Abstract

We demonstrate the bistable behavior of a unidirectional ring resonator that employs photorefractive loss as well as photorefractive gain. The gain and loss are established by two-beam coupling in two separate photorefractive BaTiO3 crystals. Two-beam coupling loss plays the role of a programmable saturable absorber. Irreversible bistability occurs when the maximum net gain exceeds unity, while reversible bistability is obtained when the maximum net gain is less than one.

© 1989 Optical Society of America

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References

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  1. For a review of optical bistability, see H. Gibbs, Optical Bistability: Controlling Light With Light (Academic, Orlando, Fla., 1985).
  2. The unidirectional ring resonator with photorefractive gain alone was first demonstrated in J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
    [CrossRef]
  3. V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, Usp. Fiz. Nauk 129, 113 (1979)[Sov. Phys. Usp. 22, 742 (1979)].
    [CrossRef]
  4. B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
    [CrossRef] [PubMed]
  5. P. Yeh, J. Opt. Soc. Am. B 2, 1924 (1985).
    [CrossRef]
  6. A. Yariv, S.-K. Kwong, Opt. Lett. 10, 454 (1985).
    [CrossRef] [PubMed]
  7. J. J. Di Stefano, A. R. Stubberud, I. J. Williams, Schaum's Outline Series: Theory and Problems of Feedback and Control Systems (McGraw-Hill, New York, 1967), Chap. 11.
  8. D. Z. Anderson, J. Feinberg, IEEE J. Quantum Electron. QE-25, 635 (1989).
    [CrossRef]

1989

D. Z. Anderson, J. Feinberg, IEEE J. Quantum Electron. QE-25, 635 (1989).
[CrossRef]

1985

1982

The unidirectional ring resonator with photorefractive gain alone was first demonstrated in J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

1981

1979

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, Usp. Fiz. Nauk 129, 113 (1979)[Sov. Phys. Usp. 22, 742 (1979)].
[CrossRef]

Anderson, D. Z.

D. Z. Anderson, J. Feinberg, IEEE J. Quantum Electron. QE-25, 635 (1989).
[CrossRef]

Cronin-Golomb, M.

The unidirectional ring resonator with photorefractive gain alone was first demonstrated in J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
[CrossRef] [PubMed]

Di Stefano, J. J.

J. J. Di Stefano, A. R. Stubberud, I. J. Williams, Schaum's Outline Series: Theory and Problems of Feedback and Control Systems (McGraw-Hill, New York, 1967), Chap. 11.

Feinberg, J.

D. Z. Anderson, J. Feinberg, IEEE J. Quantum Electron. QE-25, 635 (1989).
[CrossRef]

Fischer, B.

The unidirectional ring resonator with photorefractive gain alone was first demonstrated in J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
[CrossRef] [PubMed]

Gibbs, H.

For a review of optical bistability, see H. Gibbs, Optical Bistability: Controlling Light With Light (Academic, Orlando, Fla., 1985).

Kukhtarev, N. V.

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, Usp. Fiz. Nauk 129, 113 (1979)[Sov. Phys. Usp. 22, 742 (1979)].
[CrossRef]

Kwong, S.-K.

Odulov, S. G.

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, Usp. Fiz. Nauk 129, 113 (1979)[Sov. Phys. Usp. 22, 742 (1979)].
[CrossRef]

Soskin, M. S.

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, Usp. Fiz. Nauk 129, 113 (1979)[Sov. Phys. Usp. 22, 742 (1979)].
[CrossRef]

Stubberud, A. R.

J. J. Di Stefano, A. R. Stubberud, I. J. Williams, Schaum's Outline Series: Theory and Problems of Feedback and Control Systems (McGraw-Hill, New York, 1967), Chap. 11.

Vinetskii, V. L.

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, Usp. Fiz. Nauk 129, 113 (1979)[Sov. Phys. Usp. 22, 742 (1979)].
[CrossRef]

White, J. O.

The unidirectional ring resonator with photorefractive gain alone was first demonstrated in J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
[CrossRef] [PubMed]

Williams, I. J.

J. J. Di Stefano, A. R. Stubberud, I. J. Williams, Schaum's Outline Series: Theory and Problems of Feedback and Control Systems (McGraw-Hill, New York, 1967), Chap. 11.

Yariv, A.

A. Yariv, S.-K. Kwong, Opt. Lett. 10, 454 (1985).
[CrossRef] [PubMed]

The unidirectional ring resonator with photorefractive gain alone was first demonstrated in J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
[CrossRef] [PubMed]

Yeh, P.

Appl. Phys. Lett.

The unidirectional ring resonator with photorefractive gain alone was first demonstrated in J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

IEEE J. Quantum Electron.

D. Z. Anderson, J. Feinberg, IEEE J. Quantum Electron. QE-25, 635 (1989).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Usp. Fiz. Nauk

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, Usp. Fiz. Nauk 129, 113 (1979)[Sov. Phys. Usp. 22, 742 (1979)].
[CrossRef]

Other

J. J. Di Stefano, A. R. Stubberud, I. J. Williams, Schaum's Outline Series: Theory and Problems of Feedback and Control Systems (McGraw-Hill, New York, 1967), Chap. 11.

For a review of optical bistability, see H. Gibbs, Optical Bistability: Controlling Light With Light (Academic, Orlando, Fla., 1985).

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Figures (6)

Fig. 1
Fig. 1

Unidirectional ring-resonator circuit with two-beam coupling gain and loss.

Fig. 2
Fig. 2

Open-loop characteristics of gain and loss. (a) The gain (solid curve) and the loss (dashed curve) are functions of input intensity ratios rG and rL, respectively. The gain and loss pump intensities are equal, as are the magnitudes of the small-signal gain and loss. (b) The combined gain for the cases L0 > G0 and IGPILP; the loss medium follows the gain medium. P ≡ log {ILP/IGP}. Points A, , and C indicate the steady-state solutions for the resonator intensity in closed-loop operation. Point is unstable.

Fig. 3
Fig. 3

Experimental arrangement for the bistable ring resonator. Two BaTiO3 crystals provide the gain and saturable loss. A single-frequency argon-ion laser operating at 515 nm supplies all beams. The pump power into the gain crystal is 65 mW, and the probe power into the loss crystal is 0.2 mW. A 0.8-mm pinhole aperture is placed at the cavity waist to suppress oscillation of higher-order transverse modes. Mirror M2 is mounted on a piezo mirror to stabilize the cavity length. Mirror M3 is a 1-m-radius spherical mirror. Variable attenuator 1 controls the input intensity, while variable attenuator 2 is a computer-driven variable beam splitter used to ramp the input intensity. Photodetector 1 monitors the input intensity, while photodetector 2 measures the resonator intensity. The beam block is used when measuring the single-pass net gain.

Fig. 4
Fig. 4

Experimental single-pass gain data. Circles, the gain only; triangles, the gain and loss.

Fig. 5
Fig. 5

Experimental data demonstrating the two stable states of the resonator. Increasing intensity is indicated downward on the ordinate. The upper trace shows the injected signal, and the lower trace shows the resonator output. The horizontal scale is 20 sec/division; the vertical scale is logarithmic, with 0.5 decade per division.

Fig. 6
Fig. 6

Experimental data showing hysteresis in the circulating optical power in the resonator as the intensity of the injected beam is slowly increased (circles) and then decreased (triangles).

Equations (2)

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GAIN = r G + 1 r G + exp ( Γ G l G ) ,
γ L γ G > G 0 C L 0 + C ,

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