Abstract

Photorefractive resonators exhibit an extremely small frequency difference (Δω/ω ~ 10−15) between the oscillating and pumping beams. The observed frequency difference is proportional to cavity-length detuning. This dependence is explained by a photorefractive phase shift that is due to slightly nondegenerate two-wave mixing that compensates for cavity detuning and satisfies the round-trip phase condition for steady-state oscillation. The measured onset or threshold of oscillation as a function of photorefractive gain and intensity agrees with theory.

© 1985 Optical Society of America

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References

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  1. J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
    [CrossRef]
  2. R. McFarlane, D. Steel, Opt. Lett. 8, 208 (1983).
    [CrossRef] [PubMed]
  3. J. Feinberg, Opt. Lett. 8, 480 (1983).
    [CrossRef] [PubMed]
  4. J. Feinberg, G. D. Bacher, Opt. Lett. 9, 420 (1984).
    [CrossRef] [PubMed]
  5. K. R. MacDonald, J. Feinberg, J. Opt. Soc. Am. A 1, 1213 (A)1984.
  6. J. F. Lam, J. Opt. Soc. Am. A 1, 1223 (A)1984.
  7. W. Whitten, J. Ramsey, Opt. Lett. 9, 44 (1984).
    [CrossRef] [PubMed]
  8. H. Rajbenbach, J. P. Huignard, Opt. Lett. 10, 137 (1985).
    [CrossRef] [PubMed]
  9. P. Yeh, J. Opt. Soc. Am. B 2 (to be published, November1985).
  10. G. Valley, G. Dunning, Opt. Lett. 9, 513 (1984).
    [CrossRef] [PubMed]
  11. P. Gunter, Phys. Rep. 93, 199 (1982).
    [CrossRef]
  12. As the orientation of the two-wave mixing fringe pattern with respect to the crystal axes changes, the effective electro-optic coefficient (and coupling efficiency of the index grating) is modified. γL is independently measured by removing ring-cavity mirror M2 and using an attenuated probe beam from BS2 with an external angle of 20° between probe and pump beams.
  13. Provided by R. Neurganokar, Rockwell International, Thousand Oaks, Calif.
  14. B. Fischer, M. Cronin-Goulomb, J. O. White, A. Yariv, R. Neurgaonkar, Appl. Phys. Lett. 40, 863 (1982).
    [CrossRef]
  15. P. Yeh, M. D. Ewbank, M. Khoshnevisan, J. M. Tracy, Opt. Lett. 9, 41(1984).
    [CrossRef] [PubMed]

1985 (1)

1984 (6)

1983 (2)

1982 (3)

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

P. Gunter, Phys. Rep. 93, 199 (1982).
[CrossRef]

B. Fischer, M. Cronin-Goulomb, J. O. White, A. Yariv, R. Neurgaonkar, Appl. Phys. Lett. 40, 863 (1982).
[CrossRef]

Bacher, G. D.

Cronin-Golomb, M.

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

Cronin-Goulomb, M.

B. Fischer, M. Cronin-Goulomb, J. O. White, A. Yariv, R. Neurgaonkar, Appl. Phys. Lett. 40, 863 (1982).
[CrossRef]

Dunning, G.

Ewbank, M. D.

Feinberg, J.

Fischer, B.

B. Fischer, M. Cronin-Goulomb, J. O. White, A. Yariv, R. Neurgaonkar, Appl. Phys. Lett. 40, 863 (1982).
[CrossRef]

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

Gunter, P.

P. Gunter, Phys. Rep. 93, 199 (1982).
[CrossRef]

Huignard, J. P.

Khoshnevisan, M.

Lam, J. F.

J. F. Lam, J. Opt. Soc. Am. A 1, 1223 (A)1984.

MacDonald, K. R.

K. R. MacDonald, J. Feinberg, J. Opt. Soc. Am. A 1, 1213 (A)1984.

McFarlane, R.

Neurgaonkar, R.

B. Fischer, M. Cronin-Goulomb, J. O. White, A. Yariv, R. Neurgaonkar, Appl. Phys. Lett. 40, 863 (1982).
[CrossRef]

Rajbenbach, H.

Ramsey, J.

Steel, D.

Tracy, J. M.

Valley, G.

White, J. O.

B. Fischer, M. Cronin-Goulomb, J. O. White, A. Yariv, R. Neurgaonkar, Appl. Phys. Lett. 40, 863 (1982).
[CrossRef]

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

Whitten, W.

Yariv, A.

B. Fischer, M. Cronin-Goulomb, J. O. White, A. Yariv, R. Neurgaonkar, Appl. Phys. Lett. 40, 863 (1982).
[CrossRef]

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

Yeh, P.

P. Yeh, M. D. Ewbank, M. Khoshnevisan, J. M. Tracy, Opt. Lett. 9, 41(1984).
[CrossRef] [PubMed]

P. Yeh, J. Opt. Soc. Am. B 2 (to be published, November1985).

Appl. Phys. Lett. (2)

J. O. White, M. Cronin-Golomb, B. Fischer, A. Yariv, Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

B. Fischer, M. Cronin-Goulomb, J. O. White, A. Yariv, R. Neurgaonkar, Appl. Phys. Lett. 40, 863 (1982).
[CrossRef]

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

K. R. MacDonald, J. Feinberg, J. Opt. Soc. Am. A 1, 1213 (A)1984.

J. F. Lam, J. Opt. Soc. Am. A 1, 1223 (A)1984.

Opt. Lett. (7)

Phys. Rep. (1)

P. Gunter, Phys. Rep. 93, 199 (1982).
[CrossRef]

Other (3)

As the orientation of the two-wave mixing fringe pattern with respect to the crystal axes changes, the effective electro-optic coefficient (and coupling efficiency of the index grating) is modified. γL is independently measured by removing ring-cavity mirror M2 and using an attenuated probe beam from BS2 with an external angle of 20° between probe and pump beams.

Provided by R. Neurganokar, Rockwell International, Thousand Oaks, Calif.

P. Yeh, J. Opt. Soc. Am. B 2 (to be published, November1985).

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Figures (4)

Fig. 1
Fig. 1

Optical setup for the photorefractive unidirectional ring resonator with variable cavity length. The beat frequency between the self-oscillation and pump beams is derived from the motion of the interferograms at D2 or D3.

Fig. 2
Fig. 2

Characteristics of the unidirectional self-oscillation as a function of ring-cavity length (i.e., PZT voltage or cavity detuning, where 100% implies a detuning of one full optical wave): (a) ring-cavity intensity (right) and beat-frequency signature (left); (b) frequency difference between the self-oscillation and the pumping beam.

Fig. 3
Fig. 3

Oscillation threshold behavior for the unidirectional ring resonator: (a) maximum beat frequency as a function of pumping-beam or ring-cavity power along with a linear fit (solid line); (b) maximum beat frequency (left) and cavity detuning (right) as a function of two-wave mixing gain, γL where γL is related to the external angle that the pumping beam makes the crystal’s c axis as shown (top scale). Note: the two solid curves in (b) correspond to the evaluation of expressions (2a) and (2b) as described in text.

Fig. 4
Fig. 4

Self-pumped phase conjugator using external reflectors to generate the self-oscillation with a frequency shift δ and the phase-conjugate reflection with a frequency shift 2δ, where δ is proportional to the linear cavity length.

Equations (3)

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Ω = - [ 2 ( Δ Γ + 2 m π ) / τ A ] ,
Ω ( 1 / τ ) ( γ L / A - 1 ) 1 / 2 ,
Δ Γ ( A / 2 ) ( γ L / A - 1 ) 1 / 2 ,

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