General beam propagation through non-orthogonal optical systems

The methods of propagation of simple paraxial Gaussian beams through rotationally symmetric optical systems have long been established. A theoretical method for the propagation of Gaussian beams through non-orthogonal optical systems has been published and generalized for non-Gaussian beams, but the combined capability has not been widely implemented. To design and build optical systems using lasers and cylindrical optics, it is important to have these computational tools available. In this paper, the theory will be reviewed and the mathematical details of its practice will be given. Some aspects of beams with general astigmatism will be presented. For example, the theory explains in detail how a circular Gaussian beam will be converted into a rotating elliptical beam after passing through crossed cylinder tenses. An example of such a system will be discussed and measurements compared to the predicted results.