Synchronization of coupled laser arrays with all-to-all and limited coupling topology

Synchronization of coupled laser arrays is required in many applications of high-power laser systems. While the problem is approached by numerical or experimental methods traditionally, we propose a new approach to rigorously characterize the synchronization condition inspired by recent advances in cooperative control. We study synchronization of an array of coupled solid state lasers where each individual laser is modeled by a second-order nonlinear oscillators. We analyze synchronization conditions over a mean-field model for all-to-all coupling configuration, and prove that the coupled lasers with identical frequencies can be stabilized on the synchronization state for any positive coupling strength. We then extend the all-to-all coupling to the limited communication case, and similar synchronization conditions are proved for undirected connected graphs. Our analysis is conducted using tools from algebraic graph theory and Lyapunov dynamic system theory. Simulation examples are given to illustrate the results.