Abstract

The maximum visibility achievable in arbitrary lossless linear interferometers illuminated with two vectorial transversal electromagnetic beams is determined.

© 2007 Optical Society of America

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References

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2007 (2)

2005 (1)

2003 (2)

2002 (1)

1994 (1)

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Phys. Rev. Lett. 73, 58 (1994).
[CrossRef] [PubMed]

1981 (1)

J. C. Samson and J. V. Olson, SIAM J. Appl. Math. 40, 137 (1981).
[CrossRef]

1977 (1)

R. Barakat, Opt. Commun. 23, 147 (1977).
[CrossRef]

1963 (1)

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

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

Opt. Commun. (1)

R. Barakat, Opt. Commun. 23, 147 (1977).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

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. Lett. (1)

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, Phys. Rev. Lett. 73, 58 (1994).
[CrossRef] [PubMed]

SIAM J. Appl. Math. (1)

J. C. Samson and J. V. Olson, SIAM J. Appl. Math. 40, 137 (1981).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Illustration of a 4 × 4 interferometer leading to the maximum visibility allowed by the input fields.

Equations (17)

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E 1 = E 1 , x , E 2 = E 1 , y , E 3 = E 2 , x , E 4 = E 2 , y ,
V ̃ max = λ ̃ M λ ̃ m λ ̃ M + λ ̃ m ,
V ̃ max = { 2 [ tr ( M ̃ 2 ) ( tr M ̃ ) 2 1 2 ] } 1 2 .
λ ̃ M = E ̃ M E ̃ M * = E ̃ M M E ̃ M λ M ,
λ ̃ m = E ̃ m E ̃ m * = E ̃ m M E ̃ m λ m ,
V max = λ M λ m λ M + λ m .
M = ( 1 0 0.1 0 0 0.2 0 0.1 0.1 0 1 0 0 0.1 0 0.2 ) .
E M ( 1 0 1 0 ) , E m ( 0 1 0 1 ) .
V max = 0.83 .
μ 1 = tr Γ 1 , 2 tr Γ 1 , 1 Γ 2 , 2 = 0.17 ,
Γ 1 , 2 = ( 0.1 0 0 0.1 ) , Γ 1 , 1 = Γ 2 , 2 = ( 1 0 0 0.2 ) .
μ 2 = tr ( Γ 1 , 2 Γ 1 , 2 ) tr Γ 1 , 1 tr Γ 2 , 2 = 0.12 .
μ 3 = maxeig ( Γ 1 , 1 1 2 Γ 1 , 2 Γ 2 , 2 1 2 ) = 0.5 ,
μ 4 = { 4 3 [ tr ( M 2 ) ( tr M ) 2 1 4 ] } 1 2 = 0.40 ,
V 3 2 tr M tr M ̃ μ 4 = 0.98 ,
μ 5 = { 1 12 [ tr ( L 2 ) 4 ] } 1 2 = 0.21 ,
P j = { 2 [ tr ( Γ j , j 2 ) ( tr Γ j , j ) 2 1 2 ] } 1 2 = 0.67 .

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