Abstract

We study the mechanism of operation of a ring-cavity self-pumped phase-conjugate mirror and focus our interest on the influence of reflection gratings on the response time and the reflectivity of the mirror. Our ring-cavity self-pumped phase-conjugate mirror is constructed around an Fe-doped KNbO3 crystal. In the analysis we consider six possible two-wave-mixing processes in the photorefractive crystal and select the crystal orientation that maximizes these couplings in the desired two-wave-mixing processes. By use of a vibrating mirror in the ring cavity or a decrease in the coherence length of the laser below the length of the ring cavity, the response time becomes short and the reflectivity increases. The results show that the buildup of reflection gratings in a ring-cavity self-pumped phase-conjugate mirror presents an obstacle to good performance.

© 1997 Optical Society of America

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References

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  1. P. Günter and J. Huignard, eds., Photorefractive Material and their Applications II (Springer-Verlag, Berlin, 1989).
  2. P. Yeh, “Photorefractive phase conjugator,” Proc. IEEE 80, 436–450 (1992).
    [CrossRef]
  3. 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]
  4. M. Cronin-Golomb, K. Y. Lau, and A. Yariv, “Infrared photorefractive passive phase conjugation with BaTiO3. Demonstrations with GaAlAs and 1.09 -µm Ar+ lasers,” Appl. Phys. Lett. 47, 567–569 (1985).
    [CrossRef]
  5. B. Fisher and S. Sternkar, “New optical gyroscope based on the ring passive phase conjugator,” Appl. Phys. Lett. 47, 1–3 (1985).
    [CrossRef]
  6. K. Nakagawa, M. Zgonik, T. Minemoto, and P. Günter, “Optical thresholding in a self-pumped phase conjugate mirror with a ring cavity,” Opt. Commun. 122, 43–47 (1995).
    [CrossRef]
  7. M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “Passive phase conjugate mirror based on self-induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42, 919–921 (1983).
    [CrossRef]
  8. V. A. D’yakov, S. A. Korol’kov, A. V. Mamaev, V. V. Shunov, and A. A. Zozulya, “Reflection-grating photorefractive self-pumped ring mirror,” Opt. Lett. 20, 1614–1616 (1991).
    [CrossRef]
  9. M. H. Garrett, J. Y. Chang, H. P. Jenssen, and C. Warde, “Self-pumped phase conjugation and four-wave mixing in 0°- and 45°-cut n-type BaTiO3:Co,” Opt. Lett. 18, 405–407 (1993).
    [CrossRef] [PubMed]
  10. P. Lambelet, R. P. Salathe, M. H. Garrett, and D. Rytz, “Characterization of a photorefractive phase conjugator by optical low-coherence reflectometry,” Appl. Phys. Lett. 64, 1079–1081 (1994).
    [CrossRef]
  11. S.-C. D. L. Cruz, S. MacCormack, J. Feinberg, Q. B. He, H.-K. Liu, and P. Yeh, “Effect of beam coherence on mutually pumped phase conjugators,” J. Opt. Soc. Am. B 12, 1363–1369 (1995).
    [CrossRef]
  12. M. Cronin-Golomb, J. Paslaski, and A. Yariv, “Vibration resistance, short coherence length operation, and mode-locked pump in passive conjugate mirrors,” Appl. Phys. Lett. 47, 1131–1133 (1985).
    [CrossRef]
  13. M. Cronin-Golomb, “Almost all transmission grating self-pumped phase-conjugate mirrors are equivalent,” Opt. Lett. 15, 897–899 (1990).
    [CrossRef] [PubMed]
  14. J. Feinberg, “Asymmetric self-defocusing of an optical beam from the photorefractive effect,” J. Opt. Soc. Am. 72, 46–51 (1982).
    [CrossRef]
  15. C. Medrano, M. Zgonik, S. Berents, P. Bernasconi, and P. Günter, “Self-pumped and incoherent phase conjugation in Fe-doped KNbO3,” J. Opt. Soc. Am. B 11, 1718–1726 (1994).
    [CrossRef]
  16. M. Zgonik, K. Nakagawa, and P. Günter, “Electro-optic and dielectric properties of photorefractive BaTiO3 and KNbO3,” J. Opt. Soc. Am. B 12, 1416–1421 (1995).
    [CrossRef]
  17. S. A. Korol’kov, Y. S. Kuzminov, A. V. Mamev, V. V. Shkunov, and A. A. Zozulya, “Spatial structure of scattered radiation in a self-pumped photorefractive passive ring mirror,” J. Opt. Soc. Am. B 9, 664–671 (1992).
    [CrossRef]

