Theoretical Analysis Of Optical-axis Perturbation In Planar Ring Resonators

A mathematical model of a four-sided folded planar ring resonator has been established. The model can be modified into some idiographic resonators such as a square ring resonator and a triangular ring resonator by changing certain design parameters such as incident angle Ai and side ratio H. By utilizing the extended optical matrix formulation, the optical axis perturbation, including optical axis decentration and optical axis tilt, in the idiographic square ring resonator and triangular ring resonator is analyzed in detail. It has been found 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. For 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. Detail of the effect of Ai on the optical axis tilt of a triangular ring resonator has also been presented. The difference between the square ring resonator and the triangular ring resonator is disclosed. The second stable region for triangular ring resonator has been found, and 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, because those resonators have a second stable region. These findings are important for cavity design, cavity improvement, and alignment of the square ring resonator and triangular ring resonator.