Abstract

It is proved that, when the vector modal theory of coherence is applied to a pair of fixed points, exact results are obtained for the mode structure. In particular, it is shown that the field radiated by the pinholes of a Young interferometer can always be represented by the incoherent superposition of no more than four perfectly correlated and polarized modes. The role of such modes is illustrated through a simple example.

© 2006 Optical Society of America

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References

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

2005

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

2004

2003

1998

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

1994

1982

Borghi, R.

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]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Friberg, A. T.

Gori, F.

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]

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]

James, D. F. V.

Mandel, L.

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

Piquero, G.

Roychowdhury, H.

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

Santarsiero, M.

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]

Setälä, T.

Simon, R.

Tervo, J.

Vicalvi, S.

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

Wolf, E.

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

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

E. Wolf, J. Opt. Soc. Am. 72, 343 (1982).
[CrossRef]

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

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

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

Phys. Lett. A

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

Pure Appl. Opt.

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

Other

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

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

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Equations (25)

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Λ φ α ( u ) = β J α β ( u , v ) φ β ( v ) d 2 v ( α , β = x , y ) ,
V α ( u , t ) = S i = 1 , 2 V α i ( t ) δ ( u r i ) ,
J α β ( u , v ) = S 2 i = 1 , 2 j = 1 , 2 J α β i j δ ( u r i ) δ ( v r j ) ,
φ α ( u ) = S i = 1 , 2 φ α i δ ( u r i ) ,
Λ i = 1 , 2 φ α i δ ( u r i ) = S β = x , y i = 1 , 2 j = 1 , 2 J α β i j φ β j δ ( u r i )
λ φ α i = β = x , y j = 1 , 2 J α β i j φ β j ( α = x , y ; i = 1 , 2 ) ,
Φ n = [ φ x 1 ( n ) φ x 2 ( n ) φ y 1 ( n ) φ y 2 ( n ) ] ( n = 1 , , 4 ) .
J α β i j = n = 1 4 λ n φ α i ( n ) * φ β j ( n ) ( α , β = x , y ; i , j = 1 , 2 ) .
α = x , y i = 1 , 2 J α α i i = n = 1 4 λ n .
T ̂ = ( J x x 11 J x x 12 J x y 11 J x y 12 J x x 21 J x x 22 J x y 21 J x y 22 J y x 11 J y x 12 J y y 11 J y y 12 J y x 21 J y x 22 J y y 21 J y y 22 ) .
α , β = x , y i , j = 1 , 2 J α β i j f α i * g β j 0 ,
J x x 12 = λ 1 φ x 1 ( 1 ) * φ x 2 ( 1 ) + λ 2 φ x 1 ( 2 ) * φ x 2 ( 2 ) .
J x x ( r 1 , r 2 ) = I x exp [ ( r 1 2 + r 2 2 ) 4 σ 2 ( r 1 r 2 ) 2 2 δ x 2 ] ,
J y y ( r 1 , r 2 ) = I y exp [ ( r 1 2 + r 2 2 ) 4 σ 2 ( r 1 r 2 ) 2 2 δ y 2 ] ,
J x y ( r 1 , r 2 ) = J y x ( r 1 , r 2 ) = 0 ,
T ̂ = I x exp ( x 2 2 σ 2 ) [ 1 c 0 0 c 1 0 0 0 0 R R d 0 0 R d R ] ,
R = I y I x , c = exp ( 2 x 2 δ x 2 ) , d = exp ( 2 x 2 δ y 2 ) .
λ 1 = 1 + c , λ 2 = 1 c , λ 3 = R ( 1 + d ) , λ 4 = R ( 1 d ) ,
Φ 1 = 1 2 [ 1 1 0 0 ] ,
Φ 2 = 1 2 [ 1 1 , 0 0 ] ,
Φ 3 = 1 2 [ 0 0 1 1 ] ,
Φ 4 = 1 2 [ 0 0 1 1 ] .
μ eq = I max I min I max + I min = c + R d 1 + R .
P = λ 1 λ 3 λ 1 + λ 3 = 1 + c R ( 1 + d ) 1 + c + R ( 1 + d ) ,
P 0 = I x I y I x + I y = 1 R 1 + R .

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