Calculating the parameters of a synchronisation zone of the frequencies of counterpropagating waves of a laser gyro

Based on the analysis of a well-known system of equations describing the dynamics of a two-isotope laser gyro with an equal-Q resonator under conditions of its fine-tuning to the centre of the emission line and balanced currents in the discharge arms, we have derived the formulas for calculating the parameters of the synchronisation zone for the frequencies of counterpropagating electromagnetic waves generated in the device. The formulas make it possible to calculate the coordinates on the axis of the angular velocity of the left and right boundaries of the synchronisation zone, the coordinate of its centre and half-width. It follows from the analysis that, in the general case of the asymmetric linear coupling between the counterpropagating waves via backscattering, absorption, and transmission of radiation from the mirrors of the gyro, the left and right boundaries of the synchronisation zone are located at different distances with respect to the origin of coordinates, so that the centre of the region is displaced along the axis of the angular velocity. The analysis of the formulas also implies that the shift of the centre of the synchronisation zone and its half-width decrease with increasing medium gain.