Abstract

The normalized intensity fluctuations of arbitrary electromagnetic wave fields obeying Gaussian statistics are expressed in terms of the three-dimensional degree of polarization. This general formulation implies an important physical result concerning the polarization of planar fields and the dimensionality of the formalism. The results are expected to be particularly useful in intensity interferometry.

© 2004 Optical Society of America

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References

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  1. E. Wolf, Proc. Phys. Soc. (London) 76, 424 (1960).
    [Crossref]
  2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, England, 1995).
    [Crossref]
  3. W. H. Carter and E. Wolf, J. Opt. Soc. Am. 63, 1619 (1973).
  4. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, England, 1999).
    [Crossref]
  5. T. Setälä, J. Tervo, and A. T. Friberg, Opt. Commun. 238, 229 (2004).
    [Crossref]
  6. T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
    [Crossref]
  7. An anonymous reviewer pointed out an alternative method to derive Eq. (19). It is based on diagonalizing the coherence tensor and making use of the following observations: (i) Ir,t and ΔIr,t2 are invariant under such a transformation, and (ii) the electric field components obey Gaussian statistics and are fully uncorrelated. One then readily obtains Ir,t=∑i=13λi=trΓ↔3r,r,0 and ΔIr,t2=∑i=13λi2=trΓ↔32r,r,0, where λi are the eigenvalues of the 3×3 coherence tensor, and so Eq. (19) directly follows from Eq. (8). Yet another way to derive Eq. (19) can be found in our paper titled “Intensity fluctuations and the degree of polarization in Gaussian random electromagnetic fields,” that will be published in Vol. 5622 of Proc. SPIE.
  8. T. Setälä, M. Kaivola, and A. T. Friberg, Opt. Lett. 28, 1069 (2003).
    [Crossref]
  9. C. L. Mehta and E. Wolf, Phys. Rev. 161, 1328 (1967).
    [Crossref]
  10. R. H. Brown and R. Q. Twiss, Nature 177, 27 (1956).
    [Crossref]

2004 (1)

T. Setälä, J. Tervo, and A. T. Friberg, Opt. Commun. 238, 229 (2004).
[Crossref]

2003 (1)

2002 (1)

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[Crossref]

1973 (1)

1967 (1)

C. L. Mehta and E. Wolf, Phys. Rev. 161, 1328 (1967).
[Crossref]

1960 (1)

E. Wolf, Proc. Phys. Soc. (London) 76, 424 (1960).
[Crossref]

1956 (1)

R. H. Brown and R. Q. Twiss, Nature 177, 27 (1956).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, England, 1999).
[Crossref]

Brown, R. H.

R. H. Brown and R. Q. Twiss, Nature 177, 27 (1956).
[Crossref]

Carter, W. H.

Friberg, A. T.

T. Setälä, J. Tervo, and A. T. Friberg, Opt. Commun. 238, 229 (2004).
[Crossref]

T. Setälä, M. Kaivola, and A. T. Friberg, Opt. Lett. 28, 1069 (2003).
[Crossref]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[Crossref]

Kaivola, M.

T. Setälä, M. Kaivola, and A. T. Friberg, Opt. Lett. 28, 1069 (2003).
[Crossref]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[Crossref]

Mandel, L.

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

Mehta, C. L.

C. L. Mehta and E. Wolf, Phys. Rev. 161, 1328 (1967).
[Crossref]

Setälä, T.

T. Setälä, J. Tervo, and A. T. Friberg, Opt. Commun. 238, 229 (2004).
[Crossref]

T. Setälä, M. Kaivola, and A. T. Friberg, Opt. Lett. 28, 1069 (2003).
[Crossref]

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[Crossref]

Shevchenko, A.

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[Crossref]

Tervo, J.

T. Setälä, J. Tervo, and A. T. Friberg, Opt. Commun. 238, 229 (2004).
[Crossref]

Twiss, R. Q.

