Abstract

The spatiotemporal coherence properties of partially polarized light with Gaussian probability distributions are analyzed using the mutual information that is a standard measure of statistical dependence. This approach leads to intrinsic degrees of coherence that have powerful invariance properties and that provide new information in comparison with other recently introduced degrees of coherence.

© 2005 Optical Society of America

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References

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  1. E. Wolf, Phys. Lett. A 312, 263 (2003).
    [CrossRef]
  2. J. Tervo, T. Setälä, and A. T. Friberg, Opt. Express 11, 1137 (2003).
    [CrossRef] [PubMed]
  3. J. Tervo, T. Setälä, and A. T. Friberg, J. Opt. Soc. Am. A 21, 2205 (2004).
    [CrossRef]
  4. J. W. Goodman, Statistical Optics (Wiley, 1985), pp. 116–156.
  5. T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, 1991), pp. 12–49 and 279–335.
  6. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), pp. 160–170.
  7. Ph. Réfrégier and F. Goudail, Opt. Express 13, 6051 (2005).
    [CrossRef]
  8. C. Brosseau, in Fundamentals of Polarized Light: A Statistical Approach (Wiley, 1998), pp. 339–345.

2005 (1)

2004 (1)

2003 (2)

Brosseau, C.

C. Brosseau, in Fundamentals of Polarized Light: A Statistical Approach (Wiley, 1998), pp. 339–345.

Cover, T. M.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, 1991), pp. 12–49 and 279–335.

Friberg, A. T.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 1985), pp. 116–156.

Goudail, F.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), pp. 160–170.

Réfrégier, Ph.

Setälä, T.

Tervo, J.

Thomas, J. A.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, 1991), pp. 12–49 and 279–335.

Wolf, E.

E. Wolf, Phys. Lett. A 312, 263 (2003).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), pp. 160–170.

J. Opt. Soc. Am. A (1)

Opt. Express (2)

Phys. Lett. A (1)

E. Wolf, Phys. Lett. A 312, 263 (2003).
[CrossRef]

Other (4)

C. Brosseau, in Fundamentals of Polarized Light: A Statistical Approach (Wiley, 1998), pp. 339–345.

J. W. Goodman, Statistical Optics (Wiley, 1985), pp. 116–156.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, 1991), pp. 12–49 and 279–335.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), pp. 160–170.

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Equations (16)

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M I ( r 1 , r 2 , t 1 , t 2 ) = P r 1 , r 2 , t 1 , t 2 ( E 1 , E 2 ) log [ P r 1 , r 2 , t 1 , t 2 ( E 1 , E 2 ) P r 1 , t 1 ( E 1 ) P r 2 , t 2 ( E 2 ) ] d E 1 d E 2 .
P r 1 , r 2 , t 1 , t 2 ( E 1 , E 2 ) = 1 π 2 det [ Υ ( r 1 , r 2 , t 1 , t 2 ) ] exp [ ( E 1 * , E 2 * ) Υ ( r 1 , r 2 , t 1 , t 2 ) 1 ( E 1 , E 2 ) T ] ,
M I ( r 1 , r 2 , t 1 , t 2 ) = P r 1 , r 2 , t 1 , t 2 ( E 1 , E 2 ) [ F ( E 1 , E 2 ) + R ] d E 1 d E 2 ,
F ( E 1 , E 2 ) = ( E 1 , E 2 ) * Υ 1 ( E 1 , E 2 ) T + E 1 E 1 I ( r 1 , t 1 ) + E 2 E 2 I ( r 2 , t 2 ) and R = log [ I ( r 1 , t 1 ) I ( r 2 , t 2 ) det Υ ] .
M I ( r 1 , r 2 , t 1 , t 2 ) = log [ 1 ρ ( r 1 , r 2 , t 1 , t 2 ) 2 ] .
Υ ( r 1 , r 2 , t 1 , t 2 ) = E ( r 1 , r 2 , t 1 , t 2 ) E ( r 1 , r 2 , t 1 , t 2 ) .
P r 1 , r 2 , t 1 , t 2 ( E ) = 1 π 4 det [ Υ ( r 1 , r 2 , t 1 , t 2 ) ] exp [ E Υ ( r 1 , r 2 , t 1 , t 2 ) 1 E ] .
M I ( r 1 , r 2 , t 1 , t 2 ) = log [ det Υ ( r 1 , r 2 , t 1 , t 2 ) det Γ ( r 1 , t 1 ) det Γ ( r 2 , t 2 ) ] .
M 12 = M ( r 1 , r 2 , t 1 , t 2 ) = [ ρ X X u ρ X Y u ρ Y X u ρ Y Y u ] .
M ( r 1 , r 2 , t 1 , t 2 ) = N 2 D ( r 1 , r 2 , t 1 , t 2 ) N 1 ,
M I ( r 1 , r 2 , t 1 , t 2 ) = log [ 1 μ S 2 ( r 1 , r 2 , t 1 , t 2 ) ] log [ 1 μ I 2 ( r 1 , r 2 , t 1 , t 2 ) ] .
μ ¯ ( r 1 , r 2 , t 1 , t 2 ) = tr [ Ω ( r 1 , r 2 , t 1 , t 2 ) ] { t r [ Γ ( r 1 , t 1 ) ] t r [ Γ ( r 2 , t 2 ) ] } 1 2 ,
μ ̃ 2 ( r 1 , r 2 , t 1 , t 2 ) = t r [ Ω ( r 1 , r 2 , t 1 , t 2 ) Ω ( r 1 , r 2 , t 1 , t 2 ) ] t r [ Γ ( r 1 , t 1 ) ] t r [ Γ ( r 2 , t 2 ) ] .
Γ ( r 1 , t 1 ) = Γ ( r 2 , t 2 ) = [ α 0 0 β ] ,
R π 2 = [ 0 1 1 0 ] , D = [ μ 2 0 0 μ 1 ] ,
η ( r 1 , r 2 , t 1 , t 2 ) = e 2 U 2 Ω ( r 1 , r 2 , t 1 , t 2 ) U 1 e 1 [ e 1 U 1 Γ ( r 1 , t 1 ) U 1 e 1 ] 1 2 [ e 2 U 2 Γ ( r 2 , t 2 ) U 2 e 2 ] 1 2 ,

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