Abstract

The definition of degree of polarization for non-Gaussian partially polarized light is analyzed. A general framework based on the Kullback relative entropy is developed, and properties that enlighten the physical meaning of the degree of polarization are established. In particular, it is shown how the degree of polarization is related to the measure of proximity between probability density functions and to the measure of disorder provided by the Shannon entropy.

© 2005 Optical Society of America

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References

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  1. T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. Lett. 88, 123902 (2002).
    [CrossRef]
  2. Ph. Réfrégier, F. Goudail, P. Chavel, and A. Friberg, J. Opt. Soc. Am. A 21, 2124 (2004).
    [CrossRef]
  3. A. Picozzi, Opt. Lett. 29, 1653 (2004).
    [CrossRef] [PubMed]
  4. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), pp. 116–156.
  5. T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, New York, 1991), pp. 12–49.
    [CrossRef]
  6. Ph. Réfrégier, Noise Theory and Application to Physics: from Fluctuations to Information (Springer, New York, 2004).
    [CrossRef]
  7. V. Vedral, M. B. Plenio, and P. L. Knight, The Physics of Quantum Information, D. Bouwmeestern, A. Ekert, and A. Zeilinger, eds. (Springer, New York, 2000), pp. 210–220.
  8. Ref. 5, pp. 279–335.
  9. C. W. Therrien, Decision Estimation and Classification (Wiley, New York, 1989), pp. 139–155.

2004 (2)

2002 (1)

T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. Lett. 88, 123902 (2002).
[CrossRef]

Chavel, P.

Cover, T. M.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, New York, 1991), pp. 12–49.
[CrossRef]

Friberg, A.

Friberg, A. T.

T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. Lett. 88, 123902 (2002).
[CrossRef]

Goodman, J. W.

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

Goudail, F.

Kaivola, M.

T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. Lett. 88, 123902 (2002).
[CrossRef]

Knight, P. L.

V. Vedral, M. B. Plenio, and P. L. Knight, The Physics of Quantum Information, D. Bouwmeestern, A. Ekert, and A. Zeilinger, eds. (Springer, New York, 2000), pp. 210–220.

Picozzi, A.

Plenio, M. B.

V. Vedral, M. B. Plenio, and P. L. Knight, The Physics of Quantum Information, D. Bouwmeestern, A. Ekert, and A. Zeilinger, eds. (Springer, New York, 2000), pp. 210–220.

Réfrégier, Ph.

Ph. Réfrégier, F. Goudail, P. Chavel, and A. Friberg, J. Opt. Soc. Am. A 21, 2124 (2004).
[CrossRef]

Ph. Réfrégier, Noise Theory and Application to Physics: from Fluctuations to Information (Springer, New York, 2004).
[CrossRef]

Setälä, T.

T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. Lett. 88, 123902 (2002).
[CrossRef]

Therrien, C. W.

C. W. Therrien, Decision Estimation and Classification (Wiley, New York, 1989), pp. 139–155.

Thomas, J. A.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, New York, 1991), pp. 12–49.
[CrossRef]

Vedral, V.

V. Vedral, M. B. Plenio, and P. L. Knight, The Physics of Quantum Information, D. Bouwmeestern, A. Ekert, and A. Zeilinger, eds. (Springer, New York, 2000), pp. 210–220.

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

Opt. Lett. (1)

Phys. Rev. Lett. (1)

T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. Lett. 88, 123902 (2002).
[CrossRef]

Other (6)

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

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, New York, 1991), pp. 12–49.
[CrossRef]

Ph. Réfrégier, Noise Theory and Application to Physics: from Fluctuations to Information (Springer, New York, 2004).
[CrossRef]

V. Vedral, M. B. Plenio, and P. L. Knight, The Physics of Quantum Information, D. Bouwmeestern, A. Ekert, and A. Zeilinger, eds. (Springer, New York, 2000), pp. 210–220.

Ref. 5, pp. 279–335.

C. W. Therrien, Decision Estimation and Classification (Wiley, New York, 1989), pp. 139–155.

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Figures (1)

Fig. 1
Fig. 1

Schematic illustrations of the consequences of (a) Property A and (b) Property C.

Equations (14)

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Γ = [ E 1 2 E 1 E 2 * E 2 E 1 * E 2 2 ] ,
P = ( 1 4 det [ Γ ] tr [ Γ ] 2 ) 1 2 ,
[ P ] 2 = 1 exp [ S ( P ̃ ) ] ( 4 π e ) ,
P a 2 = 1 exp [ K ( P Γ a P Γ 0 ) ] .
[ P a NL ] 2 = 1 exp [ K ( P a P Γ 0 ) ]
K ( P a P Γ ) = K ( P a P Γ a ) + K ( P Γ a P Γ ) .
K ( P a P Γ 0 ) = K ( P a P Γ a ) + K ( P Γ a P Γ 0 ) .
[ P a NL ] 2 [ P a 2 ]
K ( P a P Γ a ) = S ( P Γ a ) S ( P a ) ,
K ( P a P Γ 0 ) = S ( P Γ 0 ) S ( P a ) ,
K ( P Γ a P Γ 0 ) = S ( P Γ 0 ) S ( P Γ a ) .
S ( P a ) S ( P Γ a ) S ( P Γ 0 ) .
P a 2 = 1 4 I 1 I 2 ( I 1 + I 2 ) 2 = ( I 1 I 2 I 1 + I 2 ) 2 ,
[ P a NL ] 2 = 1 4 e 2 4 I 1 I 2 ( I 1 + I 2 ) 2 .

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