Statistical analysis of phase locking of optically coupled lasers with external injection of low-noise radiation

Phase locking of an array of optically coupled lasers with the long-range type of interaction and with injection of an external signal is investigated in terms of the theory of critical phenomena. The threshold intensities of the injected signal needed for phase-locked operation are determined. These intensities are shown to depend strongly on the detuning of the injected-signal frequency from the centre of the gain profile of the active medium and on the coefficient representing coupling of the lasers to one another. Analytical dependences are obtained for the dependence of the half-width of the phase-locking band and of the output power on the injected-signal intensity, on the scatter of the resonance frequencies, and on other parameters of the laser array.