Abstract

The theory of distortion correction by phase conjugation, developed since the discovery of this phenomenon many years ago, applies to situations when the field that is conjugated is monochromatic and the medium with which it interacts is deterministic. In this Letter a generalization of the theory is presented that applies to phase conjugation of partially coherent waves interacting with either deterministic or random weakly scattering nonabsorbing media.

© 1999 Optical Society of America

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References

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  1. B. Ya. Zel'dovich, V. I. Popovichev, V. V. Ragul'skii, and F. S. Faizullov, JETP Lett. 15, 109 (1972).
  2. O. Y. Nosach, V. I. Popovichev, V. V. Ragul'skii, and F. S. Faizullov, JETP Lett. 16, 435 (1972).
  3. D. N. Bloom and C. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977).
    [CrossRef]
  4. V. Wang and C. R. Giuliano, Opt. Lett. 2, 4 (1978)R. K. Jain and R. C. Lind, J. Opt. Soc. Am. 73, 647 (1983).
    [CrossRef] [PubMed]
  5. A. Yariv, Opt. Commun. 21, 49 (1977).
    [CrossRef]
  6. G. S. Agarwal and E. Wolf, J. Opt. Soc. Am. 72, 321 (1982).
    [CrossRef]
  7. G. S. Agarwal, A. T. Friberg, and E. Wolf, Opt. Commun. 43, 446 (1982).
    [CrossRef]
  8. G. S. Agarwal, A. T. Friberg, and E. Wolf, J. Opt. Soc. Am. 73, 529 (1983).
    [CrossRef]
  9. The effects of partial coherence on phase conjugation were recently discussed in X. Yi and P. Yeh, Opt. Commun. 147, 126 (1998).?The investigations in that paper, however, concern specific effects caused by the temporal coherence of the incident beam, not the spectral degree of coherence, which we are concerned with.
    [CrossRef]
  10. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
    [CrossRef]
  11. E. Wolf, J. Opt. Soc. Am. 70, 1311 (1980).
    [CrossRef]
  12. A somewhat similar result was established not long ago in A. J. Devaney, A. T. Friberg, A. T. N. Kumar, and E. Wolf, Opt. Lett. 22, 1672 (1997).
    [CrossRef]

1998 (1)

The effects of partial coherence on phase conjugation were recently discussed in X. Yi and P. Yeh, Opt. Commun. 147, 126 (1998).?The investigations in that paper, however, concern specific effects caused by the temporal coherence of the incident beam, not the spectral degree of coherence, which we are concerned with.
[CrossRef]

1997 (1)

1983 (1)

1982 (2)

G. S. Agarwal and E. Wolf, J. Opt. Soc. Am. 72, 321 (1982).
[CrossRef]

G. S. Agarwal, A. T. Friberg, and E. Wolf, Opt. Commun. 43, 446 (1982).
[CrossRef]

1980 (1)

1978 (1)

1977 (2)

A. Yariv, Opt. Commun. 21, 49 (1977).
[CrossRef]

D. N. Bloom and C. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977).
[CrossRef]

1972 (2)

B. Ya. Zel'dovich, V. I. Popovichev, V. V. Ragul'skii, and F. S. Faizullov, JETP Lett. 15, 109 (1972).

O. Y. Nosach, V. I. Popovichev, V. V. Ragul'skii, and F. S. Faizullov, JETP Lett. 16, 435 (1972).

Agarwal, G. S.

Bjorklund, C. C.

D. N. Bloom and C. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977).
[CrossRef]

Bloom, D. N.

D. N. Bloom and C. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977).
[CrossRef]

Devaney, A. J.

Faizullov, F. S.

B. Ya. Zel'dovich, V. I. Popovichev, V. V. Ragul'skii, and F. S. Faizullov, JETP Lett. 15, 109 (1972).

O. Y. Nosach, V. I. Popovichev, V. V. Ragul'skii, and F. S. Faizullov, JETP Lett. 16, 435 (1972).

Friberg, A. T.

Giuliano, C. R.

Kumar, A. T. N.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
[CrossRef]

Nosach, O. Y.

O. Y. Nosach, V. I. Popovichev, V. V. Ragul'skii, and F. S. Faizullov, JETP Lett. 16, 435 (1972).

Popovichev, V. I.

