Generalized model for beam-path variation induced by spherical mirrors' radial displacements in square ring resonator and its applications in backscattering coupling effect

Abstract

Based on augmented ray matrix approach, a generalized model for beam-path variation induced by spherical mirrors' radial displacements has been established. The model can be applied to analyze beam-path variation induced by all the possible perturbation sources in various ring resonators. Backscattering coupling coefficient r is obtained as a function of mirrors' radial displacements. Some novel results of backscattering coupling effect have been obtained. The results indicate that radial displacements cause bigger beam-path variation than the same value of axial displacements. r can not be reduced to zero because of the initial machining errors of terminal surfaces of plane mirrors. However, <i>r</i> can be reduced to almost zero when stabilizing frequency of laser gyro by adjusting the radial displacements of spherical mirrors. This generalized model is useful for the cavity design, cavity improvement, and alignment of planar ring resonators. The model is also useful for controlling the shape of laser beams and researching backscattering coupling effect in high precision laser gyroscopes.