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.

© 1989 Optical Society of America

Gaussian amplitude functions that are exact solutions to the scalar Helmholtz equation; Geometrical representation of the fundamental mode of a Gaussian beam in oblate spheroidal coordinates: comment

L. B. Felsen
J. Opt. Soc. Am. A 6(10) 1640-1641 (1989)

Gaussian amplitude functions that are exact solutions to the scalar Helmholtz equation; Geometrical representation of the fundamental mode of a Gaussian beam in oblate spheroidal coordinates: reply to comment

B. T. Landesman
J. Opt. Soc. Am. A 6(10) 1642-1642 (1989)

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

B. Tehan Landesman and H. H. Barrett
J. Opt. Soc. Am. A 5(10) 1610-1619 (1988)

Skew line ray model of nonparaxial Gaussian beam

Shuhe Zhang, Jinhua Zhou, and Lei Gong
Opt. Express 26(3) 3381-3393 (2018)

Expansion of an arbitrarily oriented, located, and shaped beam in spheroidal coordinates

Feng Xu, Kuanfang Ren, and Xiaoshu Cai
J. Opt. Soc. Am. A 24(1) 109-118 (2007)