Abstract

One of the typical methods to generate the phase-conjugate beam is four-wave mixing with a photorefractive crystal. It is known that the phase-conjugate reflectivity shows the bistability in some cases. Analyzing the temporal property of four-wave mixing, we offer a new method to control the bistable phase-conjugate reflectivity, and we perform an experiment of the bistability control by the method. An equation to obtain the threshold value of the coupling strength for showing the bistability is derived by a steady-state analysis of four-wave mixing, and the temporal property of four-wave mixing is studied with two different initial conditions that are used for letting the phase-conjugate reflectivity R converge to an off state (R=0) or to an on state (R>0). The initial condition for the converging off state is that the forward pump beam is turned off throughout. The condition for the converging on state is that the forward pump beam is turned on in advance, and after enough time passes, it is turned off. In both conditions, the backward pump beam and the probe beam continue to illuminate throughout. Whereas both optical arrangements are equivalent after setting up these initial conditions, each phase-conjugate reflectivity converges to different stationary values, R=0 and R>0. Besides, an experiment is performed and we actually control the bistability by this method. Furthermore, the temporal and the spatial variation of the refractive-index grating in the photorefractive crystal is investigated, and the process of the bistability is explained.

© 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. K. S. Syed, G. J. Crofts, and M. J. Damzen, “Transient analysis of four-grating copolarized four-wave mixing insaturable gain media with finite probe,” J. Opt. Soc. Am. B 13, 1892–1904 (1996).
    [CrossRef]
  4. J. B. Norman, “Phase-conjugate Michelson interferometers for all-optical image processingand computing,” Am. J. Phys. 60, 212–220 (1992).
    [CrossRef]
  5. 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]
  6. 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]
  7. F. T. S. Yu and S. Yin, “Applications of photorefractive crystals to signal processing,” Int. J. Opt. Comput. 2, 143–163 (1991).
  8. S. Campbell, Y. Zhang, and P. Yeh, “Writing and copying in volume holographic memories: approaches andanalysis,” Opt. Commun. 123, 27–33 (1996).
    [CrossRef]
  9. T. K. Das and G. C. Bhar, “Phase-conjugate bistability and multistability in moving–gratingoperated orthogonally polarized pump four-wave mixing in photorefractives,” Opt. Quantum Electron. 26, 1019–1032 (1994).
    [CrossRef]
  10. S.-K. Kwong, M. Cronin-Golomb, and A. Yariv, “Optical bistability and hysteresis with a photorefractive self-pumpedphase conjugate mirror,” Appl. Phys. Lett. 45, 1016–1018 (1984).
    [CrossRef]
  11. Y. Ding and H. J. Eichler, “Increase and bistability of the four-wave mixing reflectivity in photorefractiveInP:Fe by grating-shift control,” J. Opt. Soc. Am. B 11, 119–123 (1994).
    [CrossRef]
  12. B. M. Jost, “Photorefractive two-wave mixing bistability in Fe:KNbO3 without external feedback: increasinggain bistability,” Appl. Phys. Lett. 69, 1346–1348 (1996).
    [CrossRef]
  13. 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]

1996 (4)

S. Campbell, Y. Zhang, and P. Yeh, “Writing and copying in volume holographic memories: approaches andanalysis,” Opt. Commun. 123, 27–33 (1996).
[CrossRef]

B. M. Jost, “Photorefractive two-wave mixing bistability in Fe:KNbO3 without external feedback: increasinggain bistability,” Appl. Phys. Lett. 69, 1346–1348 (1996).
[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]

K. S. Syed, G. J. Crofts, and M. J. Damzen, “Transient analysis of four-grating copolarized four-wave mixing insaturable gain media with finite probe,” J. Opt. Soc. Am. B 13, 1892–1904 (1996).
[CrossRef]

1994 (2)

Y. Ding and H. J. Eichler, “Increase and bistability of the four-wave mixing reflectivity in photorefractiveInP:Fe by grating-shift control,” J. Opt. Soc. Am. B 11, 119–123 (1994).
[CrossRef]

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

1992 (1)

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

1991 (2)

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 (1)

1984 (2)

S.-K. Kwong, M. Cronin-Golomb, and A. Yariv, “Optical bistability and hysteresis with a photorefractive self-pumpedphase conjugate mirror,” Appl. Phys. Lett. 45, 1016–1018 (1984).
[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]

Bhar, G. C.

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

Campbell, S.

S. Campbell, Y. Zhang, and P. Yeh, “Writing and copying in volume holographic memories: approaches andanalysis,” Opt. Commun. 123, 27–33 (1996).
[CrossRef]

Crofts, G. J.

Cronin-Golomb, M.

