Abstract

A mathematical model of a four-sided folded planar ring resonator is established. The model can be modified into a triangular ring resonator, a square ring resonator, and a four-sided folded ring resonator, all of which are widely used for ring laser gyroscopes by changing certain design parameters such as incident angle Ai and side ratio H. By use of the extended matrix formulation, the optical axis perturbation, including optical axis decentration and optical axis tilt, in those planar ring resonators is analyzed in detail resulting in some novel findings. It has been determined that the longer the mirror radius, the larger the mode volume, the higher the sensitivity of optical axis decentration and the lower the sensitivity of optical axis tilt. The same mirror misalignment value, mostly the misalignment induced by optical axis decentration in the x and y components, has the conventional ratio of 1:${\left[\cos \left(Ai\right)\right]}^2$ for the symmetrical points of the resonator. Details of the effect of Ai and H on the optical axis tilt have also been determined. The difference in optical axis tilt between different kinds of ring resonator is disclosed. The sensitivity of optical axis tilt was found to undergo singular rapid change along with the right edge of the second stable area. This singular behavior is useful for those resonators that have a small incident angle, such as $Ai=15°$, because those resonators have a second stable region. These interesting findings are important for cavity design, cavity improvement, and alignment of planar ring resonators.

© 2007 Optical Society of America

Optical-axis perturbation in triaxial ring resonator

Jie Yuan, Xingwu Long, and Linmei Liang
Appl. Opt. 47(5) 628-631 (2008)

Generalized sensitivity factors for optical-axis perturbation in nonplanar ring resonators

Dandan Wen, Dong Li, and Jianlin Zhao
Opt. Express 19(20) 19752-19757 (2011)

Reanalysis of generalized sensitivity factors for optical-axis perturbation in nonplanar ring resonators

Jie Yuan, Meixiong Chen, Yingying Li, Zhongqi Tan, and Zhiguo Wang
Opt. Express 21(2) 2297-2306 (2013)

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

Dong Li, Chao Bi, Yajun Jiang, and Jianlin Zhao
Appl. Opt. 57(8) 1765-1771 (2018)

Optical-axis perturbation singularity in an out-of-plane ring resonator

Shinan-Chur Sheng
Opt. Lett. 19(10) 683-685 (1994)