Abstract

We derive a spectral interference law that governs the behavior of the four Stokes parameters in Young’s two-pinhole experiment with a random electromagnetic beam. In addition to the visibility of intensity fringes, we introduce three new contrast parameters that describe the interference-induced changes in the field’s state of partial polarization. The polarization modulation depends on the electric field correlations at the pinholes and is closely related to the two-point Stokes parameters. The results are expected to be particularly useful in polarization interferometry and electromagnetic coherence theory. The formalism is demonstrated with specific examples.

© 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. C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998).
  3. H. Roychowdhury and E. Wolf, Opt. Commun. 252, 268 (2005).
    [CrossRef]
  4. J. Ellis and A. Dogariu, Opt. Lett. 29, 536 (2004).
    [CrossRef] [PubMed]
  5. O. Korotkova and E. Wolf, Opt. Lett. 30, 198 (2005).
    [CrossRef] [PubMed]

2005

H. Roychowdhury and E. Wolf, Opt. Commun. 252, 268 (2005).
[CrossRef]

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

2004

Brosseau, C.

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

Dogariu, A.

Ellis, J.

Korotkova, O.

Mandel, L.

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

Roychowdhury, H.

H. Roychowdhury and E. Wolf, Opt. Commun. 252, 268 (2005).
[CrossRef]

Wolf, E.

H. Roychowdhury and E. Wolf, Opt. Commun. 252, 268 (2005).
[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).

Opt. Commun.

H. Roychowdhury and E. Wolf, Opt. Commun. 252, 268 (2005).
[CrossRef]

Opt. Lett.

Other

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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Figures (1)

Fig. 1
Fig. 1

Geometry of Young’s interference experiment.

Equations (17)

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E ( r , ω ) = K 1 E ( Q 1 , ω ) exp ( i k R 1 ) R 1 + K 2 E ( Q 2 , ω ) exp ( i k R 2 ) R 2 ,
ϕ i j ( r , ω ) = E i * ( r , ω ) E j ( r , ω ) , ( i , j ) = ( x , y ) ,
ϕ i j ( r , ω ) = ϕ i j ( 1 ) ( r , ω ) + ϕ i j ( 2 ) ( r , ω ) + tr Φ ( 1 ) ( r , ω ) tr Φ ( 2 ) ( r , ω ) × { η i j ( Q 1 , Q 2 , ω ) exp [ i k ( R 1 R 2 ) ] + η i j ( Q 2 , Q 1 , ω ) exp [ i k ( R 1 R 2 ) ] } ,
η i j ( Q 1 , Q 2 , ω ) = W i j ( Q 1 , Q 2 , ω ) tr Φ ( Q 1 , ω ) tr Φ ( Q 2 , ω ) ,
S 0 ( r , ω ) = ϕ x x ( r , ω ) + ϕ y y ( r , ω ) ,
S 1 ( r , ω ) = ϕ x x ( r , ω ) ϕ y y ( r , ω ) ,
S 2 ( r , ω ) = ϕ x y ( r , ω ) + ϕ y x ( r , ω ) ,
S 3 ( r , ω ) = i [ ϕ y x ( r , ω ) ϕ x y ( r , ω ) ] .
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 ) μ n ( Q 1 , Q 2 , ω ) × cos { arg [ μ n ( Q 1 , Q 2 , ω ) ] k ( R 1 R 2 ) } ,
μ 0 ( Q 1 , Q 2 , ω ) = η x x ( Q 1 , Q 2 , ω ) + η y y ( Q 1 , Q 2 , ω ) ,
μ 1 ( Q 1 , Q 2 , ω ) = η x x ( Q 1 , Q 2 , ω ) η y y ( Q 1 , Q 2 , ω ) ,
μ 2 ( Q 1 , Q 2 , ω ) = η x y ( Q 1 , Q 2 , ω ) + η y x ( Q 1 , Q 2 , ω ) ,
μ 3 ( Q 1 , Q 2 , ω ) = i [ η y x ( Q 1 , Q 2 , ω ) η x y ( Q 1 , Q 2 , ω ) ] .
C n ( r , ω ) = max [ S n ( r , ω ) ] min [ S n ( r , ω ) ] max [ S 0 ( r , ω ) ] + min [ S 0 ( r , ω ) ] ,
C n ( ω ) = 2 r S ( ω ) r S ( ω ) + 1 μ n ( Q 1 , Q 2 , ω ) , n = 0 3 ,
C n ( ω ) = μ n ( Q 1 , Q 2 , ω ) , n = 0 3 ,
P ( r , ω ) = [ S 1 2 ( r , ω ) + S 2 2 ( r , ω ) + S 3 2 ( r , ω ) ] 1 2 S 0 ( r , ω ) .

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