Abstract

We use stimulated Brillouin scattering to investigate phase conjugation of a laser beam aberrated by one or more phase screens when the aberrated beam is incompletely sampled by the phase-conjugate mirror. Good agreement is found between our experimental results and previous theoretical work. We find that the fraction of the reflected beam that is phase conjugate after the double pass is proportional to the fraction of the original beam sampled by the phase-conjugate mirror. We also show that it is possible to increase the resolution of a phase-conjugate mirror by inserting an aberrator.

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References

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  1. C. Gu and P. Yeh, “Partial phase conjugation, fidelity and reciprocity,” Opt. Commun. 107, 353–357 (1994).
    [CrossRef]
  2. E. Jakeman and K. D. Ridley, “Incomplete phase conjugation through a random phase screen. I. Theory,” J. Opt. Soc. Am. A 13, 2279–2287 (1996).
    [CrossRef]
  3. K. D. Ridley and E. Jakeman, “Incomplete phase conjugation through a random phase screen. II. numericalsimulations,” J. Opt. Soc. Am. A 13, 2393–2402 (1996).
    [CrossRef]
  4. S. Campbell, P. Yeh, C. Gu, and Q. B. He, “Fidelity of image restoration by partial phase conjugation throughmultimode fibres,” Opt. Commun. 114, 50–56 (1995).
    [CrossRef]
  5. I. McMichael, M. D. Ewbank, and F. Vachss, “Efficiency of phase conjugation for highly scattered light,” Opt. Commun. 119, 13–16 (1995).
    [CrossRef]
  6. I. Yu. Anikeev, A. A. Gordeev, I. G. Zubarev, and S. I. Mikhailov, “Compensation for phase distortions by means of a phase-conjugationmirror with an aperture loss,” JETP Lett. 46, 442–445 (1987).
  7. L. P. Schelonka and C. M. Clayton, “Effect of focal intensity on stimulated-Brillouin-scattering reflectivityand fidelity,” Opt. Lett. 13, 42–44 (1988).
    [CrossRef] [PubMed]
  8. D. C. Jones, “Characterisation of liquid Brillouin media at 532 nm,” J. Nonlinear Opt. Phys. Mater. 6, 69–79 (1997).
    [CrossRef]
  9. K. D. Ridley and A. M. Scott, “High-reflectivity phase conjugation using Brillouin preamplification,” Opt. Lett. 15, 777–779 (1990).
    [CrossRef] [PubMed]
  10. K. D. Ridley, D. C. Jones, G. Cook, and A. M. Scott, “Brillouin amplification with a Gaussian pump beam,” J. Opt. Soc. Am. B 8, 2453–2458 (1991).
    [CrossRef]
  11. V. E. Yashin and V. I. Kryzhanovskii, “Apodization and spatial filtering of light beams in stimulated Brillouinscattering,” Opt. Spectrosc. (USSR) 55, 101–104 (1983).
  12. H. Bruesselbach, D. Cris Jones, D. A. Rockwell, R. C. Lind, and G. Vogel, “Real-time atmospheric compensation by stimulated Brillouin-scatteringphase conjugation,” J. Opt. Soc. Am. B 12, 1434–1447 (1995).
    [CrossRef]

1997 (1)

D. C. Jones, “Characterisation of liquid Brillouin media at 532 nm,” J. Nonlinear Opt. Phys. Mater. 6, 69–79 (1997).
[CrossRef]

1996 (2)

1995 (3)

S. Campbell, P. Yeh, C. Gu, and Q. B. He, “Fidelity of image restoration by partial phase conjugation throughmultimode fibres,” Opt. Commun. 114, 50–56 (1995).
[CrossRef]

I. McMichael, M. D. Ewbank, and F. Vachss, “Efficiency of phase conjugation for highly scattered light,” Opt. Commun. 119, 13–16 (1995).
[CrossRef]

H. Bruesselbach, D. Cris Jones, D. A. Rockwell, R. C. Lind, and G. Vogel, “Real-time atmospheric compensation by stimulated Brillouin-scatteringphase conjugation,” J. Opt. Soc. Am. B 12, 1434–1447 (1995).
[CrossRef]

1994 (1)

C. Gu and P. Yeh, “Partial phase conjugation, fidelity and reciprocity,” Opt. Commun. 107, 353–357 (1994).
[CrossRef]

1991 (1)

1990 (1)

1988 (1)

1987 (1)

I. Yu. Anikeev, A. A. Gordeev, I. G. Zubarev, and S. I. Mikhailov, “Compensation for phase distortions by means of a phase-conjugationmirror with an aperture loss,” JETP Lett. 46, 442–445 (1987).

