Abstract

We show that the correlation matrix of any electromagnetic planar source endowed with complete polarization must be of a universal form, no matter how the field components are correlated across the source plane. Such form entails that both the realizability conditions and the search of vector modes of the source reduce to scalar problems. We shall also briefly dwell on how propagation affects the polarization properties of the field and, in particular, we discuss cases in which propagated light remains completely polarized.

© 2008 Optical Society of America

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References

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2008

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2003

2001

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A 3, 1 (2001).
[CrossRef]

F. Gori, J. Opt. Soc. Am. A 18, 1612 (2001).
[CrossRef]

2000

1998

P. L. Greene and D. G. Hall, J. Opt. Soc. Am. A 15, 3020 (1998).
[CrossRef]

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, J. Opt. A 7, 941 (1998).

F. Gori, Opt. Lett. 23, 241 (1998).
[CrossRef]

1994

1990

Alonso, M. A.

Baykal, Y.

Borghi, R.

Brown, D. P.

D. P. Brown, A. K. Spilman, T. G. Brown, R. Borghi, S. N. Volkov, and E. Wolf, Opt. Commun. 281, 5287 (2008).
[CrossRef]

Brown, T. G.

D. P. Brown, A. K. Spilman, T. G. Brown, R. Borghi, S. N. Volkov, and E. Wolf, Opt. Commun. 281, 5287 (2008).
[CrossRef]

Cai, Y.

Dogariu, A.

Ellis, J.

Eyyuboglu, H. T.

Foley, J. T.

Ford, D. H.

Friberg, A. T.

Gori, F.

Greene, P. L.

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, J. Opt. A 7, 941 (1998).

Hall, D. G.

Hall, G. D.

James, D. F.

Jordan, R. H.

Kimura, W. D.

Korotkova, O.

O. Korotkova, T. D. Visser, and E. Wolf, Opt. Commun. 281, 515 (2008).
[CrossRef]

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
[CrossRef]

Lin, Q.

Martínez-Herrero, R.

Mejías, P.

Mondello, A.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A 3, 1 (2001).
[CrossRef]

Piquero, G.

Ponomarenko, S.

Ramírez-Sánchez, V.

Réfrégier, P.

Roychowdhury, H.

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
[CrossRef]

Santarsiero, M.

Schoonover, R. W.

Setälä, T.

Simon, 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, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A 3, 1 (2001).
[CrossRef]

Spilman, A. K.

D. P. Brown, A. K. Spilman, T. G. Brown, R. Borghi, S. N. Volkov, and E. Wolf, Opt. Commun. 281, 5287 (2008).
[CrossRef]

Tervo, J.

Tidwell, S. C.

Vicalvi, S.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, J. Opt. A 7, 941 (1998).

Visser, T. D.

Volkov, S. N.

D. P. Brown, A. K. Spilman, T. G. Brown, R. Borghi, S. N. Volkov, and E. Wolf, Opt. Commun. 281, 5287 (2008).
[CrossRef]

Wolf, E.

D. P. Brown, A. K. Spilman, T. G. Brown, R. Borghi, S. N. Volkov, and E. Wolf, Opt. Commun. 281, 5287 (2008).
[CrossRef]

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

O. Korotkova, T. D. Visser, and E. Wolf, Opt. Commun. 281, 515 (2008).
[CrossRef]

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Lett. 29, 1536 (2004).
[CrossRef] [PubMed]

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

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

Appl. Opt.

J. Opt. A

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, J. Opt. A 7, 941 (1998).

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A 3, 1 (2001).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
[CrossRef]

O. Korotkova, T. D. Visser, and E. Wolf, Opt. Commun. 281, 515 (2008).
[CrossRef]

D. P. Brown, A. K. Spilman, T. G. Brown, R. Borghi, S. N. Volkov, and E. Wolf, Opt. Commun. 281, 5287 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

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

Other

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

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Figures (1)

Fig. 1
Fig. 1

Field lines in the form of lemniscates of Bernoulli.

Equations (16)

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W ̂ ( ρ 1 , ρ 2 ) = F ( ρ 1 , ρ 2 ) Ψ ( ρ 1 ) Ψ ( ρ 2 ) ,
Ψ ( ρ ) = [ C ( ρ ) S ( ρ ) exp [ i γ ( ρ ) ] ] ,
W μ ν ( ρ , ρ ) = E μ * ( ρ ) E ν ( ρ ) ,
E μ ( ρ ) = A μ ( ρ ) exp [ i δ μ ( ρ ) ] ,
M ̂ ( ρ ) = [ 1 0 0 exp [ i γ ( ρ ) ] ] ,
W ̂ ( ρ 1 , ρ 2 ) = M ̂ ( ρ 1 ) W ̂ ( ρ 1 , ρ 2 ) M ̂ ( ρ 2 ) .
P ̂ ( ρ ) = [ A x 2 ( ρ ) A x ( ρ ) A y ( ρ ) A x ( ρ ) A y ( ρ ) A y 2 ( ρ ) ] .
R ̂ ( ρ ) = [ C ( ρ ) S ( ρ ) S ( ρ ) C ( ρ ) ] ,
W ̂ ( ρ 1 , ρ 2 ) = R ̂ ( ρ 1 ) W ̂ ( ρ 1 , ρ 2 ) R ̂ ( ρ 2 ) = R ̂ ( ρ 1 ) M ̂ ( ρ 1 ) W ̂ ( ρ 1 , ρ 2 ) M ̂ ( ρ 2 ) R ̂ ( ρ 2 ) ,
P ̂ ( ρ ) = [ A x 2 ( ρ ) + A y 2 ( ρ ) 0 0 0 ] .
W ̂ ( ρ 1 , ρ 2 ) = F ( ρ 1 , ρ 2 ) [ 1 0 0 0 ] .
W ̂ ( ρ 1 , ρ 2 ) = M ̂ ( ρ 1 ) R ̂ ( ρ 1 ) W ̂ ( ρ 1 , ρ 2 ) R ̂ ( ρ 2 ) M ̂ ( ρ 2 ) .
F ( ρ 1 , ρ 2 ) = n λ n Φ n * ( ρ 1 ) Φ n ( ρ 2 ) ,
W ̂ ( ρ 1 , ρ 2 ) = n λ n u n ( ρ 1 ) u n ( ρ 2 ) ,
u n ( ρ ) = Φ n * ( ρ ) [ C ( ρ ) S ( ρ ) exp [ i γ ( ρ ) ] ] .
E ( ρ , φ ) = f ( ρ ) [ cos ( m φ + α ) ± sin ( m φ + α ) ] ,

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