Generalized model for beam-path variation in ring resonator and its applications in backscattering coupling effect

Abstract

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.

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

“…Backscattering coupling effect in square ring resonators has been analyzed in detail. Radial displacements 1 2 , x x δ δ cause more beam-path variation than the same axial displacements 1 …”

“…(12) into Eq. (2), backscattering coupling coefficient r is obtained as a function of mirror's displacements , ( 1,2) As shown in Fig. 4 and Fig.…”

“…Axial displacements have been considered in our previous paper. As shown in Fig.1, the mirror's radial displacements of spherical mirrors along the axis of ( 1,2) m i m = v will be treated as the main sources of perturbation. Radial displacements of spherical mirrors along the axis of j v which can induce magnetic bias are out of consideration.…”

“…(11) and solving Eq. (11), beam-path lengths 1 2 3 4 , , , L L L L are considered as variables, and expressions of beam-path lengths are obtained as functions of radial displacements ( 1,2,3,4) i i …”