Frequency locking of a laser by injected atomic coherence

We consider a single-mode unidirectional ring laser containing a homogeneously broadened two-level medium whose atoms are injected in a coherent superposition of states. Provided that appropriate phase-matching conditions are met, the injected coherence contributes directly to the polarization of the medium and hence to the laser gain. We assume that the field is classical and perfectly phase matched with the injected coherence. We find that laser oscillation can occur below the usual laser threshold, and even in the absence of an inversion, with a frequency locked to the atomic line center. Mode locking is unstable for sufficiently strong relative excitation.