Reanalysis of optical-axis perturbation in nonplanar ring resonators in ray matrix approach with appropriate coordinate systems

Ray matrix approach with appropriate coordinate systems has been proposed in this paper. It is employed to analyze the optical-axis perturbation in nonplanar ring resonators. The sensitivities of optical-axis decentration (SD) and optical-axis tilt (ST) in nonplanar resonators with 90° and 270° image rotation are discussed in detail in the region of 0 < K < 8, where K is the ratio of the total cavity length to the radius of the curvature mirrors. There are both four singular points in the whole region of 0 < K < 8. On the left of the first singularity, it is found that the longer the mirror radius, the less the optical-axis decentration sensitivity. This is opposite the behavior of planar ring resonators, but the behaviors of optical-axis tilt sensitivity in planar and nonplanar ring resonators are similar. It is worth to note that SD and ST in the nonplanar resonator with certain parameters have the similar singularities. The analysis in this paper is important for the cavity design and alignment of nonplanar ring resonators.