Abstract

We investigated 2k-grating-assisted self-pumped phase conjugation in photorefractive Ce:BaTiO3 crystals. The phase-conjugation process involves a combination of four-wave mixing and stimulated photorefractive backscattering. An approximation involving separate interaction regions is used to theoretically calculate the reflectivity of phase conjugation as a function of the coupling strength of four-wave mixing and stimulated photorefractive backscattering. In our experiments, grating-erasure techniques are employed at the interaction regions to investigate the dependence of phase-conjugate reflectivity on the coupling strength of four-wave mixing and stimulated photorefractive backscattering. The experimental results are in good agreement with the theoretical prediction.

© 1996 Optical Society of America

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References

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  1. See, for example, P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).
  2. M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12 (1984).
    [Crossref]
  3. See, for example, P. Gunter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications (Springer-Verlag, Berlin, 1988), Vols. I and II.
    [Crossref]
  4. J. Feinberg, “Self-pumped, continuous-wave phase conjugator using internal reflections,” Opt. Lett. 42, 919 (1983).
  5. K. R. Macdonald and J. Feinberg, “Theory of a self-pumped phase conjugator with two coupled interaction regions,” J. Opt. Soc. Am. 73, 548 (1983).
    [Crossref]
  6. T. Y. Chang and R. W. Hellwarth, “Optical phase conjugation by backscattering in barium titanate,” Opt. Lett. 10, 408 (1985).
    [Crossref] [PubMed]
  7. J. F. Lam, “Origin of phase conjugate waves in self-pumped photorefractive mirrors,” Appl. Phys. Lett. 46, 909 (1985).
    [Crossref]
  8. G. C. Valley, “Evolution of phase-conjugate waves in stimulated photorefractive backscattering,” J. Opt. Soc. Am. B 9, 1440 (1992).
    [Crossref]
  9. Y. W. Lian, H. Gao, P. Ye, Q. Guan, and J. Wang, “Self-pumped phase conjugation with a new mechanism in KTa1-x Nbx O3:Fe crystals,” Appl. Phys. Lett. 63, 1754 (1993).
    [Crossref]
  10. Y. W. Lian, S. X. Dou, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Mechanism transformation with wavelength of self-pumped phase conjugation in BaTiO3:Ce,” Opt. Lett. 19, 610 (1994).
    [Crossref] [PubMed]
  11. A. A. Zozulya, M. Saffman, and 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 (1994).
    [Crossref] [PubMed]
  12. Y. W. Lian, S. X. Dou, J. Zhang, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Variation of mechanism transition wavelength of self-pumped phase conjugation with Ce-content in BaTiO3:Ce crystals,” Opt. Commun. 110, 192 (1994).
    [Crossref]
  13. Y. W. Lian, H. Gao, S. X. Dou, H. Wang, P. Ye, Q. Guan, and J. Wang, “Mechanism transition of self-pumped phase conjugation in KTa1-x Nbx O3:Fe crystals,” Appl. Phys. B 59, 655 (1994).
    [Crossref]
  14. Y. W. Lian, S. H. Lin, S. Campbell, K. Y. Hsu, P. Yeh, and Y. Zhu, “Polarization-dependent mechanism transformation during self-pumped phase conjugation in BaTiO3:Ce,” Opt. Lett. 20, 1683 (1995).
    [Crossref]
  15. M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, “Passing (self-pumped) phase conjugate mirror: theoretical and experimental investigation,” Appl. Phys. Lett. 41, 689 (1982).
    [Crossref]
  16. P. Yeh, “Two-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484 (1989).
    [Crossref]
  17. Q. He, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-24, 2507 (1988).
  18. G. L. Wood, E. J. Sharp, and G. J. Salamo, “Performance of photorefractive self-pumped phase conjugators,” Proc. SPIE 1626, 21 (1992).
    [Crossref]

1995 (1)

1994 (4)

Y. W. Lian, S. X. Dou, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Mechanism transformation with wavelength of self-pumped phase conjugation in BaTiO3:Ce,” Opt. Lett. 19, 610 (1994).
[Crossref] [PubMed]

A. A. Zozulya, M. Saffman, and 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 (1994).
[Crossref] [PubMed]

Y. W. Lian, S. X. Dou, J. Zhang, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Variation of mechanism transition wavelength of self-pumped phase conjugation with Ce-content in BaTiO3:Ce crystals,” Opt. Commun. 110, 192 (1994).
[Crossref]

