Abstract

The simplest form for the correlation matrix of a completely unpolarized electromagnetic beam is the product of a scalar correlation function times a unit matrix. We show, however, that classes of unpolarized beams exist for which the diagonal elements of the correlation matrix are not equal to each other and the off-diagonal elements do not vanish identically. This gives rise to a distinction between pure and impure unpolarized beams. The two types of beams can be distinguished at the experimental level by their behavior in a Young’s interferometer.

© 2009 Optical Society of America

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References

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2008

2007

2006

2005

2004

2003

2001

G. Piquero, R. Borghi, A. Mondello, and M. Santarsiero, Opt. Commun. 195, 339 (2001).
[CrossRef]

1998

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

Borghi, R.

F. Gori, M. Santarsiero, and R. Borghi, Opt. Lett. 32, 588 (2007).
[CrossRef] [PubMed]

G. Piquero, R. Borghi, A. Mondello, and M. Santarsiero, Opt. Commun. 195, 339 (2001).
[CrossRef]

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

Friberg, A. T.

Gori, F.

Goudail, F.

Guattari, G.

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

Korotkova, O.

Luis, A.

Martínez-Herrero, R.

Mejías, P. M.

Mondello, A.

G. Piquero, R. Borghi, A. Mondello, and M. Santarsiero, Opt. Commun. 195, 339 (2001).
[CrossRef]

Piquero, G.

G. Piquero, R. Borghi, A. Mondello, and M. Santarsiero, Opt. Commun. 195, 339 (2001).
[CrossRef]

Réfrégier, Ph.

Santarsiero, M.

F. Gori, M. Santarsiero, and R. Borghi, Opt. Lett. 32, 588 (2007).
[CrossRef] [PubMed]

G. Piquero, R. Borghi, A. Mondello, and M. Santarsiero, Opt. Commun. 195, 339 (2001).
[CrossRef]

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

Setälä, T.

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Tervo, J.

Vicalvi, S.

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

Wolf, E.

E. Wolf, Opt. Lett. 33, 642 (2008).
[CrossRef] [PubMed]

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

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007).

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Equations (30)

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P 2 ( r , z ) = 1 4 Det { W ̂ ( r , r , z ) } [ Tr { W ̂ ( r , r , z ) } ] 2 ,
W x x ( r , r , z ) = W y y ( r , r , z ) , W x y ( r , r , z ) = 0 ,
W ̂ ( r 1 , r 2 , z ) = W ( r 1 , r 2 , z ) ( 1 0 0 1 ) ,
E μ ( r , z ) = [ α μ exp ( i k t r ) + β μ exp ( i k t r ) ] exp ( i k z z ) .
α μ * β ν = 0 ,
α x 2 + β x 2 = α y 2 + β y 2 ,
α x * α y = β x * β y .
W μ μ ( r 1 , r 2 , z ) = S cos [ k t ( r 2 r 1 ) ] + i D μ sin [ k t ( r 2 r 1 ) ] ,
W x y ( r 1 , r 2 , z ) = 2 i M sin [ k t ( r 2 r 1 ) ] ,
S = α x 2 + β x 2 ,
D μ = α μ 2 β μ 2 ,
M = α x * α y .
E μ ( r , 0 ) = exp ( r 2 w 0 2 ) r w 0 [ α μ exp ( i ϑ ) + β μ exp ( i ϑ ) ] ,
W μ μ ( r 1 , r 2 , 0 ) = exp ( r 1 2 + r 2 2 w 0 2 ) r 1 r 2 w 0 2 [ S cos ϑ 21 + i D μ sin ϑ 21 ] ,
W x y ( r 1 , r 2 , 0 ) = exp ( r 1 2 + r 2 2 w 0 2 ) 2 i M r 1 r 2 w 0 2 sin ϑ 21 ,
E ( r , z ) = F ( r , z ) m ( r , z ) ,
m ( r , 0 ) = cos ( n ϑ + α ) ,
E ( r , z ) = F ( r , z ) cos ( n ϑ + α ) ,
F ( r , z ) = ( i ) n + 1 k z exp [ i k ( z + r 2 2 z ) ] × 0 F ( ρ , 0 ) J n ( k ρ r z ) exp ( i k ρ 2 2 z ) ρ d ρ .
U ( r , z ) = R ( r , z ) + i I ( r , z ) ,
E μ ( r , z ) = F ( r , z ) [ α μ U ( r , z ) + β μ U * ( r , z ) ] ,
W μ μ ( r 1 , r 2 , z ) = F * ( r 1 , z ) F ( r 2 , z ) { S [ R ( r 1 , z ) R ( r 2 , z ) + I ( r 1 , z ) I ( r 2 , z ) ] + i D μ [ R ( r 1 , z ) I ( r 2 , z ) I ( r 1 , z ) R ( r 2 , z ) ] } ,
W x y ( r 1 , r 2 , z ) = F * ( r 1 , z ) F ( r 2 , z ) 2 i M [ R ( r 1 , z ) I ( r 2 , z ) I ( r 1 , z ) R ( r 2 , z ) ] .
W ̂ ( Q 1 , Q 2 ) = [ A B C D ] ,
η 0 ( Q 1 , Q 2 ) = ( A + D ) ( I 1 I 2 ) 1 2 ,
η 1 ( Q 1 , Q 2 ) = ( A D ) ( I 1 I 2 ) 1 2 ,
η 2 ( Q 1 , Q 2 ) = ( C + B ) ( I 1 I 2 ) 1 2 ,
η 3 ( Q 1 , Q 2 ) = i ( C B ) ( I 1 I 2 ) 1 2 ,
S j ( r ) = S j ( 1 ) ( r ) + S j ( 2 ) ( r ) + 2 [ S 0 ( 1 ) ( r ) S 0 ( 2 ) ( r ) ] 1 2 η j ( Q 1 , Q 2 ) × cos { arg [ η j ( Q 1 , Q 2 ) k ( R 1 R 2 ) ] } ,
W ̂ ( Q 1 , Q 2 ) = A [ 1 0 0 1 ] ,

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