Gaussian beam in oblate spheroidal coordinates

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.