Y. W. Lian, H. Gao, S. X. Dou, H. Wang, P. Ye, Q. Guan, and J. Wang, “Mechanism transition of self-pumped phase conjugation in KTa1-x Nbx O3:Fe crystals,” Appl. Phys. B 59, 655 (1994).
[Crossref]

1993 (1)

Y. W. Lian, H. Gao, P. Ye, Q. Guan, and J. Wang, “Self-pumped phase conjugation with a new mechanism in KTa1-x Nbx O3:Fe crystals,” Appl. Phys. Lett. 63, 1754 (1993).
[Crossref]

1992 (2)

G. C. Valley, “Evolution of phase-conjugate waves in stimulated photorefractive backscattering,” J. Opt. Soc. Am. B 9, 1440 (1992).
[Crossref]

G. L. Wood, E. J. Sharp, and G. J. Salamo, “Performance of photorefractive self-pumped phase conjugators,” Proc. SPIE 1626, 21 (1992).
[Crossref]

1989 (1)

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

1988 (1)

Q. He, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-24, 2507 (1988).

1985 (2)

J. F. Lam, “Origin of phase conjugate waves in self-pumped photorefractive mirrors,” Appl. Phys. Lett. 46, 909 (1985).
[Crossref]

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

1984 (1)

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

1983 (2)

J. Feinberg, “Self-pumped, continuous-wave phase conjugator using internal reflections,” Opt. Lett. 42, 919 (1983).

K. R. Macdonald and J. Feinberg, “Theory of a self-pumped phase conjugator with two coupled interaction regions,” J. Opt. Soc. Am. 73, 548 (1983).
[Crossref]

1982 (1)

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, “Passing (self-pumped) phase conjugate mirror: theoretical and experimental investigation,” Appl. Phys. Lett. 41, 689 (1982).
[Crossref]

Anderson, D. Z.

A. A. Zozulya, M. Saffman, and 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 (1994).
[Crossref] [PubMed]

Campbell, S.

Chang, T. Y.

Cronin-Golomb, M.

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

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, “Passing (self-pumped) phase conjugate mirror: theoretical and experimental investigation,” Appl. Phys. Lett. 41, 689 (1982).
[Crossref]

Dou, S. X.

Y. W. Lian, H. Gao, S. X. Dou, H. Wang, P. Ye, Q. Guan, and J. Wang, “Mechanism transition of self-pumped phase conjugation in KTa1-x Nbx O3:Fe crystals,” Appl. Phys. B 59, 655 (1994).
[Crossref]

Y. W. Lian, S. X. Dou, J. Zhang, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Variation of mechanism transition wavelength of self-pumped phase conjugation with Ce-content in BaTiO3:Ce crystals,” Opt. Commun. 110, 192 (1994).
[Crossref]

Y. W. Lian, S. X. Dou, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Mechanism transformation with wavelength of self-pumped phase conjugation in BaTiO3:Ce,” Opt. Lett. 19, 610 (1994).
[Crossref] [PubMed]

Feinberg, J.

K. R. Macdonald and J. Feinberg, “Theory of a self-pumped phase conjugator with two coupled interaction regions,” J. Opt. Soc. Am. 73, 548 (1983).
[Crossref]

J. Feinberg, “Self-pumped, continuous-wave phase conjugator using internal reflections,” Opt. Lett. 42, 919 (1983).

Fisher, B.

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

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, “Passing (self-pumped) phase conjugate mirror: theoretical and experimental investigation,” Appl. Phys. Lett. 41, 689 (1982).
[Crossref]

Gao, H.

Y. W. Lian, H. Gao, S. X. Dou, H. Wang, P. Ye, Q. Guan, and J. Wang, “Mechanism transition of self-pumped phase conjugation in KTa1-x Nbx O3:Fe crystals,” Appl. Phys. B 59, 655 (1994).
[Crossref]

Y. W. Lian, S. X. Dou, J. Zhang, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Variation of mechanism transition wavelength of self-pumped phase conjugation with Ce-content in BaTiO3:Ce crystals,” Opt. Commun. 110, 192 (1994).
[Crossref]

Y. W. Lian, S. X. Dou, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Mechanism transformation with wavelength of self-pumped phase conjugation in BaTiO3:Ce,” Opt. Lett. 19, 610 (1994).
[Crossref] [PubMed]

Y. W. Lian, H. Gao, P. Ye, Q. Guan, and J. Wang, “Self-pumped phase conjugation with a new mechanism in KTa1-x Nbx O3:Fe crystals,” Appl. Phys. Lett. 63, 1754 (1993).
[Crossref]

Guan, Q.

