The impact of resonator geometry on RLG performances

In a Ring laser Gyroscope (RLG) the beat note between the two countepropagating modes of the ring resonator is proportional to the rotation rate. Among inertial rotation sensors, RLGs provide the best performances in sensitivity and accuracy available today. Sensitivity and accuracy of high resolution RLGs are still limited by systematic errors, arising from deformations of resonator geometry, modifications of resonator orientation, and non-linear laser dynamics. The geometry and orientation in space associated to the light beam paths are determined by the position and orientation of the optical elements forming the resonator. To enhance RLG accuracy to the level required by the recently proposed General Relativity tests, the stability of the beams geometry and orientation have to be further improved. To this aim, in high sensitivity RLGs, the optical elements relevant for the beams steering are driven by high precision mechanic handlers, and their relative position is measured by dedicated metrology systems. In this paper we review our progresses on the modelization of square ring resonators geometry. We investigate the ring laser open loop response to mirror displacement by a linear perturbation analysis of our model complemented by numerical simulations. Our findings are relevant for the design and alignment of square ring resonators, and pave the way to the development of multivariable automatic control schemes of square ring cavities.