1983 (1)

V. E. Yashin and V. I. Kryzhanovskii, “Apodization and spatial filtering of light beams in stimulated Brillouinscattering,” Opt. Spectrosc. (USSR) 55, 101–104 (1983).

Anikeev, I. Yu.

I. Yu. Anikeev, A. A. Gordeev, I. G. Zubarev, and S. I. Mikhailov, “Compensation for phase distortions by means of a phase-conjugationmirror with an aperture loss,” JETP Lett. 46, 442–445 (1987).

Bruesselbach, H.

Campbell, S.

S. Campbell, P. Yeh, C. Gu, and Q. B. He, “Fidelity of image restoration by partial phase conjugation throughmultimode fibres,” Opt. Commun. 114, 50–56 (1995).
[CrossRef]

Clayton, C. M.

Cook, G.

Ewbank, M. D.

I. McMichael, M. D. Ewbank, and F. Vachss, “Efficiency of phase conjugation for highly scattered light,” Opt. Commun. 119, 13–16 (1995).
[CrossRef]

Gordeev, A. A.

I. Yu. Anikeev, A. A. Gordeev, I. G. Zubarev, and S. I. Mikhailov, “Compensation for phase distortions by means of a phase-conjugationmirror with an aperture loss,” JETP Lett. 46, 442–445 (1987).

Gu, C.

S. Campbell, P. Yeh, C. Gu, and Q. B. He, “Fidelity of image restoration by partial phase conjugation throughmultimode fibres,” Opt. Commun. 114, 50–56 (1995).
[CrossRef]

C. Gu and P. Yeh, “Partial phase conjugation, fidelity and reciprocity,” Opt. Commun. 107, 353–357 (1994).
[CrossRef]

He, Q. B.

S. Campbell, P. Yeh, C. Gu, and Q. B. He, “Fidelity of image restoration by partial phase conjugation throughmultimode fibres,” Opt. Commun. 114, 50–56 (1995).
[CrossRef]

Jakeman, E.

Jones, D. C.

D. C. Jones, “Characterisation of liquid Brillouin media at 532 nm,” J. Nonlinear Opt. Phys. Mater. 6, 69–79 (1997).
[CrossRef]

K. D. Ridley, D. C. Jones, G. Cook, and A. M. Scott, “Brillouin amplification with a Gaussian pump beam,” J. Opt. Soc. Am. B 8, 2453–2458 (1991).
[CrossRef]

Jones, D. Cris

Kryzhanovskii, V. I.

V. E. Yashin and V. I. Kryzhanovskii, “Apodization and spatial filtering of light beams in stimulated Brillouinscattering,” Opt. Spectrosc. (USSR) 55, 101–104 (1983).

Lind, R. C.

McMichael, I.

I. McMichael, M. D. Ewbank, and F. Vachss, “Efficiency of phase conjugation for highly scattered light,” Opt. Commun. 119, 13–16 (1995).
[CrossRef]

Mikhailov, S. I.

I. Yu. Anikeev, A. A. Gordeev, I. G. Zubarev, and S. I. Mikhailov, “Compensation for phase distortions by means of a phase-conjugationmirror with an aperture loss,” JETP Lett. 46, 442–445 (1987).

Ridley, K. D.

Rockwell, D. A.

Schelonka, L. P.

Scott, A. M.

Vachss, F.

I. McMichael, M. D. Ewbank, and F. Vachss, “Efficiency of phase conjugation for highly scattered light,” Opt. Commun. 119, 13–16 (1995).
[CrossRef]

Vogel, G.

