. 59, 417–422 (1986).
[CrossRef]

Siahmakoun, A.

Sonderer, N.

N. Sonderer and P. Günter, “Near infrared nonlinear optical phase conjugation in photorefractive crystals and semiconductor materials part II: materials and applications,” Int. J. Nonlinear Opt. Phys. 3, 373–438 (1994).
[CrossRef]

Su, X.

Sun, D.

Sun, W.

Wang, J.

X. Mu, Z. Shao, X. Yue, J. Chen, Q. Guan, and J. Wang, “High reflectivity self-pumped phase conjugation in an unusually cut Fe-doped KTaxNb1−xO3 crystal,” Appl. Phys. Lett. 66, 1047–1049 (1995).
[CrossRef]

Y. Lian, H. Gao, P. Ye, Q. Guan, and J. Wang, “Self-pumped phase conjugation with a new mechanism in KTaxNb1−xO3 crystals,” Appl. Phys. Lett. 63, 1745–1747 (1993).
[CrossRef]

Wang, M.

White, J. O.

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

Wood, G. L.

J. Rodriguez, A. Siahmakoun, G. Salamo, M. J. Miller, W. W. Clark III, G. L. Wood, E. J. Sharp, and R. R. Neurgaonkar, “BSKNN as a self-pumped phase conjugator,” Appl. Opt. 26, 1732–1736 (1987).
[CrossRef] [PubMed]

G. Salamo, M. J. Miller, W. W. Clark III, G. L. Wood, and E. J. Sharp, “Strontium barium niobate as a self-pumped phase conjugator,” Opt. Commun. 59, 417–422 (1986).
[CrossRef]

Xu, K.

Yariv, A.

M. Cronin-Golomb, J. Paslaski, and A. Yariv, “Vibration resistance, short coherence length operation, and mode-locked pumping in passive phase conjugate mirrors,” Appl. Phys. Lett. 47, 1131–1133 (1985).
[CrossRef]

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

Ye, P.

J. Zhang, H. Gao, Y. Zhu, and P. Ye, “Reduction of fanning influence in two-wave-mixing coefficient measurements in thick crystal,” Appl. Phys. Lett. 68, 2174–2176 (1996).
[CrossRef]

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

J. Zhang, Y. Lian, S. X. Dou, and P. Ye, “Theory of a ‘stimulated photorefractive backscattering and four-wave mixing’ self-pumped phase conjugator,” Opt. Commun. 110, 631–637 (1994).
[CrossRef]

Y. Lian, H. Gao, P. Ye, Q. Guan, and J. Wang, “Self-pumped phase conjugation with a new mechanism in KTaxNb1−xO3 crystals,” Appl. Phys. Lett. 63, 1745–1747 (1993).
[CrossRef]

Yeh, P.

Yi, X.

Yue, X.

X. Mu, Z. Shao, X. Yue, J. Chen, Q. Guan, and J. Wang, “High reflectivity self-pumped phase conjugation in an unusually cut Fe-doped KTaxNb1−xO3 crystal,” Appl. Phys. Lett. 66, 1047–1049 (1995).
[CrossRef]

Zgonik, M.

Zhang, J.

J. Zhang, H. Gao, Y. Zhu, and P. Ye, “Reduction of fanning influence in two-wave-mixing coefficient measurements in thick crystal,” Appl. Phys. Lett. 68, 2174–2176 (1996).
[CrossRef]

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

J. Zhang, Y. Lian, S. X. Dou, and P. Ye, “Theory of a ‘stimulated photorefractive backscattering and four-wave mixing’ self-pumped phase conjugator,” Opt. Commun. 110, 631–637 (1994).
[CrossRef]

S. Bian, J. Zhang, X. Su, K. Xu, W. Sun, Q. Jiang, H. Chen, and D. Sun, “Self-pumped phase conjugation of a 18°-cut Ce-doped KNSBN crystal at 632.8 nm,” Opt. Lett. 18, 769–771 (1993).
[CrossRef] [PubMed]

Zhang, L.

X. Mu, L. Zhang, Z. Shao, and M. Jiang, “Characters of the contradirectional two-wave mixing in the tetragonal photorefractive crystals,” in Photorefractive Materials, R. R. Neurgaonkar, T. Shimura, and P. Ye, eds., Proc. SPIE 2896, 167–172 (1996).
[CrossRef]

Zhu, Y.

J. Zhang, H. Gao, Y. Zhu, and P. Ye, “Reduction of fanning influence in two-wave-mixing coefficient measurements in thick crystal,” Appl. Phys. Lett. 68, 2174–2176 (1996).
[CrossRef]

S. H. Lin, Y. W. Lian, P. Yeh, K. Y. Hsu, and Y. Zhu, “2k-Grating-assisted self-pumped phase conjugation: the-oretical and experimental studies,” J. Opt. Soc. Am. B 13, 1772–1779 (1996).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (5)

Y. Lian, H. Gao, P. Ye, Q. Guan, and J. Wang, “Self-pumped phase conjugation with a new mechanism in KTaxNb1−xO3 crystals,” Appl. Phys. Lett. 63, 1745–1747 (1993).
[CrossRef]

M. Cronin-Golomb, J. Paslaski, and A. Yariv, “Vibration resistance, short coherence length operation, and mode-locked pumping in passive phase conjugate mirrors,” Appl. Phys. Lett. 47, 1131–1133 (1985).
[CrossRef]

J. Zhang, H. Gao, Y. Zhu, and P. Ye, “Reduction of fanning influence in two-wave-mixing coefficient measurements in thick crystal,” Appl. Phys. Lett. 68, 2174–2176 (1996).
[CrossRef]

