Analysis on the characteristic of the optical axis perturbation in a total reflection prismring resonator

The deduction of the augmented 5×5 matrix describing all the possible angular and decentration misalignment perturbation sources on a spherical prism plane during the refraction is presented in detail for the first time. Combining the augmented matrices and the condition of eigenmode self-consistency, the optical axis perturbation properties (described with the optical axis perturbation sensitivity factor SD1, ST1, SD2, and ST2) in a total reflection prism ring resonator are also analyzed. The singular points of the optical axis perturbation sensitivity factor are found at L/R=0.417 for the cases where the misalignments may originate from distinguished type of prisms P₁ and P₄ in the resonator, respectively. It is shown that the small errors of the prism can cause large optical axis disturbance in the position of the perturbed singular point and its nearby area, and the disturbance for the case where the misalignments originate from prism P₁ is more violent than that of prism P₄. With some upgrades to find and avoid the singularity of the optical axis in the total reflection prism ring resonator structure successfully, we expect this work will have great potential for designing and optimizing the structure of super-high-precision ring laser gyroscopes.