Stability results for in-phase and splay-phase states of solid-state laser arrays

We present a theoretical study of synchronization in N-element solid-state laser arrays. We carry out the linear stability analysis for three types of solution: the nonlasing state, the in-phase periodic state, and the splayphase state. Both nearest-neighbor (on a ring) coupling and global (all-to-all) coupling are treated; the system symmetries enable us to solve the linear stability problem for arbitrary N. We consider the general case in which the coupling coefficient iκ is complex and find that stability depends crucially on the sign of the imaginary part of κ. In the case of global coupling, we discover a surprising result: the existence of an N − 2 parameter family of frequency-locked neutrally stable states. These states should display substantial phase diffusion in the presence of noise.