Abstract

When a Young’s interferometer is fed by an electromagnetic beam, fringes of low, or even zero, visibility do not necessarily indicate lack of correlation between two typical field components at the pinholes. The passage of light that emerges from one of the pinholes through a nonabsorbing anisotropic optical element may enhance the visibility. We inquire about the maximum visibility that can be attained through such a reversible transformation (polarizers being excluded). We find that such a quantity can be evaluated in closed form. Its value is directly related to the Ky Fan 1-norm of the correlation matrix of the illuminating beam.

© 2007 Optical Society of America

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References

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2006 (3)

2005 (2)

P. Réfrégier and F. Goudail, Opt. Express 13, 6051 (2005).
[CrossRef] [PubMed]

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

2004 (5)

2003 (3)

2002 (1)

S. P. Walborn, M. O. Terra Cunha, S. Padua, and C. H. Monken, Phys. Rev. A 65, 033818 (2002).
[CrossRef]

2000 (1)

1999 (1)

1998 (2)

F. Gori, Opt. Lett. 23, 41 (1998).

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

1994 (1)

1963 (2)

B. Karczewski, Phys. Lett. 5, 191 (1963).
[CrossRef]

B. Karczewski, Nuovo Cimento 30, 906 (1963).
[CrossRef]

Agrawal, G. P.

Borghi, R.

Brosseau, C.

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

Dogariu, A.

Friberg, A. T.

Gori, F.

Goudail, F.

Guattari, G.

F. Gori, M. Santarsiero, R. Simon, G. Piquero, R. Borghi, and G. Guattari, J. Opt. Soc. Am. A 20, 78 (2003).
[CrossRef]

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

Horn, R. A.

R. A. Horn and C. R. Johnson, Topics in Matrix Analysis (Cambridge U. Press, 1991).
[CrossRef]

James, D. F. V.

Johnson, C. R.

R. A. Horn and C. R. Johnson, Topics in Matrix Analysis (Cambridge U. Press, 1991).
[CrossRef]

Karczewski, B.

B. Karczewski, Phys. Lett. 5, 191 (1963).
[CrossRef]

B. Karczewski, Nuovo Cimento 30, 906 (1963).
[CrossRef]

Mandel, L.

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

Monken, C. H.

S. P. Walborn, M. O. Terra Cunha, S. Padua, and C. H. Monken, Phys. Rev. A 65, 033818 (2002).
[CrossRef]

Mujat, M.

Padua, S.

S. P. Walborn, M. O. Terra Cunha, S. Padua, and C. H. Monken, Phys. Rev. A 65, 033818 (2002).
[CrossRef]

Piquero, G.

Réfrégier, P.

Roueff, A.

Roychowdhury, H.

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

Santarsiero, M.

Seshadri, S. R.

Setälä, T.

Simon, R.

Terra Cunha, M. O.

S. P. Walborn, M. O. Terra Cunha, S. Padua, and C. H. Monken, Phys. Rev. A 65, 033818 (2002).
[CrossRef]

Tervo, J.

Vicalvi, S.

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

Walborn, S. P.

S. P. Walborn, M. O. Terra Cunha, S. Padua, and C. H. Monken, Phys. Rev. A 65, 033818 (2002).
[CrossRef]

Wolf, E.

J. Opt. Soc. Am. A (6)

Nuovo Cimento (1)

B. Karczewski, Nuovo Cimento 30, 906 (1963).
[CrossRef]

Opt. Commun. (1)

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

Opt. Express (2)

Opt. Lett. (7)

Phys. Lett. (1)

B. Karczewski, Phys. Lett. 5, 191 (1963).
[CrossRef]

Phys. Lett. A (1)

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

Phys. Rev. A (1)

S. P. Walborn, M. O. Terra Cunha, S. Padua, and C. H. Monken, Phys. Rev. A 65, 033818 (2002).
[CrossRef]

Pure Appl. Opt. (1)

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

Other (3)

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

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

R. A. Horn and C. R. Johnson, Topics in Matrix Analysis (Cambridge U. Press, 1991).
[CrossRef]

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Equations (14)

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

J ̂ ( r 1 , r 2 ) = [ J x x ( r 1 , r 2 ) J x y ( r 1 , r 2 ) J y x ( r 1 , r 2 ) J y y ( r 1 , r 2 ) ] ,
J eq ( r 1 , r 2 ) = Tr { J ̂ ( r 1 , r 2 ) } ,
V = 2 J eq ( r 1 , r 2 ) I ( r 1 ) + I ( r 2 ) ,
M ̂ M ̂ = M ̂ M ̂ = I ̂ ,
J ̂ 12 = U ̂ S ̂ V ̂ ,
J ̂ 12 v i = σ i u i , J ̂ 12 u i = σ i v i .
N n ( J ̂ 12 ) = ( σ 1 n + σ 2 n ) 1 n .
N 1 ( J ̂ 12 ) = σ 1 + σ 2 = max { Tr { J ̂ 12 M ̂ } : M ̂ U ( 2 ) } ,
J ̂ 12 M ̂ = U ̂ S ̂ V ̂ V ̂ U ̂ = U ̂ S ̂ U ̂ ,
Tr { J ̂ 12 M ̂ } = Tr { U ̂ S ̂ U ̂ } = Tr { S ̂ } = σ 1 + σ 2 ,
J eq Max = N 1 ( J ̂ 12 ) = σ 1 + σ 2 ,
J eq Max = [ Tr { J ̂ 12 J ̂ 12 } + 2 Det { J ̂ 12 } ] 1 2 ,
J E = Tr { J ̂ 12 J ̂ 12 } ,
J eq Max = [ J E 2 + 2 Det { J ̂ 12 } ] 1 2 ,

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