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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 21, Iss. 12 — Dec. 1, 2004
  • pp: 2382–2385

Spectral degree of coherence of a random three-dimensional electromagnetic field

Olga Korotkova and Emil Wolf  »View Author Affiliations

JOSA A, Vol. 21, Issue 12, pp. 2382-2385 (2004)

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The complex spectral degree of coherence of a general random, statistically stationary electromagnetic field is introduced in a manner similar to the way it is defined for a beamlike field, namely, by means of Young’s interference experiment. Both its modulus and its phase are measurable. We illustrate the definition by applying it to blackbody radiation emerging from a cavity. The results are of particular interest for near-field optics.

© 2004 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(030.6600) Coherence and statistical optics : Statistical optics
(260.2110) Physical optics : Electromagnetic optics
(260.3160) Physical optics : Interference

Original Manuscript: April 8, 2004
Revised Manuscript: June 11, 2004
Manuscript Accepted: June 11, 2004
Published: December 1, 2004

Olga Korotkova and Emil Wolf, "Spectral degree of coherence of a random three-dimensional electromagnetic field," J. Opt. Soc. Am. A 21, 2382-2385 (2004)

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  1. F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica 5, 785–795 (1938). [CrossRef]
  2. F. Zernike, “Diffraction and optical image formation,” Proc. Phys. Soc. London 61, 158–164 (1948). [CrossRef]
  3. E. Wolf, “A macroscopic theory of interference and diffraction of light from finite sources II. Fields with a spectral range of arbitrary width,” Proc. R. Soc. London, Ser. A 230, 246–265 (1955). [CrossRef]
  4. B. Karczewski, “Coherence theory of the electromagnetic field,” Nuovo Cimento 30, 906–915 (1963). [CrossRef]
  5. W. H. Carter, E. Wolf, “Far-zone behavior of electromag-netic fields generated by fluctuating current distributions,” Phys. Rev. A 36, 1258–1269 (1987). [CrossRef] [PubMed]
  6. L. Mandel, E. Wolf, “Spectral coherence and concept of cross-spectral purity,” J. Opt. Soc. Am. 66, 529–535 (1976). [CrossRef]
  7. E. Wolf, W. H. Carter, “Angular distribution of radiant intensity from sources of different degrees of spatial coherence,” Opt. Commun. 13, 205–209 (1975). [CrossRef]
  8. E. Wolf, W. H. Carter, “A radiometric generalization of the van Cittert–Zernike theorem for fields generated by sources of arbitrary state of coherence,” Opt. Commun. 16, 297–302 (1976). see also Ref. 9. [CrossRef]
  9. M. J. Bastiaans, “A frequency-domain treatment of partial coherence,” Opt. Acta 24, 261–274 (1977). [CrossRef]
  10. E. Wolf, “Unified theory of coherence and polarization of statistical electromagnetic beams,” Phys. Rev. Lett. 312, 263–267 (2003). [CrossRef]
  11. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995).
  12. B. Karczewski, E. Wolf, “Comparison of three theories of electromagnetic diffraction at an aperture. Part I: Coherence matrices,” J. Opt. Soc. Am. 56, 1207–1214 (1966). [CrossRef]
  13. R. K. Luneberg, Mathematical Theory of Optics (University of California Press, Berkeley and Los Angeles, Calif., 1964), pp. 319–320.
  14. M. Born, E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge U. Press, Cambridge, UK, 1999).
  15. Expression (3.14) was noted previously (Ref. 5, Eq. 6.16) as the degree of coherence in a particular case, namely, in the far field generated by three-dimensional fluctuating charge current distribution in free space.
  16. D. F. V. James, E. Wolf, “Determination of the degree of coherence of light from spectroscopic measurements,” Opt. Commun. 145, 1–4 (1998). [CrossRef]
  17. V. N. Kumar, D. N. Rao, “Two-beam interference experiments in the frequency-domain to measure the complex degree of spectral coherence,” J. Mod. Opt. 48, 1455–1465 (2001).
  18. An analogous definition of the degree of coherence of a beamlike field in the space–time domain was obtained many years ago by Karczewski in a little-known paper.4
  19. C. L. Mehta, E. Wolf, “Coherence properties of blackbody radiation. III. Cross-spectral tensors,” Phys. Rev. 161, 1328–1334 (1967). [CrossRef]

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