Based on the rotation vector method, this paper combines the coupling rule and the image rotation property of the eigenmode in nonplanar ring resonator to derive expression for the lock region threshold caused by the backscattering light in a nonplanar ring laser resonator and investigate the influence of nonplanar cavity structural parameters on backscattering light and its impact on the lock region threshold. Under the condition that the lock region of left-hand and right-hand components changes synchronously, the objective of reducing and eliminating the lock region is achieved by adjusting the nonplanar cavity folding angle α of the different plane cavity. The results obtained in this paper demonstrate the convenience and accuracy of using the rotation vector method to analyze the threshold of backscattering light on the locked area of nonplanar laser gyro.

This paper guides students to combine the characteristics of Gaussian beams learned in the course of Laser Principles and Technology with the principle of Brewster's law. Taking the Total Reflection Prism (TRP) resonator as an example, the impact of incident angle error on the polarization loss of eigenmodes in the resonator during the total reflection process of Gaussian beams on the TRP surface is studied. The influence of incident angle error, beam waist position (distance from beam waist to prism) z₀ and focal parameter f on polarization loss are discussed. The results show that in a certain range, the polarization loss of s and p components increase with the increasing of angle error, and finally tends to be stable. At the same time, for the same angle error, the polarization loss of s and p components decreases with the increase of z₀ and f, and the identical increment of z₀ and f will cause smaller polarization loss of s and p components. The research results of this article can provide a theoretical basis for the reduction of eigenmodes polarization loss, resonator structure design and optimization in TRP resonators.