Abstract

We demonstrate theoretically that the distortion-correction property of phase-conjugate beams propagating in reverse through aberrating media is also operative when the indices of refraction of the media depend on the intensity. A necessary condition is that the phase-conjugate mirror that generates the reflected beam possess a unity (magnitude) “reflection” coefficient.

© 1980 Optical Society of America

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References

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  1. A. Yariv, Opt. Commun. 21, 49 (1977).
    [CrossRef]
  2. A. Yariv, IEEE J. Quantum Electron. QE-14, 650 (1978).
    [CrossRef]
  3. W. B. Bridges, J. E. Pearson [Appl. Phys. Lett. 26, 539 (1975)] demonstrated partial compensation for thermal blooming by electro-optic aperture phase control of a single, forward-propagating beam. The criterion for the phase distribution of the launched wave was the maximization of the irradiance incident on a target glint following the distorting medium. This differs from our scheme, which depends on phase conjugation and reverse propagation for the correction.
    [CrossRef]
  4. R. W. Hellwarth, J. Opt. Soc. Am. 67, 1 (1977).
    [CrossRef]
  5. A. Yariv, D. M. Pepper, Opt. Lett. 1, 16 (1977).
    [CrossRef] [PubMed]
  6. D. M. Pepper, D. Fekete, A. Yariv, Appl. Phys. Lett. 33, 41 (1978).
    [CrossRef]
  7. D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 3, 58 (1978).
    [CrossRef]
  8. J. AuYeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
    [CrossRef]

1979 (1)

J. AuYeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

1978 (3)

D. M. Pepper, D. Fekete, A. Yariv, Appl. Phys. Lett. 33, 41 (1978).
[CrossRef]

D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 3, 58 (1978).
[CrossRef]

A. Yariv, IEEE J. Quantum Electron. QE-14, 650 (1978).
[CrossRef]

1977 (3)

1975 (1)

W. B. Bridges, J. E. Pearson [Appl. Phys. Lett. 26, 539 (1975)] demonstrated partial compensation for thermal blooming by electro-optic aperture phase control of a single, forward-propagating beam. The criterion for the phase distribution of the launched wave was the maximization of the irradiance incident on a target glint following the distorting medium. This differs from our scheme, which depends on phase conjugation and reverse propagation for the correction.
[CrossRef]

AuYeung, J.

J. AuYeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

Bloom, D. M.

D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 3, 58 (1978).
[CrossRef]

Bridges, W. B.

W. B. Bridges, J. E. Pearson [Appl. Phys. Lett. 26, 539 (1975)] demonstrated partial compensation for thermal blooming by electro-optic aperture phase control of a single, forward-propagating beam. The criterion for the phase distribution of the launched wave was the maximization of the irradiance incident on a target glint following the distorting medium. This differs from our scheme, which depends on phase conjugation and reverse propagation for the correction.
[CrossRef]

Economou, N. P.

D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 3, 58 (1978).
[CrossRef]

Fekete, D.

J. AuYeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

D. M. Pepper, D. Fekete, A. Yariv, Appl. Phys. Lett. 33, 41 (1978).
[CrossRef]

Hellwarth, R. W.

Liao, P. F.

D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 3, 58 (1978).
[CrossRef]

Pearson, J. E.

W. B. Bridges, J. E. Pearson [Appl. Phys. Lett. 26, 539 (1975)] demonstrated partial compensation for thermal blooming by electro-optic aperture phase control of a single, forward-propagating beam. The criterion for the phase distribution of the launched wave was the maximization of the irradiance incident on a target glint following the distorting medium. This differs from our scheme, which depends on phase conjugation and reverse propagation for the correction.
[CrossRef]

Pepper, D. M.

J. AuYeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

D. M. Pepper, D. Fekete, A. Yariv, Appl. Phys. Lett. 33, 41 (1978).
[CrossRef]

A. Yariv, D. M. Pepper, Opt. Lett. 1, 16 (1977).
[CrossRef] [PubMed]

Yariv, A.

J. AuYeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

D. M. Pepper, D. Fekete, A. Yariv, Appl. Phys. Lett. 33, 41 (1978).
[CrossRef]

A. Yariv, IEEE J. Quantum Electron. QE-14, 650 (1978).
[CrossRef]

A. Yariv, D. M. Pepper, Opt. Lett. 1, 16 (1977).
[CrossRef] [PubMed]

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

Appl. Phys. Lett. (2)

W. B. Bridges, J. E. Pearson [Appl. Phys. Lett. 26, 539 (1975)] demonstrated partial compensation for thermal blooming by electro-optic aperture phase control of a single, forward-propagating beam. The criterion for the phase distribution of the launched wave was the maximization of the irradiance incident on a target glint following the distorting medium. This differs from our scheme, which depends on phase conjugation and reverse propagation for the correction.
[CrossRef]

D. M. Pepper, D. Fekete, A. Yariv, Appl. Phys. Lett. 33, 41 (1978).
[CrossRef]

IEEE J. Quantum Electron. (2)

J. AuYeung, D. Fekete, D. M. Pepper, A. Yariv, IEEE J. Quantum Electron. QE-15, 1180 (1979).
[CrossRef]

A. Yariv, IEEE J. Quantum Electron. QE-14, 650 (1978).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

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

Opt. Lett. (2)

A. Yariv, D. M. Pepper, Opt. Lett. 1, 16 (1977).
[CrossRef] [PubMed]

D. M. Bloom, P. F. Liao, N. P. Economou, Opt. Lett. 3, 58 (1978).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Typical geometry for a PCM in order to compensate for nonlinear phase distortions, . Solid (dashed) curves correspond to the incident (conjugate, or time-reversed) equiphase surfaces. Arrows indicate local propagation vectors. If |R| < 1, then the use of a conventional laser amplifier satisfying |R|exp(2gL) = 1 is required to ensure proper nonlinear phase compensation.

Equations (11)

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

E 1 = ψ ( r ) exp [ i ( ω t - k z ) ] + c . c . ,
E 2 = f ( r ) exp [ i ( ω t + k z ) ] + c . c .
E = [ ψ ( r ) exp ( - i k z ) + f ( r ) exp ( i k z ) ] exp ( i ω t ) + c . c .
= 0 ( r ) + n = 1 2 n ( r ) E 2 n ,
2 E - μ c 2 [ 0 ( r ) + 2 ( r ) E 2 ] 2 E t 2 = 0.
{ 2 ψ ( r ) + [ ω 2 μ c 2 0 ( r ) - k 2 ] ψ ( r ) + ω 2 μ c 2 2 ( r ) E 2 ψ ( r ) - 2 i k ψ ( r ) z } exp ( - i k z ) + { 2 f ( r ) + [ ω 2 μ c 2 0 ( r ) - k 2 ] f ( r ) + ω 2 μ c 2 2 ( r ) E 2 f ( r ) + 2 i k f ( r ) z } exp ( + i k z ) = 0.
E ( r ) 2 = ψ ( r ) 2 + f ( r ) 2 + ψ f * exp ( - 2 i k z ) + ψ * f exp ( 2 i k z ) .
2 ψ + [ ω 2 μ 0 ( r ) c 2 - k 2 ] ψ + ω 2 μ 2 ( r ) c 2 ( ψ 2 + 2 f 2 ) ψ - 2 i k ψ z = 0 ,
2 f + [ ω 2 μ 0 ( r ) c 2 - k 2 ] f + ω 2 μ 2 ( r ) c 2 ( f 2 + 2 ψ 2 ) f + 2 i k f z = 0 ,
2 ψ * + [ ω 2 μ 0 ( r ) c 2 - k 2 ] ψ * + ω 2 μ 2 ( r ) c 2 ( ψ 2 + 2 f 2 ) ψ * + 2 i k ψ * z = 0.
f ( r ) = ψ * ( r )

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