Y. W. Lian, H. Gao, S. X. Dou, H. Wang, P. Ye, Q. Guan, and J. Wang, “Mechanism transition of self-pumped phase conjugation in KTa1-x Nbx O3:Fe crystals,” Appl. Phys. B 59, 655 (1994).
[Crossref]

Y. W. Lian, H. Gao, P. Ye, Q. Guan, and J. Wang, “Self-pumped phase conjugation with a new mechanism in KTa1-x Nbx O3:Fe crystals,” Appl. Phys. Lett. 63, 1754 (1993).
[Crossref]

He, Q.

Q. He, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-24, 2507 (1988).

Hellwarth, R. W.

Hsu, K. Y.

Lam, J. F.

J. F. Lam, “Origin of phase conjugate waves in self-pumped photorefractive mirrors,” Appl. Phys. Lett. 46, 909 (1985).
[Crossref]

Lian, Y. W.

Y. W. Lian, S. H. Lin, S. Campbell, K. Y. Hsu, P. Yeh, and Y. Zhu, “Polarization-dependent mechanism transformation during self-pumped phase conjugation in BaTiO3:Ce,” Opt. Lett. 20, 1683 (1995).
[Crossref]

Y. W. Lian, S. X. Dou, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Mechanism transformation with wavelength of self-pumped phase conjugation in BaTiO3:Ce,” Opt. Lett. 19, 610 (1994).
[Crossref] [PubMed]

Y. W. Lian, H. Gao, S. X. Dou, H. Wang, P. Ye, Q. Guan, and J. Wang, “Mechanism transition of self-pumped phase conjugation in KTa1-x Nbx O3:Fe crystals,” Appl. Phys. B 59, 655 (1994).
[Crossref]

Y. W. Lian, S. X. Dou, J. Zhang, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Variation of mechanism transition wavelength of self-pumped phase conjugation with Ce-content in BaTiO3:Ce crystals,” Opt. Commun. 110, 192 (1994).
[Crossref]

Y. W. Lian, H. Gao, P. Ye, Q. Guan, and J. Wang, “Self-pumped phase conjugation with a new mechanism in KTa1-x Nbx O3:Fe crystals,” Appl. Phys. Lett. 63, 1754 (1993).
[Crossref]

Lin, S. H.

Macdonald, K. R.

Saffman, M.

A. A. Zozulya, M. Saffman, and 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 (1994).
[Crossref] [PubMed]

Salamo, G. J.

G. L. Wood, E. J. Sharp, and G. J. Salamo, “Performance of photorefractive self-pumped phase conjugators,” Proc. SPIE 1626, 21 (1992).
[Crossref]

Sharp, E. J.

G. L. Wood, E. J. Sharp, and G. J. Salamo, “Performance of photorefractive self-pumped phase conjugators,” Proc. SPIE 1626, 21 (1992).
[Crossref]

Valley, G. C.

Wang, H.

Y. W. Lian, H. Gao, S. X. Dou, H. Wang, P. Ye, Q. Guan, and J. Wang, “Mechanism transition of self-pumped phase conjugation in KTa1-x Nbx O3:Fe crystals,” Appl. Phys. B 59, 655 (1994).
[Crossref]

Wang, J.

Y. W. Lian, H. Gao, S. X. Dou, H. Wang, P. Ye, Q. Guan, and J. Wang, “Mechanism transition of self-pumped phase conjugation in KTa1-x Nbx O3:Fe crystals,” Appl. Phys. B 59, 655 (1994).
[Crossref]

Y. W. Lian, H. Gao, P. Ye, Q. Guan, and J. Wang, “Self-pumped phase conjugation with a new mechanism in KTa1-x Nbx O3:Fe crystals,” Appl. Phys. Lett. 63, 1754 (1993).
[Crossref]

White, J. O.

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

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, “Passing (self-pumped) phase conjugate mirror: theoretical and experimental investigation,” Appl. Phys. Lett. 41, 689 (1982).
[Crossref]

Wood, G. L.

G. L. Wood, E. J. Sharp, and G. J. Salamo, “Performance of photorefractive self-pumped phase conjugators,” Proc. SPIE 1626, 21 (1992).
[Crossref]

Wu, X.

Y. W. Lian, S. X. Dou, J. Zhang, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Variation of mechanism transition wavelength of self-pumped phase conjugation with Ce-content in BaTiO3:Ce crystals,” Opt. Commun. 110, 192 (1994).
[Crossref]

Y. W. Lian, S. X. Dou, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Mechanism transformation with wavelength of self-pumped phase conjugation in BaTiO3:Ce,” Opt. Lett. 19, 610 (1994).
[Crossref] [PubMed]

Yang, C.

