Theory of a ring laser with triangular and trapezoidal modulation of the resonator frequency nonreciprocity

A rigorous analytic solution is obtained of an equation describing evolution of the difference between the phases opposite waves in a ring laser characterized by a resonator frequency nonreciprocity varying linearly with time. This solution is used in combination with the Floquet method to investigate the frequency characteristic of a ring laser with a periodic resonator frequency nonreciprocity of triangular and trapezoidal forms. It is shown that in the case of sufficiently slow modulation of resonator frequency nonreciprocity this characteristic represents a system of parametric locking bands located near a quasistatic frequency characteristic. It is shown that in the case of trapezoidal modulation of the resonator frequency nonreciprocity and a specific (optimal) ratio of the durations of constant and linearly varying components of the nonreciprocity the quasistatic frequency characteristic coincides with the ideal characteristic at low angular velocities.