Abstract

We analyze the modulation of the Stokes parameters in Young’s two-pinhole interference experiment with a random electromagnetic beam. We demonstrate that the electromagnetic (spectral) degree of coherence put forward in Opt. Lett. 29, 328 (2004) [or its space–time analog in Opt. Express 11, 1137 (2003) ] is physically related to the contrasts of modulation in the four Stokes parameters. More explicitly, the electromagnetic degree of coherence is a measure of both the visibility of the intensity fringes and the modulation contrasts of the three polarization Stokes parameters. We also show that by using suitable wave plates the modulation in any Stokes parameter can be transformed into the form of intensity variation, and hence the electromagnetic degree of coherence can be obtained experimentally by four visibility measurements.

© 2006 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. E. Wolf, Phys. Lett. A 312, 263 (2003).
    [CrossRef]
  3. F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, Opt. Lett. 31, 688 (2006).
    [CrossRef] [PubMed]
  4. T. Setälä, J. Tervo, and A. T. Friberg, Opt. Lett. 31, 2208 (2006).
    [CrossRef] [PubMed]
  5. O. Korotkova and E. Wolf, Opt. Lett. 30, 298 (2005).
    [CrossRef]
  6. J. Tervo, T. Setälä, and A. T. Friberg, Opt. Express 11, 1137 (2003).
    [CrossRef] [PubMed]
  7. T. Setälä, J. Tervo, and A. T. Friberg, Opt. Lett. 29, 328 (2004).
    [CrossRef] [PubMed]
  8. J. Tervo, T. Setälä, and A. T. Friberg, J. Opt. Soc. Am. A 21, 2205 (2004).
    [CrossRef]
  9. C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).
  10. T. Setälä, J. Tervo, and A. T. Friberg, Opt. Commun. 238, 229 (2004).
    [CrossRef]
  11. Ph. Réfrégier and F. Goudail, Opt. Express 13, 6051 (2005).
    [CrossRef] [PubMed]
  12. J. Ellis and A. Dogariu, Opt. Lett. 29, 536 (2004).
    [CrossRef] [PubMed]

2006 (2)

2005 (2)

2004 (4)

2003 (2)

Borghi, R.

Brosseau, C.

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

Dogariu, A.

Ellis, J.

Friberg, A. T.

Gori, F.

Goudail, F.

Korotkova, O.

O. Korotkova and E. Wolf, Opt. Lett. 30, 298 (2005).
[CrossRef]

Mandel, L.

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

Réfrégier, Ph.

Santarsiero, M.

Setälä, T.

Tervo, J.

Wolf, E.

F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, Opt. Lett. 31, 688 (2006).
[CrossRef] [PubMed]

O. Korotkova and E. Wolf, Opt. Lett. 30, 298 (2005).
[CrossRef]

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

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

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

Opt. Commun. (1)

T. Setälä, J. Tervo, and A. T. Friberg, Opt. Commun. 238, 229 (2004).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Phys. Lett. A (1)

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

Other (2)

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 (13)

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W i j ( r 1 , r 2 , ω ) = E i * ( r 1 , ω ) E j ( r 2 , ω ) , ( i , j ) = ( x , y ) .
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 x y ( r 1 , r 2 , ω ) + W y x ( 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 ( r 1 , r 2 , ω ) = 1 2 n = 0 3 S n ( r 1 , r 2 , ω ) σ n ,
S n ( r , ω ) = S n ( r , r , ω ) , n = 0 3 .
μ 2 ( r 1 , r 2 , ω ) = tr [ W ( r 1 , r 2 , ω ) W ( r 2 , r 1 , ω ) ] tr W ( r 1 , r 1 , ω ) tr W ( r 2 , r 2 , ω ) = i j c i j ( r 1 , r 2 , ω ) 2 W i i ( r 1 , r 1 , ω ) W j j ( r 2 , r 2 , ω ) i j W i i ( r 1 , r 1 , ω ) W j j ( r 2 , r 2 , ω ) .
c i j ( r 1 , r 2 , ω ) = W i j ( r 1 , r 2 , ω ) [ W i i ( r 1 , r 1 , ω ) W j j ( r 2 , r 2 , ω ) ] 1 2 ,
S n ( r , ω ) = S n ( 1 ) ( r , ω ) + S n ( 2 ) ( r , ω ) + 2 [ S 0 ( 1 ) ( r , ω ) S 0 ( 2 ) ( r , ω ) ] 1 2 η n ( Q 1 , Q 2 , ω ) × cos { arg [ η n ( Q 1 , Q 2 , ω ) ] k ( R 1 R 2 ) } ,
η n ( Q 1 , Q 2 , ω ) = S n ( Q 1 , Q 2 , ω ) [ tr W ( Q 1 , Q 1 , ω ) tr W ( Q 2 , Q 2 , ω ) ] 1 2 ,
V n ( ω ) = η n ( Q 1 , Q 2 , ω ) , n = 0 3 ,
μ 2 ( Q 1 , Q 2 , ω ) = 1 2 n = 0 3 V n 2 ( ω ) .

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