1995 (3)

1994 (2)

P. Lambelet, R. P. Salathe, M. H. Garrett, and D. Rytz, “Characterization of a photorefractive phase conjugator by optical low-coherence reflectometry,” Appl. Phys. Lett. 64, 1079–1081 (1994).
[CrossRef]

C. Medrano, M. Zgonik, S. Berents, P. Bernasconi, and P. Günter, “Self-pumped and incoherent phase conjugation in Fe-doped KNbO3,” J. Opt. Soc. Am. B 11, 1718–1726 (1994).
[CrossRef]

1993 (1)

1992 (2)

1991 (1)

V. A. D’yakov, S. A. Korol’kov, A. V. Mamaev, V. V. Shunov, and A. A. Zozulya, “Reflection-grating photorefractive self-pumped ring mirror,” Opt. Lett. 20, 1614–1616 (1991).
[CrossRef]

1990 (1)

1985 (3)

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

M. Cronin-Golomb, K. Y. Lau, and A. Yariv, “Infrared photorefractive passive phase conjugation with BaTiO3. Demonstrations with GaAlAs and 1.09 -µm Ar+ lasers,” Appl. Phys. Lett. 47, 567–569 (1985).
[CrossRef]

B. Fisher and S. Sternkar, “New optical gyroscope based on the ring passive phase conjugator,” Appl. Phys. Lett. 47, 1–3 (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]

1983 (1)

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “Passive phase conjugate mirror based on self-induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42, 919–921 (1983).
[CrossRef]

1982 (1)

Berents, S.

Bernasconi, P.

Chang, J. Y.

Cronin-Golomb, M.

M. Cronin-Golomb, “Almost all transmission grating self-pumped phase-conjugate mirrors are equivalent,” Opt. Lett. 15, 897–899 (1990).
[CrossRef] [PubMed]

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

M. Cronin-Golomb, K. Y. Lau, and A. Yariv, “Infrared photorefractive passive phase conjugation with BaTiO3. Demonstrations with GaAlAs and 1.09 -µm Ar+ lasers,” Appl. Phys. Lett. 47, 567–569 (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]

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “Passive phase conjugate mirror based on self-induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42, 919–921 (1983).
[CrossRef]

Cruz, S.-C. D. L.

D’yakov, V. A.

V. A. D’yakov, S. A. Korol’kov, A. V. Mamaev, V. V. Shunov, and A. A. Zozulya, “Reflection-grating photorefractive self-pumped ring mirror,” Opt. Lett. 20, 1614–1616 (1991).
[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]

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “Passive phase conjugate mirror based on self-induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42, 919–921 (1983).
[CrossRef]

Fisher, B.

B. Fisher and S. Sternkar, “New optical gyroscope based on the ring passive phase conjugator,” Appl. Phys. Lett. 47, 1–3 (1985).
[CrossRef]

Garrett, M. H.

P. Lambelet, R. P. Salathe, M. H. Garrett, and D. Rytz, “Characterization of a photorefractive phase conjugator by optical low-coherence reflectometry,” Appl. Phys. Lett. 64, 1079–1081 (1994).
[CrossRef]

M. H. Garrett, J. Y. Chang, H. P. Jenssen, and C. Warde, “Self-pumped phase conjugation and four-wave mixing in 0°- and 45°-cut n-type BaTiO3:Co,” Opt. Lett. 18, 405–407 (1993).
[CrossRef] [PubMed]

Günter, P.

He, Q. B.

Jenssen, H. P.

Korol’kov, S. A.

S. A. Korol’kov, Y. S. Kuzminov, A. V. Mamev, V. V. Shkunov, and A. A. Zozulya, “Spatial structure of scattered radiation in a self-pumped photorefractive passive ring mirror,” J. Opt. Soc. Am. B 9, 664–671 (1992).
[CrossRef]

V. A. D’yakov, S. A. Korol’kov, A. V. Mamaev, V. V. Shunov, and A. A. Zozulya, “Reflection-grating photorefractive self-pumped ring mirror,” Opt. Lett. 20, 1614–1616 (1991).
[CrossRef]

Kuzminov, Y. S.

Lambelet, P.

