Propagation Of Generally Astigmatic Gaussian Beams Along Skew Ray Paths

The propagation of a Gaussian beam through an asymmetric optical system results in a generally or "twisted"" astigmatic beam whose elliptical spot rotates as it propagates in free space. A general mathematical form for this beam is derived by applying the angular spectrum approach to the paraxialized wave equation. This result is compared to those derived by other researchers and it is found that the beam can be equivalently represented by a set of paraxial rays traced about the central beam ray. The application of general Gaussian beam propagation to the analysis of non-Gaussian beam propagation in arbitrary optical systems is also discussed.