R. H. Brown and R. Q. Twiss, Nature 177, 27 (1956).
[Crossref]

Wolf, E.

W. H. Carter and E. Wolf, J. Opt. Soc. Am. 63, 1619 (1973).

C. L. Mehta and E. Wolf, Phys. Rev. 161, 1328 (1967).
[Crossref]

E. Wolf, Proc. Phys. Soc. (London) 76, 424 (1960).
[Crossref]

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, England, 1999).
[Crossref]

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

J. Opt. Soc. Am. (1)

Nature (1)

R. H. Brown and R. Q. Twiss, Nature 177, 27 (1956).
[Crossref]

Opt. Commun. (1)

T. Setälä, J. Tervo, and A. T. Friberg, Opt. Commun. 238, 229 (2004).
[Crossref]

Opt. Lett. (1)

Phys. Rev. (1)

C. L. Mehta and E. Wolf, Phys. Rev. 161, 1328 (1967).
[Crossref]

Phys. Rev. E (1)

T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
[Crossref]

Proc. Phys. Soc. (London) (1)

E. Wolf, Proc. Phys. Soc. (London) 76, 424 (1960).
[Crossref]

Other (3)

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

An anonymous reviewer pointed out an alternative method to derive Eq. (19). It is based on diagonalizing the coherence tensor and making use of the following observations: (i) Ir,t and ΔIr,t2 are invariant under such a transformation, and (ii) the electric field components obey Gaussian statistics and are fully uncorrelated. One then readily obtains Ir,t=∑i=13λi=trΓ↔3r,r,0 and ΔIr,t2=∑i=13λi2=trΓ↔32r,r,0, where λi are the eigenvalues of the 3×3 coherence tensor, and so Eq. (19) directly follows from Eq. (8). Yet another way to derive Eq. (19) can be found in our paper titled “Intensity fluctuations and the degree of polarization in Gaussian random electromagnetic fields,” that will be published in Vol. 5622 of Proc. SPIE.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, England, 1999).
[Crossref]

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Equations (21)

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ΔIr,t2Ir,t2=121+P22r.
ΔIr,t=Ir,t-Ir,t
P22r=2trΓ22r,r,0tr2Γ2r,r,0-12.
Γ2,ijr1,r2,τ=Ei*r1,tEjr2,t+τ,  i,j=x,y,
Γ3,ijr1,r2,τ=Ei*r1,tEjr2,t+τ,  i,j=x,y,z.
γijr1,r2,τΓ3,ijr1,r2,τIir1,t1/2Ijr2,t1/2,
0γijr1,r2,τ1,
P32r=32trΓ32r,r,0tr2Γ3r,r,0-13.
P32r=γxyr,r,02+γxzr,r,02+γyzr,r,023.
Ir,t=Ixr,t+Iyr,t+Izr,t,
ΔIr,t=ΔIxr,t+ΔIyr,t+ΔIzr,t,
ΔIir,t=Iir,t-Iir,t,  i=x,y,z.
ΔIr1,tΔIr2,t+τ=ijΔIir1,tΔIjr2,t+τ,
ΔIir1,tΔIjr2,t+τ=Iir1,tIjr2,t×γijr1,r2,τ2,
ΔIr,t2=ijIir,tIjr,tγijr,r,02.
ΔIr,t2=Ixr,t2+Iyr,t2+Izr,t2+2Ixr,tIyr,tγxyr,r,02+2Ixr,tIzr,t×γxzr,r,02+2Iyr,tIzr,tγyzr,r,02.
Ixr,t=Iyr,t=Izr,t=13Ir,t.
ΔIr,t2=131+2γxyr,r,02+γxzr,r,02+γyzr,r,023×Ir,t2.
ΔIr,t2=131+2P32rIr,t2.
ΔIr,t2Ir,t2=121+P22r,in 2D131+2P32r,in 3D.
P32r=14+34P22r.

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