To the best of our knowledge, the generalized ray matrix, an augmented 5×5 ray matrix for a spherical mirror reflection with all the possible perturbation sources including three kinds of displacements and its detailed deducing process have been proposed in this paper for the first time. Square ring resonators and monolithic triaxial ring resonators have been chosen as examples to show its application, and some novel results of the optical-axis perturbation have been obtained. A novel method to eliminate the diaphragm mismatching error and the gain capillary mismatching error in monolithic triaxial ring resonators more effectively has also been proposed. Both those results and method have been confirmed by related experiments and the experimental results have been described with diagrammatic representation. This generalized ray matrix is valuable for ray analysis of various kinds of resonators. These results are important for the cavity design, cavity improvement and alignment of high accuracy and super high accuracy ring laser gyroscopes.
By utilizing the novel coordinate system for Gaussian beam reflection and the generalized ray matrix for spherical mirror reflection, the generalized sensitivity factors SD1, ST1, SD2 and ST2 influenced by both the radial and axial displacements of a spherical mirror in a nonplanar ring resonator have been obtained. Besides, the singular points of different kinds of non-planar ring resonators under the conditions of incident angle A ranging from 0° to 45° or total coordinate rotation angle ρ ranging from 0° to 360° have also been obtained through the analysis of the determinant of the coefficient matrix of the linear equations. The analysis in this paper is important to the cavity design of non-planar ring resonators and it could be helpful to avoid the violent movement of the optical-axis to small misalignment of the mirrors in non-planar ring resonators.
A generalized model for beam-path variation analyzed with vector method in square ring resonators is established. The model can be applied to analyze beam-path variation in various ring resonators induced by all the possible perturbation sources. The generalized model is useful for the cavity design, cavity improvement, alignment of planar ring resonators and research on backscattering coupling effect. Backscattering coupling effect in square ring resonator has been chosen as examples to show its application. Backscattering coupling coefficient r is obtained as a function of mirror's axial displacements. Some novel results of backscattering coupling effect have been acquired. The results indicate that r can not be reduced to zero because of the initial machining errors of surfaces of plane mirrors. However, r can be reduced to zero almost when stabilizing frequency of laser gyro by take the suitable values of axial displacements of plane mirrors. These results are important for high precision laser gyro.
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