Abstract

We analyze the optimal visibility one can obtain in interference experiments with partially polarized light when one acts on only one of the two interfering beams. This is a practical situation that can appear when one does not want to modify or attenuate one of the beams, such as in homodyne detection. It is shown that the optimal configuration usually does not correspond to light with the same degrees of polarization for the two interfering beams. We also demonstrate that a simple interpretation can be obtained with the recently introduced normalized mutual coherence matrix.

© 2007 Optical Society of America

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References

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  1. E. Wolf, Phys. Lett. A 312, 263 (2003).
    [CrossRef]
  2. J. Tervo, T. Setälä, and A. T. Friberg, Opt. Express 11, 1137 (2003).
    [CrossRef] [PubMed]
  3. F. Gori, M. Santarsiero, R. Simon, G. Piquero, R. Borghi, and G. Guattari, J. Opt. Soc. Am. A 20, 78 (2003).
    [CrossRef]
  4. Ph. Réfrégier and F. Goudail, Opt. Express 13, 6051 (2005).
    [CrossRef] [PubMed]
  5. G. S. Agarwal, A. Dogariu, T. D. Visser, and E. Wolf, Opt. Lett. 30, 120 (2005).
    [CrossRef] [PubMed]
  6. Ph. Réfrégier and A. Roueff, Opt. Lett. 31, 1175 (2006).
    [CrossRef] [PubMed]
  7. J. W. Goodman, in Statistical Optics (Wiley, 1985), pp. 116-156.
  8. L. Mandel and E. Wolf, in Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), pp. 160-170.
  9. C. Brosseau, in Fundamentals of Polarized Light: A Statistical Approach (Wiley, 1998).

2006 (1)

2005 (2)

2003 (3)

Agarwal, G. S.

Borghi, R.

Brosseau, C.

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

Dogariu, A.

Friberg, A. T.

Goodman, J. W.

J. W. Goodman, in Statistical Optics (Wiley, 1985), pp. 116-156.

Gori, F.

Goudail, F.

Guattari, G.

Mandel, L.

L. Mandel and E. Wolf, in Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), pp. 160-170.

Piquero, G.

Réfrégier, Ph.

Roueff, A.

Santarsiero, M.

Setälä, T.

Simon, R.

Tervo, J.

Visser, T. D.

Wolf, E.

G. S. Agarwal, A. Dogariu, T. D. Visser, and E. Wolf, Opt. Lett. 30, 120 (2005).
[CrossRef] [PubMed]

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

L. Mandel and E. Wolf, in Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), pp. 160-170.

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

Opt. Express (2)

Opt. Lett. (2)

Phys. Lett. A (1)

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

Other (3)

J. W. Goodman, in Statistical Optics (Wiley, 1985), pp. 116-156.

L. Mandel and E. Wolf, in Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), pp. 160-170.

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

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Figures (2)

Fig. 1
Fig. 1

Schematic representation of the considered experimental setup.

Fig. 2
Fig. 2

Ratio ρ = μ W ( r 1 , r 2 , τ ) 2 μ W , 0 ( r 1 , r 2 , τ ) 2 as a function of α for different values of Q . From the solid curve to the short-dashed curve: Q = 0 , 1 3 , 2 3 , 0.99 . See text for details.

Equations (13)

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Ω ( r 1 , r 2 , t 1 , t 2 ) = E ( r 2 , t 2 ) E ( r 1 , t 1 ) ,
μ W ( r 1 , r 2 , τ ) = tr [ Ω ( r 1 , r 2 , τ ) ] tr [ Γ 1 ] tr [ Γ 2 ] ,
tr [ S G ] 2 tr [ S S ] .
μ W , 0 ( r 1 , r 2 , τ ) 2 = tr [ Ω Γ 1 1 Ω ] tr [ Γ 2 ] .
μ S 2 = tr [ T ] 2 [ 1 + Q ] , μ I 2 = tr [ T ] 2 [ 1 Q ] ,
Q = 1 4 det [ T ] { tr [ T ] } 2 ,
μ W , 0 ( r 1 , r 2 , τ ) 2 = tr [ T Γ 2 ] tr [ Γ 2 ] ,
P 1 = 1 4 det [ T Γ 2 ] { tr [ T Γ 2 ] } 2 .
Γ 2 = ( I X 0 0 I Y ) , T = ( μ S 2 0 0 μ I 2 ) .
μ W ( r 1 , r 2 , τ ) 2 = tr [ Ω ] 2 tr [ Γ 2 ] 2 .
μ W ( r 1 , r 2 , τ ) 2 = μ S 2 + μ I 2 2 [ 2 α 2 + ( 1 Q ) ( 1 2 α ) + 2 α ( 1 α ) 1 Q 2 ] ,
μ W , 0 ( r 1 , r 2 , τ ) 2 = μ S 2 + μ I 2 2 [ 1 + Q ( 2 α 1 ) ] .
S = ( a b c d ) , G = ( α β γ δ ) .

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