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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 62, Iss. 10 — Oct. 1, 1972
  • pp: 1195–1201

Electromagnetic Field of a Gaussian Beam with an Elliptical Cross Section

WILLIAM H. CARTER  »View Author Affiliations


JOSA, Vol. 62, Issue 10, pp. 1195-1201 (1972)
http://dx.doi.org/10.1364/JOSA.62.001195


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Abstract

The electromagnetic field associated with a generalized beam is analyzed theoretically, where the beam may take on an irradiance cross section described by a gaussian function with arbitrary elliptical symmetry. For this analysis, the field is represented by an expansion into an angular spectrum of plane waves. Expressions for the field components throughout a medium that is free of sources are found by use of an asymptotic approximation that is common in gaussian-beam analysis. In addition, more-precise expressions for these components are found, which are valid outside the neighborhood of focus. Near focus, gaussian beams may have only approximately gaussian cross sections, and in this region the behavior of beams without circular symmetry is greatly complicated. The effects of noncircular symmetry are discussed in some detail, and a method for correcting a beam to produce circular symmetry is described.

Citation
WILLIAM H. CARTER, "Electromagnetic Field of a Gaussian Beam with an Elliptical Cross Section," J. Opt. Soc. Am. 62, 1195-1201 (1972)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-62-10-1195


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References

  1. H. Kogelnik and T. Li, Proc. IEEE 54, 1312 (1966).
  2. D. R. Rhodes, IEEE Trans. AP14, 676 (1966).
  3. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), p. 268.
  4. G. Borgiotti, Alta Frequenza 32, 196 (1963).
  5. W. H. Carter, Opt. Commun. 2, 142 (1970).
  6. The next section shows that the field behaves in this limit like a magnetic-dipole field. The Ex and Ev components of such a field have amplitudes that each behave as a scalar-dipole field.
  7. For a related analysis, see the appendix in K. Miyamoto and E. Wolf, J. Opt. Soc. Am. 52, 615 (1962).
  8. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 754.
  9. G. Goubau and F. Schwering, IRE Trans. AP9, 248 (1961).
  10. G. A. Campbell and R. M. Foster, Fourier Integrals for Practical Applications (Van Nostrand, New York, 1948), p. 85.

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