Abstract

Whereas the classic Stokes parameters are measures of intensity, the recently introduced two-point Stokes parameters characterize spatial coherence. It is shown that in analogy to the Stokes parameters, the two-point parameters have a physical interpretation as sums and differences of (scalar) cross-spectral density functions of specific electric-field components. A measurement scheme and several physical consequences of the two-point parameters are discussed.

© 2009 Optical Society of America

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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. C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).
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  9. J. Tervo, P. Réfrégier, and A. Roueff, J. Opt. A 10, 055002 (2008).
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    [CrossRef] [PubMed]
  15. Here, the two-point Stokes vector stands for a vector formed by two-point Stokes parameters Sj with j=0,...,3.
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    [CrossRef] [PubMed]
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    [CrossRef]

2009 (1)

2008 (5)

P. Réfrégier and A. Luis, J. Opt. Soc. Am. A 25, 2749 (2008).
[CrossRef]

B. Kanseri and H. C. Kandpal, Opt. Lett. 33, 2410 (2008).
[CrossRef] [PubMed]

M. A. Alonso and E. Wolf, Opt. Commun. 281, 2393 (2008).
[CrossRef]

J. Tervo, P. Réfrégier, and A. Roueff, J. Opt. A 10, 055002 (2008).
[CrossRef]

X. Du and D. Zhao, Opt. Commun. 281, 5968 (2008).
[CrossRef]

2006 (2)

2005 (1)

2004 (3)

2003 (1)

1998 (2)

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, Pure Appl. Opt. 7, 941 (1998).
[CrossRef]

F. Gori, Opt. Lett. 23, 241 (1998).
[CrossRef]

Alonso, M. A.

M. A. Alonso and E. Wolf, Opt. Commun. 281, 2393 (2008).
[CrossRef]

Borghi, R.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, Pure Appl. Opt. 7, 941 (1998).
[CrossRef]

Brosseau, C.

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).

Dogariu, A.

Du, X.

X. Du and D. Zhao, Opt. Commun. 281, 5968 (2008).
[CrossRef]

Ellis, J.

Friberg, A. T.

Gori, F.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, Pure Appl. Opt. 7, 941 (1998).
[CrossRef]

F. Gori, Opt. Lett. 23, 241 (1998).
[CrossRef]

Guattari, G.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, Pure Appl. Opt. 7, 941 (1998).
[CrossRef]

Kandpal, H. C.

Kanseri, B.

Korotkova, O.

Luis, A.

Mandel, L.

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

Rath, S.

Réfrégier, P.

P. Réfrégier and A. Luis, J. Opt. Soc. Am. A 25, 2749 (2008).
[CrossRef]

J. Tervo, P. Réfrégier, and A. Roueff, J. Opt. A 10, 055002 (2008).
[CrossRef]

Roueff, A.

J. Tervo, P. Réfrégier, and A. Roueff, J. Opt. A 10, 055002 (2008).
[CrossRef]

Santarsiero, M.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, Pure Appl. Opt. 7, 941 (1998).
[CrossRef]

Setälä, T.

Tervo, J.

Vicalvi, S.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, Pure Appl. Opt. 7, 941 (1998).
[CrossRef]

Wolf, E.

M. A. Alonso and E. Wolf, Opt. Commun. 281, 2393 (2008).
[CrossRef]

O. Korotkova and E. Wolf, Opt. Lett. 30, 198 (2005).
[CrossRef] [PubMed]

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

Zhao, D.

X. Du and D. Zhao, Opt. Commun. 281, 5968 (2008).
[CrossRef]

J. Opt. A (1)

J. Tervo, P. Réfrégier, and A. Roueff, J. Opt. A 10, 055002 (2008).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (2)

M. A. Alonso and E. Wolf, Opt. Commun. 281, 2393 (2008).
[CrossRef]

X. Du and D. Zhao, Opt. Commun. 281, 5968 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (8)

Pure Appl. Opt. (1)

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, Pure Appl. Opt. 7, 941 (1998).
[CrossRef]

Other (3)

Here, the two-point Stokes vector stands for a vector formed by two-point Stokes parameters Sj with j=0,...,3.

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

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).

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Equations (28)

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S 0 ( r , ω ) = I x ( r , ω ) + I y ( r , ω ) ,
S 1 ( r , ω ) = I x ( r , ω ) I y ( r , ω ) ,
S 2 ( r , ω ) = I α ( r , ω ) I β ( r , ω ) ,
S 3 ( r , ω ) = I r ( r , ω ) I l ( r , ω ) .
S 0 ( r 1 , r 2 , ω ) = W x x ( r 1 , r 2 , ω ) + W y y ( r 1 , r 2 , ω ) ,
S 1 ( r 1 , r 2 , ω ) = W x x ( r 1 , r 2 , ω ) W y y ( r 1 , r 2 , ω ) ,
S 2 ( r 1 , r 2 , ω ) = W y x ( r 1 , r 2 , ω ) + W x y ( r 1 , r 2 , ω ) ,
S 3 ( r 1 , r 2 , ω ) = i [ W y x ( r 1 , r 2 , ω ) W x y ( r 1 , r 2 , ω ) ] ,
W i j ( r 1 , r 2 , ω ) = E i ( r 1 , ω ) E j ( r 2 , ω ) ,
E ( r , ω ) = U E ( r , ω ) ,
U α β = 1 2 [ 1 1 1 1 ] ,     U r l = 1 2 [ 1 1 i i ] ,
[ E x ( r , ω ) E y ( r , ω ) ] = U α β [ E α ( r , ω ) E β ( r , ω ) ] ,
[ E x ( r , ω ) E y ( r , ω ) ] = U r l [ E r ( r , ω ) E l ( r , ω ) ] .
W ( r 1 , r 2 , ω ) = U W ( r 1 , r 2 , ω ) U T ,
S 0 = u 1 W u 1 + u 2 W u 2 ,
S 1 = u 1 W u 1 u 2 W u 2 ,
S 2 = u 2 W u 1 + u 1 W u 2 ,
S 3 = i [ u 2 W u 1 u 1 W u 2 ] ,
S 0 ( r 1 , r 2 , ω ) = W x x ( r 1 , r 2 , ω ) + W y y ( r 1 , r 2 , ω ) ,
S 1 ( r 1 , r 2 , ω ) = W x x ( r 1 , r 2 , ω ) W y y ( r 1 , r 2 , ω ) ,
S 2 ( r 1 , r 2 , ω ) = W α α ( r 1 , r 2 , ω ) W β β ( r 1 , r 2 , ω ) ,
S 3 ( r 1 , r 2 , ω ) = W r r ( r 1 , r 2 , ω ) W l l ( r 1 , r 2 , ω ) .
σ 0 = [ 1 0 0 1 ] ,     σ 1 = [ 1 0 0 1 ] ,
σ 2 = [ 0 1 1 0 ] ,     σ 3 = [ 0 i i 0 ] ,
2 σ 1 W = S 1 σ 0 + S 0 σ 1 + i S 3 σ 2 i S 2 σ 3 ,
2 σ 2 W = S 2 σ 0 i S 3 σ 1 + S 0 σ 2 + i S 1 σ 3 ,
2 σ 3 W = S 3 σ 0 + i S 2 σ 1 i S 1 σ 2 + S 0 σ 3 .
S j ( r 1 , r 2 , ω ) = tr [ σ j W ( r 1 , r 2 , ω ) ] ,     j = 0 , , 3 ,

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