Phase and frequency jumps in a bidirectional ring laser

Phase and frequency jumps are found to be part of the dynamical alternation of the direction of oscillation in a model for detuned homogeneously-broadened bidirectional ring lasers operating on a single mode in each direction. The frequency of each mode when it is dominant is that of the steady state unidirectional solution for that mode, but during the switching process it is increased or decreased with respect to the cavity frequency while it is declining or growing in intensity respectively. We are able to show analytically and numerically that near the minimum intensity for a suppressed mode the frequency jumps, and the combined relative phase of the fields and the population inversion grating switches by ±π radians.