Abstract

We consider stationary electromagnetic fields modeled as superpositions of unpolarized and angularly uncorrelated plane waves and show that in an isotropic case the electric cross-spectral tensor is proportional to the imaginary part of the Green tensor. This is as for blackbody radiation, but here the field need not be in thermal equilibrium. We also evaluate the degree of polarization for a homogeneous but nonisotropic field for which the plane waves propagate within a cone of angles. The results are compared with the known polarization properties of blackbody radiation.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. H. M. Nussenzveig, J. T. Foley, K. Kim, and E. Wolf, Phys. Rev. Lett. 58, 218 (1987).
    [CrossRef] [PubMed]
  2. S. A. Ponomarenko and E. Wolf, Phys. Rev. E 65, 016602 (2001).
    [CrossRef]
  3. F. Gori, D. Ambrosini, and V. Bagini, Opt. Commun. 107, 331 (1994).
    [CrossRef]
  4. W. H. Carter and E. Wolf, J. Opt. Soc. Am. 65, 1067 (1975).
  5. C. L. Mehta and E. Wolf, Phys. Rev. 161, 1328 (1967).
    [CrossRef]
  6. D. F. V. James, Opt. Commun. 109, 209 (1994).
    [CrossRef]
  7. T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. Lett. 88, 123902 (2002).
    [CrossRef]
  8. G. S. Agarwal, Phys. Rev. A 11, 230 (1975).
    [CrossRef]
  9. T. Setälä, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
    [CrossRef]
  10. R. Barakat, Opt. Acta 30, 1171 (1983).
    [CrossRef]
  11. J. C. Samson and J. V. Olson, Geophys. J. R. Astron. Soc. 61, 115 (1980).
    [CrossRef]

Other (11)

H. M. Nussenzveig, J. T. Foley, K. Kim, and E. Wolf, Phys. Rev. Lett. 58, 218 (1987).
[CrossRef] [PubMed]

S. A. Ponomarenko and E. Wolf, Phys. Rev. E 65, 016602 (2001).
[CrossRef]

F. Gori, D. Ambrosini, and V. Bagini, Opt. Commun. 107, 331 (1994).
[CrossRef]

W. H. Carter and E. Wolf, J. Opt. Soc. Am. 65, 1067 (1975).

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

D. F. V. James, Opt. Commun. 109, 209 (1994).
[CrossRef]

T. Setälä, M. Kaivola, and A. T. Friberg, Phys. Rev. Lett. 88, 123902 (2002).
[CrossRef]

G. S. Agarwal, Phys. Rev. A 11, 230 (1975).
[CrossRef]

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

R. Barakat, Opt. Acta 30, 1171 (1983).
[CrossRef]

J. C. Samson and J. V. Olson, Geophys. J. R. Astron. Soc. 61, 115 (1980).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Illustration of the notation. The plane wave’s propagation direction, represented by the azimuth (φ) and the polar (θ) angles in a spherical polar coordinate system and denoted by unit vector uˆ, is restricted to a cone that has cone angle α. Unit vectors sˆ and pˆ correspond to s and p polarization, respectively.

Fig. 2
Fig. 2

Behavior of 3D degree of polarization P3α and normalized coherence-matrix elements ϕxxα and ϕzzα as functions of cone angle α. The coherence-matrix elements have been normalized by the same factor.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

μVr1,r2,ω=CD ImGDr1,r2,ω,
μVr1,r2,ω=sinkr1-r2kr1-r2,
Eur,ω=Auˆ,ωexpikuˆ·r,
Auˆ,ω=Asuˆ,ωsˆ+Apuˆ,ωpˆ,
Er,ω=ΩAuˆ,ωexpikuˆ·rdΩ,
Wr1,r2,ω=E*r1,ωEr2,ω=Ω1Ω2A*uˆ1,ωAuˆ2,ω×exp-ikuˆ1·r1-uˆ2·r2dΩ1dΩ2,
A*uˆ1,ωAuˆ2,ω=As1*uˆ1,ωAs2uˆ2,ωsˆ1sˆ2+As1*uˆ1,ωAp2uˆ2,ωsˆ1pˆ2+Ap1*uˆ1,ωAs2uˆ2,ωpˆ1sˆ2+Ap1*uˆ1,ωAp2uˆ2,ωpˆ1pˆ2.
As1*uˆ1,ωAs2uˆ2,ω=Ap1*uˆ1,ωAp2uˆ2,ω=a0ωδuˆ1-uˆ2,
As1*uˆ1,ωAp2uˆ2,ω=Ap1*uˆ1,ωAS2uˆ2,ω=0.
Wr1,r2,ω=a0ωΩU-uˆuˆexp-ikuˆ·rdΩ,
Wr,ω=a0ωU+1k2Ωexp-ikuˆ·rdΩ,
4πexp-ikuˆ·rdΩ=4πsinkrkr,
Wr,ω=4πa0ωk ImGr,ω=4πa0ωj0kr-j1krkrU+j2krrrr2,
μEr,ω=tr Wr,ωtr W0,ω=sinkrkr,
P32r,ω=32trΦ32r,ωtr2Φ3r,ω-13,
Φxxα,ω=Φyyα,ω=πa0ω1216-15 cosα-cos3α,
Φzzα,ω=πa0ω68-9 cosα+cos3α.
P3α=¼1+cos αcos α.

Metrics