Abstract

We propose a method to obtain higher phase-conjugate reflectivity by using a pulsed pump beam as the reading beam. A qualitative explanation of our method is given. Then we calculate the transient phase-conjugate reflectivity, considering that the reading beam erases the grating in a photorefractive crystal. The reflectivity when a continuous reading beam is used is compared with that when the pulsed beam is used. We prove experimentally that approximately three times greater reflectivity can be obtained with a pulsed reading beam.

© 1997 Optical Society of America

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References

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  1. P. Yeh, Introduction to Photorefractive NonlinearOptics (Wiley, New York, 1993).
  2. M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “Theory and application of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984).
    [CrossRef]
  3. J. B. Norman, “Phase-conjugate Michelson interferometers for all-optical image processingand computing,” Am. J. Phys. 60, 212–220 (1992).
    [CrossRef]
  4. H. Kang, C. X. Yang, G. G. Mu, and Z. K. Wu, “Real-time holographic associative memory using doped LiNbO3 in a phase-conjugate resonator,” Opt. Lett. 15, 637–639 (1990).
    [CrossRef]
  5. T. K. Das and G. C. Bhar, “Phase-conjugate bistability and multistability in moving-grating operatedorthogonally polarized pump four-wave mixing in photorefractives,” Opt. Quantum Electron. 26, 1019–1032 (1994).
    [CrossRef]
  6. F. T. S. Yu and S. Yin, “Applications of photorefractive crystals to signal processing,” Int. J. Opt. Comput. 2, 143–163 (1991).
  7. F. C. Jahoda, P. R. Forman, and B. L. Mason, “Quantitative evaluation of phase-conjugate novelty filters,” Opt. Lett. 16, 1532–1534 (1991).
    [CrossRef] [PubMed]
  8. W. Królikowski, K. D. Shaw, M. Cronin-Golomb, and A. Bledowski, “Stability analysis and temporal behavior of four-wave mixing in photorefractivecrystals,” J. Opt. Soc. Am. B 6, 1828–1833 (1989).
    [CrossRef]
  9. A. A. Zozulya, “Fanning and photorefractive self-pumped four-wave mixing geometries,” IEEE J. Quantum Electron. 29, 538–555 (1993).
    [CrossRef]
  10. Y. Takayama, A. Okamoto, and K. Sato, “High-efficiency transient phase conjugation by turning on reading beamincident upon steady-state transmission grating in BaTiO3 crystal,” Opt. Commun. 123, 603–606 (1996).
    [CrossRef]
  11. Y. Takayama, A. Okamoto, K. Sato, T. Mishima, and I. Sakuraba, “Analysis and experiment on temporal response of four-wave mixing inphotorefractive crystal,” J. Inst. Electr. Inform. Commun. Eng. J77-C-I, 481–489 (1994).
  12. T. Galstyan, G. Pauliat, A. Villing, and G. Roosen, “Adaptive photorefractive neurons for self-organizing networks,” Opt. Commun. 109, 35–42 (1994).
    [CrossRef]
  13. J. Hong, “Applications of photorefractive crystals for optical neural networks,” Opt. Quantum Electron. 25, 551–568 (1993).
    [CrossRef]

1996

Y. Takayama, A. Okamoto, and K. Sato, “High-efficiency transient phase conjugation by turning on reading beamincident upon steady-state transmission grating in BaTiO3 crystal,” Opt. Commun. 123, 603–606 (1996).
[CrossRef]

1994

Y. Takayama, A. Okamoto, K. Sato, T. Mishima, and I. Sakuraba, “Analysis and experiment on temporal response of four-wave mixing inphotorefractive crystal,” J. Inst. Electr. Inform. Commun. Eng. J77-C-I, 481–489 (1994).

T. Galstyan, G. Pauliat, A. Villing, and G. Roosen, “Adaptive photorefractive neurons for self-organizing networks,” Opt. Commun. 109, 35–42 (1994).
[CrossRef]

T. K. Das and G. C. Bhar, “Phase-conjugate bistability and multistability in moving-grating operatedorthogonally polarized pump four-wave mixing in photorefractives,” Opt. Quantum Electron. 26, 1019–1032 (1994).
[CrossRef]

1993

J. Hong, “Applications of photorefractive crystals for optical neural networks,” Opt. Quantum Electron. 25, 551–568 (1993).
[CrossRef]

A. A. Zozulya, “Fanning and photorefractive self-pumped four-wave mixing geometries,” IEEE J. Quantum Electron. 29, 538–555 (1993).
[CrossRef]

1992

J. B. Norman, “Phase-conjugate Michelson interferometers for all-optical image processingand computing,” Am. J. Phys. 60, 212–220 (1992).
[CrossRef]

1991

F. T. S. Yu and S. Yin, “Applications of photorefractive crystals to signal processing,” Int. J. Opt. Comput. 2, 143–163 (1991).

