Abstract

In terms of the electric spectral density tensors associated with a random electromagnetic field, it is shown that, under certain conditions, a link can be established between two definitions of the degree of coherence for electromagnetic beams introduced not long ago by Wolf [Phys. Lett. A 312, 263 (2003)] and by Setälä et al. [Opt. Lett. 29, 328 (2004)] . This connection is formulated as a certain equivalence relationship concerning the behavior of the above degrees of coherence and the degree of polarization of the field at two points.

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References

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  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  2. E. Wolf, J. Opt. Soc. Am. 72, 343 (1982).
    [CrossRef]
  3. R. Martínez-Herrero and P. M. Mejías, J. Opt. Soc. Am. 72, 765 (1982).
    [CrossRef]
  4. R. Martínez-Herrero and P. M. Mejías, J. Opt. Soc. Am. A 1, 556 (1984).
    [CrossRef]
  5. R. Martínez-Herrero and P. M. Mejías, Opt. Commun. 94, 197 (1992).
    [CrossRef]
  6. E. Wolf, Phys. Lett. A 312, 263 (2003).
    [CrossRef]
  7. F. Gori, M. Santarsiero, and R. Borghi, Opt. Lett. 31, 858 (2006).
    [CrossRef] [PubMed]
  8. T. Setälä, J. Tervo, and A. T. Friberg, Opt. Lett. 29, 328 (2004).
    [CrossRef] [PubMed]
  9. D. F. V. James, J. Opt. Soc. Am. A 11, 1641 (1994).
    [CrossRef]
  10. S. A. Ponomarenko and E. Wolf, Opt. Commun. 227, 73 (2003).
    [CrossRef]
  11. J. Tervo, T. Setälä, and A. T. Friberg, J. Opt. Soc. Am. A 21, 2205 (2004).
    [CrossRef]
  12. J. Tervo, T. Setälä, and A. T. Friberg, Opt. Express 11, 1137 (2003).
    [CrossRef] [PubMed]
  13. C. Brosseau, Fundamentals of Polarized Light (Wiley, 1998).
  14. Concerning this discussion, we acknowledge and appreciate the comments of a referee.
  15. Ph. Réfrégier and F. Goudail, Opt. Express 13, 6051 (2005).
    [CrossRef] [PubMed]
  16. Ph. Réfrégier and A. Roueff, Opt. Lett. 31, 2827 (2006).
    [CrossRef] [PubMed]
  17. F. Gori, M. Santarsiero, and R. Borghi, Opt. Lett. 32, 588 (2007).
    [CrossRef] [PubMed]
  18. R. Martínez-Herrero and P. M. Mejías, Opt. Lett. 32, 1471 (2007).
    [CrossRef] [PubMed]

2007 (2)

2006 (2)

2005 (1)

2004 (2)

2003 (3)

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

S. A. Ponomarenko and E. Wolf, Opt. Commun. 227, 73 (2003).
[CrossRef]

J. Tervo, T. Setälä, and A. T. Friberg, Opt. Express 11, 1137 (2003).
[CrossRef] [PubMed]

1994 (1)

1992 (1)

R. Martínez-Herrero and P. M. Mejías, Opt. Commun. 94, 197 (1992).
[CrossRef]

1984 (1)

1982 (2)

Borghi, R.

Brosseau, C.

C. Brosseau, Fundamentals of Polarized Light (Wiley, 1998).

Friberg, A. T.

Gori, F.

Goudail, F.

James, D. F. V.

Mandel, L.

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

Martínez-Herrero, R.

Mejías, P. M.

Ponomarenko, S. A.

S. A. Ponomarenko and E. Wolf, Opt. Commun. 227, 73 (2003).
[CrossRef]

Réfrégier, Ph.

Roueff, A.

Santarsiero, M.

Setälä, T.

Tervo, J.

Wolf, E.

S. A. Ponomarenko and E. Wolf, Opt. Commun. 227, 73 (2003).
[CrossRef]

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

E. Wolf, J. Opt. Soc. Am. 72, 343 (1982).
[CrossRef]

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

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (3)

Opt. Commun. (2)

S. A. Ponomarenko and E. Wolf, Opt. Commun. 227, 73 (2003).
[CrossRef]

R. Martínez-Herrero and P. M. Mejías, Opt. Commun. 94, 197 (1992).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Phys. Lett. A (1)

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

Other (3)

C. Brosseau, Fundamentals of Polarized Light (Wiley, 1998).

Concerning this discussion, we acknowledge and appreciate the comments of a referee.

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

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Equations (17)

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

T = ( W 11 W 12 W 21 W 22 ) ,
W i j W ( r i , r j , ω ) = E + ( r i , ω ) E ( r j , ω ) , i , j = 1 , 2 ,
μ W 2 = tr W 12 2 tr W 11 tr W 22 ,
μ STF 2 = tr ( W 12 W 21 ) tr W 11 tr W 22 ,
μ STF 2 = tr W 11 2 ( tr W 11 ) 2 = tr W 22 2 ( tr W 22 ) 2 = 1 + P 2 2 ,
W 22 = M + W 11 M , with M M + = M + M = m 2 I ,
tr ( W 12 W 21 ) = tr ( m 2 W 11 2 ) .
det ( W 12 W 21 ) = det ( m 2 W 11 2 ) .
S = ( U 0 0 V ) .
T = S T S + = ( W 11 W 12 W 21 W 22 ) ,
W 11 = U W 11 U + , W 22 = V W 22 V + ,
W 12 = U W 12 V + = m W 11 , W 21 = m * W 11 .
W 12 = J 1 J 2 2 ( 1 1 1 1 ) .
V = 2 2 ( 1 1 1 1 ) .
det W 11 2 ( tr W 11 ) 2 = det W 22 2 ( tr W 22 ) 2 .
D 1 = ( λ a 0 0 λ b ) , D 2 = ( μ a 0 0 μ b ) ,
( 0 1 1 0 ) .

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