Y. W. Lian, S. X. Dou, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Mechanism transformation with wavelength of self-pumped phase conjugation in BaTiO3:Ce,” Opt. Lett. 19, 610 (1994).
[Crossref] [PubMed]

Y. W. Lian, S. X. Dou, J. Zhang, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Variation of mechanism transition wavelength of self-pumped phase conjugation with Ce-content in BaTiO3:Ce crystals,” Opt. Commun. 110, 192 (1994).
[Crossref]

Yariv, A.

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

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, “Passing (self-pumped) phase conjugate mirror: theoretical and experimental investigation,” Appl. Phys. Lett. 41, 689 (1982).
[Crossref]

Ye, P.

Y. W. Lian, S. X. Dou, J. Zhang, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Variation of mechanism transition wavelength of self-pumped phase conjugation with Ce-content in BaTiO3:Ce crystals,” Opt. Commun. 110, 192 (1994).
[Crossref]

Y. W. Lian, H. Gao, S. X. Dou, H. Wang, P. Ye, Q. Guan, and J. Wang, “Mechanism transition of self-pumped phase conjugation in KTa1-x Nbx O3:Fe crystals,” Appl. Phys. B 59, 655 (1994).
[Crossref]

Y. W. Lian, S. X. Dou, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Mechanism transformation with wavelength of self-pumped phase conjugation in BaTiO3:Ce,” Opt. Lett. 19, 610 (1994).
[Crossref] [PubMed]

Y. W. Lian, H. Gao, P. Ye, Q. Guan, and J. Wang, “Self-pumped phase conjugation with a new mechanism in KTa1-x Nbx O3:Fe crystals,” Appl. Phys. Lett. 63, 1754 (1993).
[Crossref]

Yeh, P.

Y. W. Lian, S. H. Lin, S. Campbell, K. Y. Hsu, P. Yeh, and Y. Zhu, “Polarization-dependent mechanism transformation during self-pumped phase conjugation in BaTiO3:Ce,” Opt. Lett. 20, 1683 (1995).
[Crossref]

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

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

Zhang, J.

Y. W. Lian, S. X. Dou, J. Zhang, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Variation of mechanism transition wavelength of self-pumped phase conjugation with Ce-content in BaTiO3:Ce crystals,” Opt. Commun. 110, 192 (1994).
[Crossref]

Zhu, Y.

Zozulya, A. A.

A. A. Zozulya, M. Saffman, and 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 (1994).
[Crossref] [PubMed]

Appl. Phys. B (1)

Y. W. Lian, H. Gao, S. X. Dou, H. Wang, P. Ye, Q. Guan, and J. Wang, “Mechanism transition of self-pumped phase conjugation in KTa1-x Nbx O3:Fe crystals,” Appl. Phys. B 59, 655 (1994).
[Crossref]

Appl. Phys. Lett. (3)

Y. W. Lian, H. Gao, P. Ye, Q. Guan, and J. Wang, “Self-pumped phase conjugation with a new mechanism in KTa1-x Nbx O3:Fe crystals,” Appl. Phys. Lett. 63, 1754 (1993).
[Crossref]

M. Cronin-Golomb, B. Fisher, J. O. White, and A. Yariv, “Passing (self-pumped) phase conjugate mirror: theoretical and experimental investigation,” Appl. Phys. Lett. 41, 689 (1982).
[Crossref]

J. F. Lam, “Origin of phase conjugate waves in self-pumped photorefractive mirrors,” Appl. Phys. Lett. 46, 909 (1985).
[Crossref]

IEEE J. Quantum Electron. (3)

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

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

Q. He, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-24, 2507 (1988).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

Y. W. Lian, S. X. Dou, J. Zhang, H. Gao, Y. Zhu, X. Wu, C. Yang, and P. Ye, “Variation of mechanism transition wavelength of self-pumped phase conjugation with Ce-content in BaTiO3:Ce crystals,” Opt. Commun. 110, 192 (1994).
[Crossref]

Opt. Lett. (4)

Phys. Rev. Lett. (1)

A. A. Zozulya, M. Saffman, and 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 (1994).
[Crossref] [PubMed]

Proc. SPIE (1)

G. L. Wood, E. J. Sharp, and G. J. Salamo, “Performance of photorefractive self-pumped phase conjugators,” Proc. SPIE 1626, 21 (1992).
[Crossref]

Other (2)

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

See, for example, P. Gunter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications (Springer-Verlag, Berlin, 1988), Vols. I and II.
[Crossref]

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Figures (11)

Fig. 1
Fig. 1

Different modes of SPPC: (a) FWM-TIR, (b) SPB, and (c) FWM-SPB.

