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

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

http://dx.doi.org/10.1364/JOSAA.21.002382

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### Abstract

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

**History**

Original Manuscript: April 8, 2004

Revised Manuscript: June 11, 2004

Manuscript Accepted: June 11, 2004

Published: December 1, 2004

**Citation**

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)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-12-2382

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### References

- F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica 5, 785–795 (1938). [CrossRef]
- F. Zernike, “Diffraction and optical image formation,” Proc. Phys. Soc. London 61, 158–164 (1948). [CrossRef]
- 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]
- B. Karczewski, “Coherence theory of the electromagnetic field,” Nuovo Cimento 30, 906–915 (1963). [CrossRef]
- 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]
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- 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]
- M. J. Bastiaans, “A frequency-domain treatment of partial coherence,” Opt. Acta 24, 261–274 (1977). [CrossRef]
- E. Wolf, “Unified theory of coherence and polarization of statistical electromagnetic beams,” Phys. Rev. Lett. 312, 263–267 (2003). [CrossRef]
- L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995).
- 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]
- R. K. Luneberg, Mathematical Theory of Optics (University of California Press, Berkeley and Los Angeles, Calif., 1964), pp. 319–320.
- M. Born, E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge U. Press, Cambridge, UK, 1999).
- 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.
- D. F. V. James, E. Wolf, “Determination of the degree of coherence of light from spectroscopic measurements,” Opt. Commun. 145, 1–4 (1998). [CrossRef]
- 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).
- 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
- 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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