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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 5, Iss. 10 — Oct. 1, 1988
  • pp: 1610–1619

Gaussian amplitude functions that are exact solutions to the scalar Helmholtz equation

B. Tehan Landesman and H. H. Barrett  »View Author Affiliations


JOSA A, Vol. 5, Issue 10, pp. 1610-1619 (1988)
http://dx.doi.org/10.1364/JOSAA.5.001610


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Abstract

A new family of exact solutions of the scalar Helmholtz equation is presented. The 0, 0 order of this family represents a new mathematical model for the fundamental mode of a propagating Gaussian beam. The family consists of nonseparable functions in the oblate spheroidal coordinate system and can easily by transformed into a different set of solutions in the prolate spheroidal coordinate system, where the 0, 0 order is a spherical wave. This transformation consists of two substitutions in the coordinate system parameters and represents a more general method of obtaining a Gaussian beam from a spherical wave than assuming a complex point source on axis. Finally, each higher-order member of the family of solutions possesses an amplitude consisting of a finite number of higher-order terms with a zero-order term that is Gaussian.

© 1988 Optical Society of America

History
Original Manuscript: December 28, 1987
Manuscript Accepted: May 20, 1988
Published: October 1, 1988

Citation
B. Tehan Landesman and H. H. Barrett, "Gaussian amplitude functions that are exact solutions to the scalar Helmholtz equation," J. Opt. Soc. Am. A 5, 1610-1619 (1988)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-5-10-1610

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