P. Lambelet, R. P. Salathe, M. H. Garrett, and D. Rytz, “Characterization of a photorefractive phase conjugator by optical low-coherence reflectometry,” Appl. Phys. Lett. 64, 1079–1081 (1994).
[CrossRef]

Lau, K. Y.

M. Cronin-Golomb, K. Y. Lau, and A. Yariv, “Infrared photorefractive passive phase conjugation with BaTiO3. Demonstrations with GaAlAs and 1.09 -µm Ar+ lasers,” Appl. Phys. Lett. 47, 567–569 (1985).
[CrossRef]

Liu, H.-K.

MacCormack, S.

Mamaev, A. V.

V. A. D’yakov, S. A. Korol’kov, A. V. Mamaev, V. V. Shunov, and A. A. Zozulya, “Reflection-grating photorefractive self-pumped ring mirror,” Opt. Lett. 20, 1614–1616 (1991).
[CrossRef]

Mamev, A. V.

Medrano, C.

Minemoto, T.

K. Nakagawa, M. Zgonik, T. Minemoto, and P. Günter, “Optical thresholding in a self-pumped phase conjugate mirror with a ring cavity,” Opt. Commun. 122, 43–47 (1995).
[CrossRef]

Nakagawa, K.

K. Nakagawa, M. Zgonik, T. Minemoto, and P. Günter, “Optical thresholding in a self-pumped phase conjugate mirror with a ring cavity,” Opt. Commun. 122, 43–47 (1995).
[CrossRef]

M. Zgonik, K. Nakagawa, and P. Günter, “Electro-optic and dielectric properties of photorefractive BaTiO3 and KNbO3,” J. Opt. Soc. Am. B 12, 1416–1421 (1995).
[CrossRef]

Paslaski, J.

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

Rytz, D.

P. Lambelet, R. P. Salathe, M. H. Garrett, and D. Rytz, “Characterization of a photorefractive phase conjugator by optical low-coherence reflectometry,” Appl. Phys. Lett. 64, 1079–1081 (1994).
[CrossRef]

Salathe, R. P.

P. Lambelet, R. P. Salathe, M. H. Garrett, and D. Rytz, “Characterization of a photorefractive phase conjugator by optical low-coherence reflectometry,” Appl. Phys. Lett. 64, 1079–1081 (1994).
[CrossRef]

Shkunov, V. V.

Shunov, V. V.

V. A. D’yakov, S. A. Korol’kov, A. V. Mamaev, V. V. Shunov, and A. A. Zozulya, “Reflection-grating photorefractive self-pumped ring mirror,” Opt. Lett. 20, 1614–1616 (1991).
[CrossRef]

Sternkar, S.

B. Fisher and S. Sternkar, “New optical gyroscope based on the ring passive phase conjugator,” Appl. Phys. Lett. 47, 1–3 (1985).
[CrossRef]

Warde, C.

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]

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “Passive phase conjugate mirror based on self-induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42, 919–921 (1983).
[CrossRef]

Yariv, A.

M. Cronin-Golomb, K. Y. Lau, and A. Yariv, “Infrared photorefractive passive phase conjugation with BaTiO3. Demonstrations with GaAlAs and 1.09 -µm Ar+ lasers,” Appl. Phys. Lett. 47, 567–569 (1985).
[CrossRef]

M. Cronin-Golomb, J. Paslaski, and A. Yariv, “Vibration resistance, short coherence length operation, and mode-locked pump in passive 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]

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “Passive phase conjugate mirror based on self-induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42, 919–921 (1983).
[CrossRef]

Yeh, P.

Zgonik, M.

Zozulya, A. A.

S. A. Korol’kov, Y. S. Kuzminov, A. V. Mamev, V. V. Shkunov, and A. A. Zozulya, “Spatial structure of scattered radiation in a self-pumped photorefractive passive ring mirror,” J. Opt. Soc. Am. B 9, 664–671 (1992).
[CrossRef]

V. A. D’yakov, S. A. Korol’kov, A. V. Mamaev, V. V. Shunov, and A. A. Zozulya, “Reflection-grating photorefractive self-pumped ring mirror,” Opt. Lett. 20, 1614–1616 (1991).
[CrossRef]

Appl. Phys. Lett. (5)

M. Cronin-Golomb, K. Y. Lau, and A. Yariv, “Infrared photorefractive passive phase conjugation with BaTiO3. Demonstrations with GaAlAs and 1.09 -µm Ar+ lasers,” Appl. Phys. Lett. 47, 567–569 (1985).
[CrossRef]