F. C. Jahoda, P. R. Forman, and B. L. Mason, “Quantitative evaluation of phase-conjugate novelty filters,” Opt. Lett. 16, 1532–1534 (1991).
[CrossRef] [PubMed]

1990

1989

1984

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

Bhar, G. C.

T. K. Das and G. C. Bhar, “Phase-conjugate bistability and multistability in moving-grating operatedorthogonally polarized pump four-wave mixing in photorefractives,” Opt. Quantum Electron. 26, 1019–1032 (1994).
[CrossRef]

Bledowski, A.

Cronin-Golomb, M.

W. Królikowski, K. D. Shaw, M. Cronin-Golomb, and A. Bledowski, “Stability analysis and temporal behavior of four-wave mixing in photorefractivecrystals,” J. Opt. Soc. Am. B 6, 1828–1833 (1989).
[CrossRef]

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

Das, T. K.

T. K. Das and G. C. Bhar, “Phase-conjugate bistability and multistability in moving-grating operatedorthogonally polarized pump four-wave mixing in photorefractives,” Opt. Quantum Electron. 26, 1019–1032 (1994).
[CrossRef]

Fischer, B.

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

Forman, P. R.

Galstyan, T.

T. Galstyan, G. Pauliat, A. Villing, and G. Roosen, “Adaptive photorefractive neurons for self-organizing networks,” Opt. Commun. 109, 35–42 (1994).
[CrossRef]

Hong, J.

J. Hong, “Applications of photorefractive crystals for optical neural networks,” Opt. Quantum Electron. 25, 551–568 (1993).
[CrossRef]

Jahoda, F. C.

Kang, H.

Królikowski, W.

Mason, B. L.

Mishima, T.

Y. Takayama, A. Okamoto, K. Sato, T. Mishima, and I. Sakuraba, “Analysis and experiment on temporal response of four-wave mixing inphotorefractive crystal,” J. Inst. Electr. Inform. Commun. Eng. J77-C-I, 481–489 (1994).

Mu, G. G.

Norman, J. B.

J. B. Norman, “Phase-conjugate Michelson interferometers for all-optical image processingand computing,” Am. J. Phys. 60, 212–220 (1992).
[CrossRef]

Okamoto, A.

Y. Takayama, A. Okamoto, and K. Sato, “High-efficiency transient phase conjugation by turning on reading beamincident upon steady-state transmission grating in BaTiO3 crystal,” Opt. Commun. 123, 603–606 (1996).
[CrossRef]

Y. Takayama, A. Okamoto, K. Sato, T. Mishima, and I. Sakuraba, “Analysis and experiment on temporal response of four-wave mixing inphotorefractive crystal,” J. Inst. Electr. Inform. Commun. Eng. J77-C-I, 481–489 (1994).

Pauliat, G.

T. Galstyan, G. Pauliat, A. Villing, and G. Roosen, “Adaptive photorefractive neurons for self-organizing networks,” Opt. Commun. 109, 35–42 (1994).
[CrossRef]

Roosen, G.

T. Galstyan, G. Pauliat, A. Villing, and G. Roosen, “Adaptive photorefractive neurons for self-organizing networks,” Opt. Commun. 109, 35–42 (1994).
[CrossRef]

Sakuraba, I.

Y. Takayama, A. Okamoto, K. Sato, T. Mishima, and I. Sakuraba, “Analysis and experiment on temporal response of four-wave mixing inphotorefractive crystal,” J. Inst. Electr. Inform. Commun. Eng. J77-C-I, 481–489 (1994).

Sato, K.

Y. Takayama, A. Okamoto, and K. Sato, “High-efficiency transient phase conjugation by turning on reading beamincident upon steady-state transmission grating in BaTiO3 crystal,” Opt. Commun. 123, 603–606 (1996).
[CrossRef]

Y. Takayama, A. Okamoto, K. Sato, T. Mishima, and I. Sakuraba, “Analysis and experiment on temporal response of four-wave mixing inphotorefractive crystal,” J. Inst. Electr. Inform. Commun. Eng. J77-C-I, 481–489 (1994).

Shaw, K. D.

Takayama, Y.

Y. Takayama, A. Okamoto, and K. Sato, “High-efficiency transient phase conjugation by turning on reading beamincident upon steady-state transmission grating in BaTiO3 crystal,” Opt. Commun. 123, 603–606 (1996).
[CrossRef]

Y. Takayama, A. Okamoto, K. Sato, T. Mishima, and I. Sakuraba, “Analysis and experiment on temporal response of four-wave mixing inphotorefractive crystal,” J. Inst. Electr. Inform. Commun. Eng. J77-C-I, 481–489 (1994).

Villing, A.

T. Galstyan, G. Pauliat, A. Villing, and G. Roosen, “Adaptive photorefractive neurons for self-organizing networks,” Opt. Commun. 109, 35–42 (1994).
[CrossRef]

White, J. O.

