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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1610-1619 |
| Number of pages | 10 |
| Journal | Journal of the Optical Society of America A: Optics and Image Science, and Vision |
| Volume | 5 |
| Issue number | 10 |
| DOIs | |
| State | Published - Oct 1988 |
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Atomic and Molecular Physics, and Optics
- Computer Vision and Pattern Recognition