Yashin, V. E.

V. E. Yashin and V. I. Kryzhanovskii, “Apodization and spatial filtering of light beams in stimulated Brillouinscattering,” Opt. Spectrosc. (USSR) 55, 101–104 (1983).

Yeh, P.

S. Campbell, P. Yeh, C. Gu, and Q. B. He, “Fidelity of image restoration by partial phase conjugation throughmultimode fibres,” Opt. Commun. 114, 50–56 (1995).
[CrossRef]

C. Gu and P. Yeh, “Partial phase conjugation, fidelity and reciprocity,” Opt. Commun. 107, 353–357 (1994).
[CrossRef]

Zubarev, I. G.

I. Yu. Anikeev, A. A. Gordeev, I. G. Zubarev, and S. I. Mikhailov, “Compensation for phase distortions by means of a phase-conjugationmirror with an aperture loss,” JETP Lett. 46, 442–445 (1987).

J. Nonlinear Opt. Phys. Mater. (1)

D. C. Jones, “Characterisation of liquid Brillouin media at 532 nm,” J. Nonlinear Opt. Phys. Mater. 6, 69–79 (1997).
[CrossRef]

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

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

JETP Lett. (1)

I. Yu. Anikeev, A. A. Gordeev, I. G. Zubarev, and S. I. Mikhailov, “Compensation for phase distortions by means of a phase-conjugationmirror with an aperture loss,” JETP Lett. 46, 442–445 (1987).

Opt. Commun. (3)

S. Campbell, P. Yeh, C. Gu, and Q. B. He, “Fidelity of image restoration by partial phase conjugation throughmultimode fibres,” Opt. Commun. 114, 50–56 (1995).
[CrossRef]

I. McMichael, M. D. Ewbank, and F. Vachss, “Efficiency of phase conjugation for highly scattered light,” Opt. Commun. 119, 13–16 (1995).
[CrossRef]

C. Gu and P. Yeh, “Partial phase conjugation, fidelity and reciprocity,” Opt. Commun. 107, 353–357 (1994).
[CrossRef]

Opt. Lett. (2)

Opt. Spectrosc. (USSR) (1)

V. E. Yashin and V. I. Kryzhanovskii, “Apodization and spatial filtering of light beams in stimulated Brillouinscattering,” Opt. Spectrosc. (USSR) 55, 101–104 (1983).

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Figures (7)

Fig. 1
Fig. 1

Schematic of incomplete phase conjugation.

Fig. 2
Fig. 2

Schematic of experimental setup. L's lenses; M's mirrors; HW, half-wave plate. Other abbreviations are defined in text.

Fig. 3
Fig. 3

Spatial profile of the phase-conjugate beam at the pinhole (a) with no aberrator, (b) with an intermediate plastic aberrator m0d=3.05 mm, (c) with a strong plastic aberrator m0d =19 cm. The camera field of view is 4 mm or 1 mrad × 1 mrad.

Fig. 4
Fig. 4

Diameter of the coherent part versus the beam-spreading distance. Experiment and fit with M2=1.3.

Fig. 5
Fig. 5

Spatial profile of the phase-conjugate beam with a double source consisting of two pinholes separated by 0.6 mm or 160 µrad: (a) no aberrator, (b) plastic aberrator m0=1.49 mrad, (c) plastic aberrator m0=12.2 mrad. The camera field of view is 4 mm, or 1 mrad×1 mrad.

Fig. 6
Fig. 6

Phase-conjugate fidelity versus the fraction of the signal collected by the PCM. Diamonds, collimation of the signal varied without aberration; squares and circles, aberrators placed in the collimated signal. The fidelity is the fraction of phase-conjugate beam passing through the pinhole.

Fig. 7
Fig. 7

Phase-conjugate fidelity versus the fraction of the signal collected by the PCM for various numbers of aberrators, both together and distributed in space.

Equations (2)

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θ=λ2π1(m0d)2+W2+1ω021/2,
θ=(0.82λM2)2(2m0d)2+D2+dph2f21/2,

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