Complex ray representation of the astigmatic Gaussian beam propagation

The method of Gaussian beam ray-equivalent modelling, first proposed by Arnaud, is generalized to the case of general astigmatism. It has been shown that a generally astigmatic Gaussian beam can be properly represented by two complex rays, or equally by four real rays, which are treated by the well-known propagation equation and ray tracing method in geometric optics, and from which the beam parameters are easily obtained. Illustrative numerical examples are given. The equivalence between the complex-ray treatment and the generalized ABCD law is also shown.