Description of propagation of a Gaussian beam with general astigmatism by the ray method and application of this method to calculation of the parameters of nonplanar ring cavities

A method is proposed for the description of ring cavities with a nonplanar axial contour. This method makes it possible to find the stability regions and the characteristics of a Gaussian mode with general astigmatism, which is formed in such cavities. Numerical calculations are reported of the field characteristics and stability regions of a four-mirror ring cavity with a nonplanar axial contour.