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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 69, Iss. 9 — Sep. 1, 1979
  • pp: 1313–1314

Depolarization term of the wave equation

D. A. de Wolf  »View Author Affiliations


JOSA, Vol. 69, Issue 9, pp. 1313-1314 (1979)
http://dx.doi.org/10.1364/JOSA.69.001313


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Abstract

The vector wave equation can be rewritten as a quasiscalar wave equation with one extra term -▽▽ • <b>E</b> (the depolarization term). Many authors utilize Poisson’s equation to replace it by ▽(<b>E</b> • ▽ln∊. However, fields <b>E</b> obtained as solutions of the ensuing equation must be made to obey Poisson’s equation (as they do not do so automatically, in general) or be rejected. Some examples are given, and it is shown why first-order solutions for ∊= 1 + δ∊ with δ∊ ≪1 are often correctly derived (unwittingly?) from an “incorrect” equation.

© 1979 Optical Society of America

Citation
D. A. de Wolf, "Depolarization term of the wave equation," J. Opt. Soc. Am. 69, 1313-1314 (1979)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-69-9-1313


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References

  1. J. C. Maxwell, A Treatise on Electricity and Magnetism, 1st ed., (Oxford University, London, 1873).
  2. M. Born and E. Wolf, Principles of Optics, 3rd ed., (Pergamon, Oxford, 1965), see §1.2.
  3. V. J. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (U.S. Dept. of Commerce, Springfield, Va., 1971), see §25.
  4. A. Ishimaru, Wave Propagation and Scattering in Random Media, Vol. 2 (Academic, New York, 1978), see §17-1.
  5. J. W. Strohbehn, "Optical propagation through the turbulent atmosphere," in Progress in Optics, Vol. IX, edited by E. Wolf (North-Holland, Amsterdam, 1971), see §3.2.
  6. The problem with Eq. (3) was pointed out by Prof. H. J. Butterweck, somewhat to the author's embarrassment on the day before his doctoral examination, as the disputed equation also occurred in the thesis.
  7. S. F. Clifford and J. W. Strohbehn, "The theory of microwave lineof-sight propagation through a turbulent atmosphere," IEEE Trans. Antennas Propagation, AP-18, 264–274 (1970).
  8. The length l is assumed to be orders of magnitude greater than the wavelength.

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