Abstract

We extend Mandel’s scalar-wave concept of cross-spectral purity to electromagnetic fields. We show that in the electromagnetic case, assumptions similar to the scalar cross-spectral purity lead to a reduction formula, analogous with the one introduced by Mandel. We also derive a condition that shows that the absolute value of the normalized zeroth two-point Stokes parameter of two cross-spectrally pure electromagnetic fields is the same for every frequency component of the field. In analogy with the scalar theory we further introduce a measure of the cross-spectral purity of two electromagnetic fields, namely, the degree of electromagnetic cross-spectral purity.

© 2009 Optical Society of America

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References

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  1. L. Mandel, J. Opt. Soc. Am. 51, 1342 (1961).
    [Crossref]
  2. L. Mandel and E. Wolf, J. Opt. Soc. Am. 66, 529 (1976).
    [Crossref]
  3. A. T. Friberg and E. Wolf, Opt. Lett. 20, 623 (1995).
    [Crossref] [PubMed]
  4. D. F. V. James and E. Wolf, Opt. Commun. 138, 257 (1997).
    [Crossref]
  5. T. Setälä, J. Tervo, and A. T. Friberg, Opt. Lett. 31, 2208 (2006).
    [Crossref] [PubMed]
  6. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  7. O. Korotkova and E. Wolf, Opt. Lett. 30, 198 (2005).
    [Crossref] [PubMed]
  8. J. Ellis and A. Dogariu, Opt. Lett. 29, 536 (2004).
    [Crossref] [PubMed]
  9. J. Tervo, T. Setälä, and A. T. Friberg, J. Opt. Soc. Am. A 21, 2205 (2004).
    [Crossref]
  10. M. A. Alonso and E. Wolf, Opt. Commun. 281, 2393 (2008).
    [Crossref]
  11. B. Karczewski, Nuovo Cimento 30, 906 (1963).
    [Crossref]

2008 (1)

M. A. Alonso and E. Wolf, Opt. Commun. 281, 2393 (2008).
[Crossref]

2006 (1)

2005 (1)

2004 (2)

1997 (1)

D. F. V. James and E. Wolf, Opt. Commun. 138, 257 (1997).
[Crossref]

1995 (1)

1976 (1)

1963 (1)

B. Karczewski, Nuovo Cimento 30, 906 (1963).
[Crossref]

1961 (1)

Alonso, M. A.

M. A. Alonso and E. Wolf, Opt. Commun. 281, 2393 (2008).
[Crossref]

Dogariu, A.

Ellis, J.

Friberg, A. T.

James, D. F. V.

D. F. V. James and E. Wolf, Opt. Commun. 138, 257 (1997).
[Crossref]

Karczewski, B.

B. Karczewski, Nuovo Cimento 30, 906 (1963).
[Crossref]

Korotkova, O.

Mandel, L.

L. Mandel and E. Wolf, J. Opt. Soc. Am. 66, 529 (1976).
[Crossref]

L. Mandel, J. Opt. Soc. Am. 51, 1342 (1961).
[Crossref]

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

Setälä, T.

Tervo, J.

Wolf, E.

M. A. Alonso and E. Wolf, Opt. Commun. 281, 2393 (2008).
[Crossref]

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

D. F. V. James and E. Wolf, Opt. Commun. 138, 257 (1997).
[Crossref]

A. T. Friberg and E. Wolf, Opt. Lett. 20, 623 (1995).
[Crossref] [PubMed]

L. Mandel and E. Wolf, J. Opt. Soc. Am. 66, 529 (1976).
[Crossref]

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

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Equations (20)

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γ ( r 1 , r 2 , τ ) = γ ( r 1 , r 2 , τ 0 ) γ ( r 1 , r 1 , τ τ 0 ) .
μ ( r 1 , r 2 , ω ) = γ ( r 1 , r 2 , τ 0 ) e i ω τ 0
S 0 ( r , ω ) = tr W ( r , r , ω ) ,
S 0 ( Q 2 , ω ) = C 12 S 0 ( Q 1 , ω ) for all ω ,
S 0 ( 1 ) ( r , ω ) = | K 1 | 2 R 1 2 S 0 ( Q 1 , ω ) ,
S 0 ( 2 ) ( r , ω ) = | K 2 | 2 R 2 2 C 12 S 0 ( Q 1 , ω ) .
S 0 ( r , ω ) = S 0 ( Q 1 , ω ) [ | K 1 | 2 R 1 2 + | K 2 | 2 R 2 2 C 12 + 2 | K 1 | | K 2 | R 1 R 2 C 12 R { η 0 ( Q 1 , Q 2 , ω ) e i ω τ } ] ,
η 0 ( Q 1 , Q 2 , ω ) = S 0 ( Q 1 , Q 2 , ω ) [ S 0 ( Q 1 , ω ) S 0 ( Q 2 , ω ) ] 1 2 .
η 0 ( Q 1 , Q 2 , ω ) e i ω τ 0 = f 0 ( Q 1 , Q 2 , τ 0 ) ,
tr Γ ( Q 1 , Q 2 , τ ) = C 12 f 0 ( Q 1 , Q 2 , τ 0 ) tr Γ ( Q 1 , Q 1 , τ τ 0 ) ,
ν 0 ( Q 1 , Q 2 , τ ) = f 0 ( Q 1 , Q 2 , τ 0 ) ν 0 ( Q 1 , Q 1 , τ τ 0 ) ,
ν 0 ( Q 1 , Q 2 , τ ) = tr Γ ( Q 1 , Q 2 , τ ) I ( Q 1 ) I ( Q 2 )
f 0 ( Q 1 , Q 2 , τ 0 ) = ν 0 ( Q 1 , Q 2 , τ 0 ) ,
ν 0 ( Q 1 , Q 2 , τ ) = ν 0 ( Q 1 , Q 2 , τ 0 ) ν 0 ( Q 1 , Q 1 , τ τ 0 )
η 0 ( Q 1 , Q 2 , ω ) = ν 0 ( Q 1 , Q 2 , τ 0 ) e i ω τ 0
| ν 0 ( Q 1 , Q 2 , τ ) | | ν 0 ( Q 1 , Q 2 , τ 0 ) |
ϕ 0 ( r , ω ) = S 0 ( r , ω ) 0 S 0 ( r , ω ) d ω .
B ( r 1 , r 2 , ω ) = ϕ 0 ( r 1 , ω ) [ ν 0 ( r 1 , r 2 , τ 0 ) e i ω τ 0 η 0 ( r 1 , r 2 , ω ) ]
μ CSP = 1 | ν 0 ( r 1 , r 2 , τ 0 ) | 2 × 0 | ψ ( r 1 , r 2 , ω ) ϕ 0 ( r 1 , ω ) | 2 d ω 0 [ | ψ ( r 1 , r 2 , ω ) | 2 + ϕ 0 2 ( r 1 , ω ) ] d ω ,
ψ ( r 1 , r 2 , ω ) = ϕ 0 ( r 1 , ω ) η 0 ( r 1 , r 2 , ω ) ν 0 ( r 1 , r 2 , τ 0 ) e i ω τ 0

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