S.-K. Kwong, M. Cronin-Golomb, and A. Yariv, “Optical bistability and hysteresis with a photorefractive self-pumpedphase conjugate mirror,” Appl. Phys. Lett. 45, 1016–1018 (1984).
[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]

Damzen, M. J.

Das, T. K.

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

Ding, Y.

Eichler, H. J.

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.

Jahoda, F. C.

Jost, B. M.

B. M. Jost, “Photorefractive two-wave mixing bistability in Fe:KNbO3 without external feedback: increasinggain bistability,” Appl. Phys. Lett. 69, 1346–1348 (1996).
[CrossRef]

Kang, H.

Kwong, S.-K.

S.-K. Kwong, M. Cronin-Golomb, and A. Yariv, “Optical bistability and hysteresis with a photorefractive self-pumpedphase conjugate mirror,” Appl. Phys. Lett. 45, 1016–1018 (1984).
[CrossRef]

Mason, B. L.

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]

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]

Syed, K. S.

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]

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]

S.-K. Kwong, M. Cronin-Golomb, and A. Yariv, “Optical bistability and hysteresis with a photorefractive self-pumpedphase conjugate mirror,” Appl. Phys. Lett. 45, 1016–1018 (1984).
[CrossRef]

Yeh, P.

S. Campbell, Y. Zhang, and P. Yeh, “Writing and copying in volume holographic memories: approaches andanalysis,” Opt. Commun. 123, 27–33 (1996).
[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).

Zhang, Y.

S. Campbell, Y. Zhang, and P. Yeh, “Writing and copying in volume holographic memories: approaches andanalysis,” Opt. Commun. 123, 27–33 (1996).
[CrossRef]

Am. J. Phys. (1)

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

Appl. Phys. Lett. (2)

S.-K. Kwong, M. Cronin-Golomb, and A. Yariv, “Optical bistability and hysteresis with a photorefractive self-pumpedphase conjugate mirror,” Appl. Phys. Lett. 45, 1016–1018 (1984).
[CrossRef]

B. M. Jost, “Photorefractive two-wave mixing bistability in Fe:KNbO3 without external feedback: increasinggain bistability,” Appl. Phys. Lett. 69, 1346–1348 (1996).
[CrossRef]

IEEE J. Quantum Electron. (1)

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]

Int. J. Opt. Comput. (1)

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

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

Opt. Commun. (2)

S. Campbell, Y. Zhang, and P. Yeh, “Writing and copying in volume holographic memories: approaches andanalysis,” Opt. Commun. 123, 27–33 (1996).
[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. (2)

Opt. Quantum Electron. (1)

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

Other (1)

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

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Figures (6)

Fig. 1
Fig. 1

General four-wave mixing.

Fig. 2
Fig. 2

Initial conditions: (a) condition 1 and (b) condition 2.

Fig. 3
Fig. 3

Calculated phase-conjugate reflectivity: (a) in the case of γL=3 and (b) in the case of γL=7.

Fig. 4
Fig. 4

Optical setup.

Fig. 5
Fig. 5

Experimental phase-conjugate reflectivity.

Fig. 6
Fig. 6

Temporal and spatial variation of grating: (a) In the case of γL=3 and (b) in the case of γL=7.

Equations (23)

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

A1(z)z=γ2I0[Ai(z)A4(z)*+A2(z)*A3(z)]A4(z),
A2(z)*z=γ2I0[A1(z)A4(z)*+A2(z)*A3(z)]A3(z)*,
A3(z)z=-γ2I0[A1(z)A4(z)*+A2(z)*A3(z)]A2(z),
A4(z)*z=-γ2I0{A1(z)A4(z)*+A2(z)*A3(z)}A1(z)*,
A1A2+A3A4=c1,
I1+I4=d1,
I2+I3=d2.
Δ=d2-d1,
P=(Δ2+4|c1|2)1/2,
A1(L)A2(L)*
=(Δ+P)D exp-γL4I0P-(Δ-P)D-1 expγL4I0P2c1*D-1 expγL4I0P-D exp-γL4I0P=c1I2(L),
A1(0)A2(0)*
=(Δ+P)D-(Δ-P)D-12c1*(D-1-D),
R=4|c1|2 tanh2-γL4I0PΔ tanh-γL4I0P+P2,
D2=I2(L)(Δ-P)+2|c1|2I2(L)(Δ+P)+2|c1|2expγL2I0P
D2=Δ-PΔ+P
tanhγL4I0P=PI0,
P>|Δ|
A1(z, t)z=Q(z, t)A4(z, t),
A2(z, t)z=Q(z, t)*A3(z, t),
A3(z, t)z=-Q(z, t)A2(z, t),
A4(z, t)z=-Q(z, t)*A1(z, t),
τ0 Q(z, t)t+Q(z, t)=γ2I0[A1(z, t)A4(z, t)*+A2(z, t)*A3(z, t)],

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