Abstract

We show that the following properties of a random electromagnetic field are equivalent: (i) the field is spatially completely coherent in the sense of the recently introduced electromagnetic degree of coherence and (ii) the electric cross-spectral density tensor factors in the two spatial variables.

© 2004 Optical Society of America

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References

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  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, England, 1995).
    [CrossRef]
  2. L. Mandel and E. Wolf, Opt. Commun. 36, 247 (1981).
    [CrossRef]
  3. J. Tervo, T. Setälä, and A. T. Friberg, Opt. Express 11, 1137 (2003), http://www.opticsexpress.org .
    [CrossRef] [PubMed]

2003 (1)

1981 (1)

L. Mandel and E. Wolf, Opt. Commun. 36, 247 (1981).
[CrossRef]

Friberg, A. T.

Mandel, L.

L. Mandel and E. Wolf, Opt. Commun. 36, 247 (1981).
[CrossRef]

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

Setälä, T.

Tervo, J.

Wolf, E.

L. Mandel and E. Wolf, Opt. Commun. 36, 247 (1981).
[CrossRef]

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

Opt. Commun. (1)

L. Mandel and E. Wolf, Opt. Commun. 36, 247 (1981).
[CrossRef]

Opt. Express (1)

Other (1)

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

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Equations (33)

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Wr1,r2,ω=V*r1,ωVr2,ω.
Wr1,r2,ω=12π-Γr1,r2,τexpiωτdτ,
Γjkr1,r2,τ=Ej*r1,tEkr2,t+τ,
Wjkr1,r2,ω=Wkj*r2,r1,ω.
p,q=1Nj,kajp*akqWjkrp,rq,ω0,
μjkr1,r2,ωWjkr1,r2,ωWjjr1,r1,ωWkkr2,r2,ω1/2,
μjkr1,r2,ω=μkj*r2,r1,ω.
0μjkr1,r2,ω1
ajp=δj,mδp,1+δj,nδp,2bjp,
bm1*bn2*Wmmr1,r1,ωWmnr1,r2,ωWnmr2,r1,ωWnnr2,r2,ω×bm1bn20.
Wmnr1,r2,ωWmmr1,r1,ωWnnr2,r2,ω1/21.
μ2r1,r2,ω=trWr1,r2,ω·Wr2,r1,ωtrWr1,r1,ωtrWr2,r2,ω,
μ2r1,r2,ω=j,kμjkr1,r2,ω2Wjjr1,r1,ωWkkr2,r2,ωj,kWjjr1,r1,ωWkkr2,r2,ω.
p,q=13j,kbjp*bkqμjkrp,rq,ω0,
bjp=δj,mδp,1+δj,nδp,2+δj,tδp,3cjp,
cm1*cn2*ct3*μmm11μmn12μmt13μnm21μnn22μnt23μtm31μtn32μtt33cm1cn2ct30,
μmm11μmn12μmt13μnm21μnn22μnt23μtm31μtn32μtt330.
2 Reμmn12μtm31μtn32*μmn122+μtm312+μtn322-1,
Reμmn12μtm31μtn32*1.
μjkpqexpiφjkpq,
φjkpq=-φkjqp.
cosφmn12+φtm31-φtn321,
φmn12+φtm31-φtn32=2πM,
μmnr1,r2,ω=expi-φtm0,r1,ω+φtn0,r2,ω.
Wmnr1,r2,ω=Em*r1,ωEnr2,ω,
Ejr,ω=Wjjr,r,ω1/2expiφtj0,r,ω,
Wr1,r2,ω=E*r1,ωEr2,ω,
Er,ω=Exr,ωuˆx+Eyr,ωuˆy+Ezr,ωuˆz,
μ2r1,r2,ω=trWr1,r1,ωtrWr2,r2,ωtrWr1,r1,ωtrWr2,r2,ω=1.
p2Wjkr1,r2,ω+ωc02Wjkr1,r2,ω=0,
jj1Wjkr1,r2,ω=0,
2Er,ω+ωc02Er,ω=0,
·Er,ω=0.

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