D. M. Pepper, “Hybrid phase conjugator/modulators using self-pumped 0°-cut and 45°-cut BaTiO3 crystals,” Appl. Phys. Lett. 49, 1001–1003 (1986), and Ref. 16 therein.
[CrossRef]

X. Mu, Z. Shao, X. Yue, J. Chen, Q. Guan, and J. Wang, “High reflectivity self-pumped phase conjugation in an unusually cut Fe-doped KTaxNb1−xO3 crystal,” Appl. Phys. Lett. 66, 1047–1049 (1995).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

Int. J. Nonlinear Opt. Phys. (1)

N. Sonderer and P. Günter, “Near infrared nonlinear optical phase conjugation in photorefractive crystals and semiconductor materials part II: materials and applications,” Int. J. Nonlinear Opt. Phys. 3, 373–438 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (3)

Opt. Commun. (2)

J. Zhang, Y. Lian, S. X. Dou, and P. Ye, “Theory of a ‘stimulated photorefractive backscattering and four-wave mixing’ self-pumped phase conjugator,” Opt. Commun. 110, 631–637 (1994).
[CrossRef]

G. Salamo, M. J. Miller, W. W. Clark III, G. L. Wood, and E. J. Sharp, “Strontium barium niobate as a self-pumped phase conjugator,” Opt. Commun. 59, 417–422 (1986).
[CrossRef]

Opt. Lett. (3)

Proc. IEEE (1)

P. Yeh, “Photorefractive phase conjugator,” Proc. IEEE 80, 436–450 (1992).
[CrossRef]

Proc. SPIE (1)

X. Mu, L. Zhang, Z. Shao, and M. Jiang, “Characters of the contradirectional two-wave mixing in the tetragonal photorefractive crystals,” in Photorefractive Materials, R. R. Neurgaonkar, T. Shimura, and P. Ye, eds., Proc. SPIE 2896, 167–172 (1996).
[CrossRef]

Other (1)

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

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Figures (10)

Fig. 1
Fig. 1

(a) Configuration for FWM in a PR crystal: (b) typical geometry for an efficient semilinear SPPCM with BaTiO3, (c) that for a cat or SPB-FWM SPPCM. (I) and (II) represent the transmission and reflection gratings, respectively; (III) and (IV) represent the two 2K gratings. All these gratings overlap spatially in the crystal. Note the similarity of the beam–crystal geometry between (b) and (c) by regarding the FWM area demarked with dotted lines in (c) as the whole crystal in (b).

Fig. 2
Fig. 2

R of the semilinear SPPCM as a function of Γ2KL at different M0. ΓTL=8, ΓR=0, and Γ2K=0. The curved line that corresponds to M0=1.0 and αL=0 is given for comparison. This is also true in Figs. 35.

Fig. 3
Fig. 3

R of the semilinear SPPCM as a function of Γ2KL at different M0. ΓTL=8, ΓR=0, and Γ2K=0.

Fig. 4
Fig. 4

R of the semilinear SPPCM as a function of ΓRL at different M0. ΓTL=8, Γ2K=0, and Γ2K=0.

Fig. 5
Fig. 5

R of the semilinear SPPCM as a function of x at different M0. ΓTL=8, ΓRL=4x, Γ2KL=5x, and Γ2KL=3x.

Fig. 6
Fig. 6

Experimental setup for the semilinear SPPCM. M, mirrors; BS, beam splitters; D, photodetectors.

Fig. 7
Fig. 7

(a) Experimentally determined R of the SPPCM as a function of the cavity length Lc of the semiresonator composed by mirror M0 and the crystal. (b) Typical temporal evolutions of R of the SPPCM. The light is switched on at t=0.

Fig. 8
Fig. 8

Experimental setup for measuring the contradirectional TBC gain coefficients of the crystal that characterize the reflection and 2K gratings in the SPPCM. The signal beam had an e polarization (i.e., horizontally polarized), and the pump beam had a polarization direction that formed an angle of 60° with the horizontal direction. P, Glan–Thomson polarizer.

Fig. 9
Fig. 9

Experimentally determined contradirectional TBC coefficients as a function of the prism position Xp of the prism. Solid curves, from polynomial fits.

Fig. 10
Fig. 10

R of the semilinear SPPCM as a function of x obtained both theoretically and experimentally. Squares, experiment; solid curve, theory. The parameters used in the theory are ΓT=655 mm-1, ΓR=3.19x (mm-1), Γ2K=3.86x (mm-1), Γ2K=1.89x (mm-1), M0=0.86, α=0.045 mm-1, L=1.49 mm, and I1(0)=0.038. The reflection by the incident crystal surface 0.15 is taken into account in the theoretical calculation.

Equations (6)

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dI1dz=1I0[ΓT(I1I4+I1I2I3I4)-ΓR(I1I3+I1I2I3I4)-Γ2KI1I2]-αI1,
dI2dz=1I0[ΓT(I2I3+I1I2I3I4)-ΓR(I2I4+I1I2I3I4)-Γ2KI1I2]+αI2,
dI3dz=1I0[-ΓT(I2I3+I1I2I3I4)-ΓR(I1I3+I1I2I3I4)-Γ2KI3I4]+αI3,
dI4dz=1I0[-ΓT(I1I4+I1I2I3I4)-ΓR(I2I4+I1I2I3I4)-Γ2KI3I4]-αI4,
I1(0)=0,I2(L)=M0I1(L),
I3(L)=0,I4(0)=1,

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