Theory of frequency synchronization in a ring laser

The self-consistent problem of the frequency synchronization of counter-propagating waves in a ring laser is rigorously solved. An intrinsic nonlinear mechanism of the phase coupling between the waves is considered for the first time. This ineradicable coupling is provided by modulation of the population difference of the energy levels of the active medium atoms in the electromagnetic field of two counter-propagating waves. The theoretical limit for the range of phase locking between the counter-propagating waves is established. The general equation of phase synchronization is obtained from the solution of a self-consistent problem. The frequency-dependent boundaries of the synchronization band calculated in the framework of this approach show good agreement with experimental results published in the literature.