Vector Formulation Of The Ray-Equivalent Method For General Gaussian Beam Propagation

The propagation of a generally astigmatic Gaussian beam through an arbitrary optical system can be expressed solely in terms of coordinate independent transverse ray vectors. With this formulation, it is relatively easy to take standard ray trace data and deduce the equivalent Gaussian beam shape. In addition, by a simple rearrangement of the equations, the beam shape can also be expressed as the convolution of two geometrically propagated Gaussians.