Synchronization with harmonics in an injected nuclear-magnetic-resonance laser

In injected lasers, only synchronization of the order 1/1 (when a frequency of laser oscillations becomes equal to the master laser frequency) is usually observed. Such locking appears due to single-photon transitions in a laser. We show that with the use of multiple-photon transitions a higher-order synchronization can arise. We present the results of numerical simulations and the preliminary experimental observations, which demonstrate that in the mercury NMR laser, with the use of triple-photon transitions, a frequency of locked laser oscillations becomes three times higher than the frequency of an external rf magnetic field. Such synchronization appears only in the case of a linearly polarized (oscillating) external magnetic field. For the circularly polarized (rotating) external field, only synchronization of the order 1/1 is possible.