### 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) |
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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 - 1988 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Computer Vision and Pattern Recognition
- Electronic, Optical and Magnetic Materials