Theory of phase locking of globally coupled laser arrays

We have carried out an investigation of the globally coupled laser array with randomly spread eigenfrequencies. It is shown that as this spread increases, either the laser action vanishes or the coherent steady-state regime is replaced by a phase-unlocked regime. The regions of the stable phase locking have been analytically and numerically determined. It is found that the gain inertia leads to cooperative phase-locking effects when the maximum detuning is close to the relaxation frequency.