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  • Vol. 29, Iss. 13 — Jul. 1, 2004
  • pp: 1536–1538

Correlation matrix of a completely polarized, statistically stationary electromagnetic field

Jeremy Ellis, Aristide Dogariu, Sergey Ponomarenko, and Emil Wolf  »View Author Affiliations


Optics Letters, Vol. 29, Issue 13, pp. 1536-1538 (2004)
http://dx.doi.org/10.1364/OL.29.001536


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Abstract

It is shown that, for a 3×3 correlation matrix Wij(r, r, ⍵), (i, j=x, y, z) of the electric vector of a random, stationary electromagnetic field to represent a field that is completely polarized at a point r and frequency ⍵, each element of the matrix must factorize. More precisely, a necessary and sufficient condition for the correlation matrix to represent a fully polarized field at a point r is that the matrix has the form Wij(r, r, ⍵)=ε*i(r, ⍵)ε j(r, ⍵), where εi(r, ⍵) (i=x, y, z) are deterministic functions, i.e., that all pairs of the Cartesian components of the electric field at a point r and frequency ⍵ are completely correlated.

© 2004 Optical Society of America

OCIS Codes
(030.6600) Coherence and statistical optics : Statistical optics
(260.5430) Physical optics : Polarization

Citation
Jeremy Ellis, Aristide Dogariu, Sergey Ponomarenko, and Emil Wolf, "Correlation matrix of a completely polarized, statistically stationary electromagnetic field," Opt. Lett. 29, 1536-1538 (2004)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-29-13-1536


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References

  1. T. Setala, A. Shevchenko, M. Kaivola, and A. T. Friberg, Phys. Rev. E 66, 016615 (2002).
  2. C. Brosseau, Fundamentals of Polarized Light (Wiley, New York, 1998).
  3. T. Carozzi, R. Karlsson, and J. Bergman, Phys. Rev. E 61, 2024 (2000).
  4. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
  5. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1999).
  6. A referee of this paper pointed out that, in Ref. c1, a definition of the degree of polarization of three-dimensional fields was put forward that gives the value unity in this limiting case. This is, however, fortuitous, because the definition proposed in Ref. is purely formal and does not have the meaning of the ratio of the intensity of a fully polarized field to the total intensity at a point.

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