Geometrical representation of the fundamental mode of a Gaussian beam in oblate spheroidal coordinates
- 1 January 1989
- journal article
- Published by Optica Publishing Group in Journal of the Optical Society of America A
- Vol. 6 (1) , 5-17
- https://doi.org/10.1364/josaa.6.000005
Abstract
A new geometrical model for the fundamental mode of a Gaussian beam is presented in the oblate spheroidal coordinate system. The model is an interpretation of a Gaussian amplitude wave function, which is an exact solution of the scalar Helmholtz equation. The model uses the skew-line generator of a hyperboloid of one sheet as a raylike element on a contour of constant amplitude. The geometrical characteristics of the skew line and the consequences of treating it as a ray are explored in depth. Finally, the skew line is used to build a nonorthogonal coordinate system that permits straight-line propagation of a Gaussian beam in three-dimensional space.Keywords
This publication has 11 references indexed in Scilit:
- Gaussian amplitude functions that are exact solutions to the scalar Helmholtz equationJournal of the Optical Society of America A, 1988
- Wave solutions under complex space–time shiftsJournal of the Optical Society of America A, 1987
- Representation of Gaussian beams by complex raysApplied Optics, 1985
- Gaussian beam ray-equivalent modeling and optical designApplied Optics, 1983
- Evanescent waves*Journal of the Optical Society of America, 1976
- VI Hamiltonian Theory of Beam Mode PropagationPublished by Elsevier ,1973
- Complex Rays with an Application to Gaussian BeamsJournal of the Optical Society of America, 1971
- Degenerate Optical CavitiesApplied Optics, 1969
- Laser beams and resonatorsProceedings of the IEEE, 1966
- Geometric Optical Derivation of Formula for the Variation of the Spot Size in a Spherical Mirror ResonatorApplied Optics, 1965