Nonreversible component of the frequency characteristic of a ring laser

Consistent application of the averaging method in the solution of equations describing generation of opposite waves in a ring laser in the presence of backscattering shows that the frequency characteristic of such a laser has a component which is not reversed when the sign of the frequency nonreciprocity of the resonator is altered. If the coupling between the waves is weak, this nonreversible component is governed by a combination of fourth-order coupling coefficients and it disappears when the coupling is symmetric. The nonreversible component depends strongly on the parameter of a nonlinear interaction of the waves in the active medium and it can vanish for a certain value of this parameter. Phenomena associated with synchronous reversal of the amplitude and frequency nonreciprocities of the resonator are also considered.