Optical axis perturbation in folded planar ring resonators

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:[cos(Ai)](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 degrees , because those resonators have a second stable region. These interesting findings are important for cavity design, cavity improvement, and alignment of planar ring resonators.