Statistical analysis on the optical axis perturbation in nonplanar ring resonators

Based on the ray matrix theory, we theoretically analyzed the property of the optical axis perturbation versus L/r (L means the total length of the resonator and r is the radius of curvature of the mirrors in the resonator) in the nonplanar ring resonators by using statistical method for the first time as we know in this paper. The results show that the root mean square of the optical axis tilt change evidently versus L/r while the optical axis decentration have a subtle change versus L/r for the case that the mirror misalignments are confined in a certain scope and chosen arbitrarily. From the perspective of optical axis perturbation, we can find the configuration parameters with which the optical axis perturbation in the resonator responds violently to the mirror radial displacement or misalignment angle. These interesting findings are important for cavity design, improvement, and alignment of nonplanar ring resonators.