Abstract

This paper provides a simple but precise geometrical interpretation for the mathematical description of the zero-order mode of a Gaussian beam, which is an exact solution to the scalar wave equation. The geometrical model is expressed in the oblate spheroidal coordinate system where the beam wavefront is a section of an oblate ellipse, and a contour of constant amplitude is a hyperboloid of one sheet. The model employs the concept of a skew-line generator of a hyperboloid of one sheet as a real raylike element. The geometrical properties of an individual skew line and families of skew lines are discussed in detail and are compared to real rays. The model enables a simple interpretation of the presence in the beam description of a pure phase term, which has an arctangent dependence. Specifically, it represents the sag of an oblate ellipse as measured along a skew line. Finally, we use the skew line to build a nonorthogonal coordinate system, which provides the unambiguous framework necessary for studying the straight-line propagation of Gaussian beams in various media.

© 1988 Optical Society of America