Ray matrix approach for the analysis of optical-axis perturbation in nonplanar ring resonators based on appropriate coordinate system

Abstract

Non-planar ring resonators are widely used for high precision ring laser gyroscopes including Zero-Lock Laser Gyroscopes. The analysis of optical-axis perturbation in nonplanar ring resonators is important for resonator design. Ray matrix approach based on appropriate coordinate systems has been 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. In planar resonators, it also demonstrates that in the region of 0<K<2, larger the mirror radius is, higher sensitivity of optical-axis decentration will be, but lower sensitivity of optical-axis tilt will be. These results are confirmed by related experiments. 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 resonator design, improvement and beam position control nonplanar ring resonators.