Locking behaviour of three coupled laser oscillators

Single-frequency operation or locking in a lateral array of three laser oscillators is studied within the composite-cavity-mode approach. We compute the regions of stable locking, which have a non-trivial shape in the plane of coupling strength versus frequency detuning. The locking regions depend drastically on the amount of amplitude-phase-coupling of the lasing field that is quantified by the parameter alpha. For small alpha, locking is possible for arbitrary coupling, but only if the middle laser has sufficient frequency detuning from the two outer lasers. In contrast, for larger alpha, locking is only possible for weak to moderate coupling provided that all three lasers have similar frequencies.