Analytical description of a Gaussian beam in a ring resonator with a nonplanar axial contour and an odd number of mirrors

Stability conditions for a ring resonator with an odd number of mirrors and a nonplanar axial contour are studied analytically. New explicit expressions are derived to describe the transverse field distribution of the Gaussian mode with general astigmatism produced in this resonator. Field characteristics for a resonator with the specified parameters are calculated.