B. Fisher and S. Sternkar, “New optical gyroscope based on the ring passive phase conjugator,” Appl. Phys. Lett. 47, 1–3 (1985).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, “Passive phase conjugate mirror based on self-induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42, 919–921 (1983).
[CrossRef]

P. Lambelet, R. P. Salathe, M. H. Garrett, and D. Rytz, “Characterization of a photorefractive phase conjugator by optical low-coherence reflectometry,” Appl. Phys. Lett. 64, 1079–1081 (1994).
[CrossRef]

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

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (4)

Opt. Commun. (1)

K. Nakagawa, M. Zgonik, T. Minemoto, and P. Günter, “Optical thresholding in a self-pumped phase conjugate mirror with a ring cavity,” Opt. Commun. 122, 43–47 (1995).
[CrossRef]

Opt. Lett. (3)

Proc. IEEE (1)

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

Other (1)

P. Günter and J. Huignard, eds., Photorefractive Material and their Applications II (Springer-Verlag, Berlin, 1989).

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Figures (9)

Fig. 1
Fig. 1

Basic geometry of a SPPCM with a ring cavity (a) When the coherence length of the laser is longer than the cavity length, there are four types of grating, i.e., the transmission grating (I) and the reflection gratings (II, III, IV). (b), (c) Two types of 4WM in the ring SPPCM.

Fig. 2
Fig. 2

Definition of parameters of 2WM at arbitrary incident directions. The beam j with the incident direction ϕj=ϕb-θ is the probe beam in this analysis.

Fig. 3
Fig. 3

Calculated value of Γ as a function of ϕb for some values of θ. The cases in which 2θ is between 5° and 60° correspond to 2WM by means of transmission gratings, and the two cases of 2θ=170° and 2θ=180° correspond to reflection gratings.

Fig. 4
Fig. 4

Six possible types of 2WM process in a ring SPPCM under the optimum condition that ϕ1=323°, ϕ2=143°, ϕ3=133°, and ϕ4=313°. These six types of 2WM process may contribute to phase conjugation in the ring SPPCM.

Fig. 5
Fig. 5

Experimental setup for a SPPCM with a ring cavity under the optimum condition that ϕ2=143° and ϕ4=313° in the crystal. The crossing angle between beams 1 and 4 in air is 40°.

Fig. 6
Fig. 6

Reflectivity of SPPCM as a function of time in the case of lc>L and lc<L. The difference between both dependencies is due to the existence of reflection gratings in the second case.

Fig. 7
Fig. 7

Reflectivity of SPPCM as a function of time in the case of lc<L when one of the mirrors in the ring cavity is vibrated with frequency 0 (filled circles), 10 (open squares), and 100 Hz (crosses). There are always only transmission gratings in the crystal in this case. As expected, the transmission gratings are not affected by the mirror’s vibrating, therefore there is no difference between the measurements.

Fig. 8
Fig. 8

Reflectivity of SPPCM as a function of time in the case of lc>L when one of the mirrors in the ring cavity is vibrated with frequency 0 (filled circles), 1 (open squares), and 100 Hz (crosses).

Fig. 9
Fig. 9

Maximum reflectivity of SPPCM in the case of lc>L and lc<L. The reflectivities are measured as a function of the frequency of mirror vibration, which has an amplitude of 256 nm.

Equations (9)

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

|Aj(d)|2=|Aj(0)|2 exp(Γd),
Γ=(2π/λ)(ninj)(3/2)reffEqED/(Eq+ED),
reff(ϕj, ϕi)=cos(ϕj)[r22eff(α)cos(ϕi)-r23eff(α)sin(ϕi)]+sin(ϕj)[-r23eff(α)cos(ϕi)+r33eff(α)sin(ϕi)],
Eq=eNeff/(εeffPRε0Kg),
ED=kBTKg/e,
εeffPR(α)=486-470 cos(2α)+27 cos(4α)-6 cos(6α),
r22eff(α)=15 cos(α)-2.5 cos(3α)-cos(5α)(pm V-1),
r33eff(α)=76 cos(α)-24 cos(3α)+6.5 cos(5α)+1.5 cos(7α)(pm V-1),
r23eff(α)=434 cos(α)-18 cos(3α)+9 cos(5α)+1.5 cos(7α)(pm V-1).

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