O. Y. Nosach, V. I. Popovichev, V. V. Ragul'skii, and F. S. Faizullov, JETP Lett. 16, 435 (1972).

B. Ya. Zel'dovich, V. I. Popovichev, V. V. Ragul'skii, and F. S. Faizullov, JETP Lett. 15, 109 (1972).

Ragul'skii, V. V.

B. Ya. Zel'dovich, V. I. Popovichev, V. V. Ragul'skii, and F. S. Faizullov, JETP Lett. 15, 109 (1972).

O. Y. Nosach, V. I. Popovichev, V. V. Ragul'skii, and F. S. Faizullov, JETP Lett. 16, 435 (1972).

Wang, V.

Wolf, E.

Yariv, A.

A. Yariv, Opt. Commun. 21, 49 (1977).
[CrossRef]

Yeh, P.

The effects of partial coherence on phase conjugation were recently discussed in X. Yi and P. Yeh, Opt. Commun. 147, 126 (1998).?The investigations in that paper, however, concern specific effects caused by the temporal coherence of the incident beam, not the spectral degree of coherence, which we are concerned with.
[CrossRef]

Yi, X.

The effects of partial coherence on phase conjugation were recently discussed in X. Yi and P. Yeh, Opt. Commun. 147, 126 (1998).?The investigations in that paper, however, concern specific effects caused by the temporal coherence of the incident beam, not the spectral degree of coherence, which we are concerned with.
[CrossRef]

Zel'dovich, B. Ya.

B. Ya. Zel'dovich, V. I. Popovichev, V. V. Ragul'skii, and F. S. Faizullov, JETP Lett. 15, 109 (1972).

Appl. Phys. Lett. (1)

D. N. Bloom and C. C. Bjorklund, Appl. Phys. Lett. 31, 592 (1977).
[CrossRef]

J. Opt. Soc. Am. (3)

JETP Lett. (2)

B. Ya. Zel'dovich, V. I. Popovichev, V. V. Ragul'skii, and F. S. Faizullov, JETP Lett. 15, 109 (1972).

O. Y. Nosach, V. I. Popovichev, V. V. Ragul'skii, and F. S. Faizullov, JETP Lett. 16, 435 (1972).

Opt. Commun. (3)

The effects of partial coherence on phase conjugation were recently discussed in X. Yi and P. Yeh, Opt. Commun. 147, 126 (1998).?The investigations in that paper, however, concern specific effects caused by the temporal coherence of the incident beam, not the spectral degree of coherence, which we are concerned with.
[CrossRef]

G. S. Agarwal, A. T. Friberg, and E. Wolf, Opt. Commun. 43, 446 (1982).
[CrossRef]

A. Yariv, Opt. Commun. 21, 49 (1977).
[CrossRef]

Opt. Lett. (2)

Other (1)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Illustrating the notation relating to the behavior of waves in the vicinity of a phase-conjugate mirror (PCM). Ur,ω and Ucr,ω represent the statistical ensembles characterizing the incident and the phase-conjugate field, respectively.

Fig. 2
Fig. 2

Illustrating phase conjugation of a partially coherent wave scattered by a medium occupying a volume V. Ur,ω and Ucr,ω have the same meaning as in Fig.  1.

Equations (12)

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

Ucr,ωz=z1=ηωU*r,ωz=z1,
Ucρ,z1;ω=ηωU*ρ,z1;ω.
Ucρ,z;ω=ηωU*ρ,z;ω.
Wr1,r2,ω=U*r1,ωUr2,ω,
Wcr1,r2,ω=Uc*r1,ωUcr2,ω,
Wcr1,r2,ω=ηω2W*r1,r2,ωwhen zz1.
Wcr1,r2,ω=ηω2Wr2,r1,ω.
μr1,r2,ω=Wr1,r2,ωWr1,r1,ωWr2,r2,ω
μcr1,r2,ω=Wcr1,r2,ωWcr1,r1,ωWcr2,r2,ω
μcr1,r2,ω=μ*r1,r2,ω when zz1
μcr1,r2,ω=μr2,r1,ω when zz1.
Ucr,ω=ηωU*r,ω,

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