Abstract

A necessary and sufficient nonnegative definiteness condition for the cross-spectral density matrix (CDM) is derived. It is also shown that this realizability condition allows the expansion of genuine CDMs in terms of recently introduced elementary fields, namely, mean-square coherent beams, and fields with position-independent stochastic behavior. The special case of uniformly polarized electromagnetic Schell-model sources is also analyzed.

© 2009 Optical Society of America

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References

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2009 (2)

2008 (3)

2007 (4)

2005 (2)

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

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

2003 (2)

Borghi, R.

Gori, F.

Goudail, F.

Guattari, G.

Korotkova, O.

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

Mandel, L.

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

Martínez-Herrero, R.

Mejías, P. M.

Piquero, G.

Réfrégier, Ph.

Roueff, A.

Ph. Réfrégier and A. Roueff, Opt. Photonics News 18(2), 30 (2007).
[CrossRef]

Roychowdhury, H.

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

Santarsiero, M.

Simon, R.

Wolf, E.

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

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

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Equations (24)

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W ( r 1 , r 2 ) = L * ( r 1 , v ) L ( r 2 , v ) d 2 v ,
W ( r 1 , r 2 ) = n c n * ( r 1 ) c n ( r 2 ) .
c n ( r ) = L ( r , v ) Φ n * ( v ) d 2 v ,
W ̂ ( r 1 , r 2 ) = R M ̂ ( r 1 , ρ ) M ̂ ( r 2 , ρ ) d ρ ,
F ( r 1 ) W ̂ ( r 1 , r 2 ) F ( r 2 ) d r 1 d r 2 = F ( r 1 ) M ̂ ( r 1 , ρ ) M ̂ ( r 2 , ρ ) F ( r 2 ) d r 1 d r 2 d ρ 0 ,
W ̂ ( r 1 , r 2 ) = n λ n 2 ϕ n ( r 1 ) ϕ n ( r 2 ) ,
W ̂ n ( r 1 , r 2 ) = λ n 2 ϕ n ( r 1 ) ϕ n ( r 2 ) ,
ϕ n ( r 1 ) W ̂ ( r 1 , r 2 ) d 2 r 1 = λ n 2 ϕ n ( r 2 ) ,
M ̂ ( r , ρ ) = n λ n G ̃ n ( ρ ) ϕ n ( r ) ,
G ̃ n ( ρ ) = ϕ n ( R ) exp ( i k R ρ ) d R ,
W ̂ ( r 1 , r 2 , ρ ) = M ̂ ( r 1 , ρ ) M ̂ ( r 2 , ρ ) .
W ̂ ( r 1 , r 2 ) = W ̂ ( r 1 r 2 ) ,
W ̂ ( r 1 r 2 ) = G ̂ ( ρ ) exp [ i k ρ ( r 1 r 2 ) ] d ρ .
v ( ρ ) G ̂ ( ρ ) v ( ρ ) 0 , for any row vector v ( ρ ) .
D ̂ 2 ( ρ ) = ( ξ 2 ( ρ ) 0 0 ζ 2 ( ρ ) ) ,
G ̂ ( ρ ) = U ̂ ( ρ ) D ̂ 2 ( ρ ) U ̂ ( ρ ) .
M ̂ ( r , ρ ) = exp [ i k r ρ ] D ̂ ( ρ ) U ̂ ( ρ ) ,
D ̂ ( ρ ) = ( ξ ( ρ ) exp [ i α ( ρ ) ] 0 0 ζ ( ρ ) exp [ i β ( ρ ) ] ) , for any α , β .
M ̂ ( r 1 , ρ ) M ̂ ( r 2 , ρ ) = exp [ i k ( r 1 r 2 ) ρ ] U ̂ ( ρ ) D ̂ 2 ( ρ ) U ̂ ( ρ ) ,
g 12 g ( r 1 , r 2 ) Tr ( W ̂ 12 W ̂ 21 ) + 2 | Det W ̂ 12 | Tr W ̂ 11 Tr W ̂ 22
W ̂ ( r 1 , r 2 ) = f * ( r 1 ) V ̂ ( r 1 ) W ̂ 0 ( r 1 r 2 ) V ̂ ( r 2 ) f ( r 2 ) ,
W ̂ 0 ( r 1 r 2 ) = M ̂ 0 ( r 1 , ρ ) M ̂ 0 ( r 2 , ρ ) d ρ ,
M ̂ 0 ( r , ρ ) = exp [ i k r ρ ] D ̂ ( ρ ) U ̂ ( ρ ) .
M ̂ ( r 1 , ρ ) M ̂ ( r 2 , ρ ) = f * ( r 1 ) f ( r 2 ) exp [ i k ( r 1 r 2 ) ρ ] V ̂ ( r 1 ) U ̂ ( ρ ) D ̂ 2 ( ρ ) U ̂ ( ρ ) V ̂ ( r 2 ) .

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