Fig. 2
Fig. 2

FWM-SPB phase conjugator with a two-interaction region: (a) photograph of the optical beam path in a Ce:BaTiO3 FWM-SPB phase conjugator; (b) theoretical model in which the forward-going fanning beam A1 overlaps well with its backward-going scattering beam A2 to form a SPB region. The amplified backscattering beam A2 enters the FWM regions, mixes with A1 and A4, and generates the phase conjugate A3.

Fig. 3
Fig. 3

Reflectivity of the SPB mirror as a function of γ2l2 with various m0.

Fig. 4
Fig. 4

Threshold coupling strength (γ1l1)th of the FWM-SPB phase conjugator versus the coupling strength of the 2k grating γ2l2 for various m0.

Fig. 5
Fig. 5

SPPC reflectivity at threshold versus γ2l2 for various m0.

Fig. 6
Fig. 6

Phase-conjugate reflectivity versus coupling strength of the 2k grating γ2l2: (a) at different coupling strengths of the transmission grating γ1l1 and (b) for various m0.

Fig. 7
Fig. 7

Experimental setup used to demonstrate SPPC in the FWM-SPB mode: PBS’s, polarizing beam splitters; BS’s, beam splitters.

Fig. 8
Fig. 8

Time evolution of the reflectivity of SPPC (solid curve) and intensity of the fanning beam (dashed curve).

Fig. 9
Fig. 9

Time-evolution of the phase-conjugate signal when the different erasing beams are applied.

Fig. 10
Fig. 10

Experimental phase-conjugate reflectivity versus γ2l2. Note the phase-conjugate threshold at γ2l2 ≈ 7.5 (corresponding to Ir = 4 W/cm2). The solid curve is from a theoretical calculation.

Fig. 11
Fig. 11

Normalized phase-conjugation reflectivity as a function of the polarization angle, Φ, of the input beam. These experimental data are not corrected for Fresnel reflections. The dashed curve is from a theoretical calculation for a pure FWM-SPB mode of SPPC.

Equations (13)

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

d A 1 d z = γ 1 2 I 0 ( A 1 A 4 * + A 2 * A 3 ) A 4 γ 2 2 I 0 A 1 A 2 * A 2 , d A 2 d z = γ 1 2 I 0 ( A 1 * A 4 + A 2 A 3 * ) A 3 γ 2 2 I 0 A 1 * A 2 A 1 , d A 3 d z = γ 1 2 I 0 ( A 1 A 4 * + A 2 * A 3 ) A 2 , d A 4 d z = γ 1 2 I 0 ( A 1 * A 4 + A 2 A 3 * ) A 1 ,
d A 1 d z = γ 2 2 I 0 A 1 A 2 * A 2 , d A 2 d z = γ 2 2 I 0 A 1 * A 2 A 1 ,
I 1 ( z ) = | A 1 ( z ) | 2 = C + C 2 + B   exp ( γ 2 z ) , I 2 ( z ) = | A 2 ( z ) | 2 = C + C 2 + B   exp ( γ 2 z ) ,
B = I 1 ( l 2 ) I 2 ( l 2 ) exp ( γ 2 l 2 ) ,     C = I 2 ( l 2 ) I 1 ( l 2 ) 2 .
R = A 2 ( 0 ) A 1 ( 0 ) 2 = ( 1 m 0 ) 2 + 2 m 0   exp ( γ 2 l 2 ) ( 1 m 0 ) ( 1 m 0 ) 2 + 4 m 0   exp ( γ 2 l 2 ) 2 m 0   exp ( γ 2 l 2 ) .
R = 1 + 2 m 0   exp ( γ 2 l 2 ) 1 + 4 m 0   exp ( γ 2 l 2 ) 2 m 0   exp ( γ 2 l 2 ) .
η = | A 3 ( z = 0 ) | 2 | A 4 ( z = 0 ) | 2 = 1 + σ 1 σ 2 1 R ,
σ = 1 ± R 2 s 2 + R s 2 R 1 + R ,
tanh γ 1 l 1 4 s = s .
( γ 1 l 1 ) th = 2 1 + R   ln 1 + R + 1 1 + R 1 ,
η th = R ( 1 + R ) 2 .
γ 2 ( I r ) = γ 2 o 1 + I r / I ,
γ 1 ( ϕ ) = γ 1 o 1 + tan 2   ϕ ,

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