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

Wu, Z. K.

Yang, C. X.

Yariv, A.

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

Yin, S.

F. T. S. Yu and S. Yin, “Applications of photorefractive crystals to signal processing,” Int. J. Opt. Comput. 2, 143–163 (1991).

Yu, F. T. S.

F. T. S. Yu and S. Yin, “Applications of photorefractive crystals to signal processing,” Int. J. Opt. Comput. 2, 143–163 (1991).

Zozulya, A. A.

A. A. Zozulya, “Fanning and photorefractive self-pumped four-wave mixing geometries,” IEEE J. Quantum Electron. 29, 538–555 (1993).
[CrossRef]

Am. J. Phys.

J. B. Norman, “Phase-conjugate Michelson interferometers for all-optical image processingand computing,” Am. J. Phys. 60, 212–220 (1992).
[CrossRef]

IEEE J. Quantum Electron.

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

A. A. Zozulya, “Fanning and photorefractive self-pumped four-wave mixing geometries,” IEEE J. Quantum Electron. 29, 538–555 (1993).
[CrossRef]

Int. J. Opt. Comput.

F. T. S. Yu and S. Yin, “Applications of photorefractive crystals to signal processing,” Int. J. Opt. Comput. 2, 143–163 (1991).

J. Inst. Electr. Inform. Commun. Eng.

Y. Takayama, A. Okamoto, K. Sato, T. Mishima, and I. Sakuraba, “Analysis and experiment on temporal response of four-wave mixing inphotorefractive crystal,” J. Inst. Electr. Inform. Commun. Eng. J77-C-I, 481–489 (1994).

J. Opt. Soc. Am. B

Opt. Commun.

T. Galstyan, G. Pauliat, A. Villing, and G. Roosen, “Adaptive photorefractive neurons for self-organizing networks,” Opt. Commun. 109, 35–42 (1994).
[CrossRef]

Y. Takayama, A. Okamoto, and K. Sato, “High-efficiency transient phase conjugation by turning on reading beamincident upon steady-state transmission grating in BaTiO3 crystal,” Opt. Commun. 123, 603–606 (1996).
[CrossRef]

Opt. Lett.

Opt. Quantum Electron.

J. Hong, “Applications of photorefractive crystals for optical neural networks,” Opt. Quantum Electron. 25, 551–568 (1993).
[CrossRef]

T. K. Das and G. C. Bhar, “Phase-conjugate bistability and multistability in moving-grating operatedorthogonally polarized pump four-wave mixing in photorefractives,” Opt. Quantum Electron. 26, 1019–1032 (1994).
[CrossRef]

Other

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

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Figures (8)

Fig. 1
Fig. 1

Four-wave mixing geometry.

Fig. 2
Fig. 2

Qualitative phase-conjugate reflectivity of a pulsed reading beam.

Fig. 3
Fig. 3

Numerical result of phase-conjugate reflectivity by a continuous backward pump beam: (a) for γL=0.5, (b) for γL =1.0.

Fig. 4
Fig. 4

Numerical results of phase-conjugate reflectivity by a pulsed backward pump beam for γL=0.5: (a) rpump=1.0, (b) rpump=10, (c) rpump=30, (d) range 0–1 s, (e) range 13–14 s.

Fig. 5
Fig. 5

Numerical result of phase-conjugate reflectivity by a pulsed backward pump beam for γL=1.0: (a) rpump=1.0, (b) rpump=10, (c) rpump=30, (d) range 0–1 s, (e) range 13–14 s.

Fig. 6
Fig. 6

Optical geometry of the experiment: A1, forward pump beam; A2 backward pump beam; A3, phase-conjugate beam; A4, probe beam; PD, photodetector; BS, beam splitter; HWP's, half-wave plates; M's, mirrors; PBS's, polarizing beam splitters.

Fig. 7
Fig. 7

Experimental phase-conjugate reflectivity with a continuous backward pump beam.

Fig. 8
Fig. 8

Experimental result of phase-conjugate reflectivity by a pulsed backward pump beam: (a) complete experimental result, (b) range 0–1 s, (c) range 13–14 s.

Equations (9)

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

Ej(z, t)=Aj(z, t)exp[i(kj·z-ωt)],
A1(z, t)t=Q(z, t)A4(z, t),
A2(z, t)t=Q(z, t)*A3(z, t),
A3(z, t)t=-Q(z, t)A2(z, t),
A4(z, t)t=-Q(z, t)*A1(z, t);
τ Q(z, t)t+Q(z, t)=γ2I0[A1(z, t)A4(z, t)*+A2(z, t)*A3(z, t)],
rpump=I2(L, t)/I1(0, t),
rprobe=I4(0, t)/[I1(0, t)+I2(L, t)],
R=I3(0, t)/I4(0, t).

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