Almost perfect in-phase and anti-phase chaotic and periodic phase synchronization in large arrays of diode lasers

In this paper we study phase synchronization in large arrays of weakly coupled single mode semiconductor laser diodes. We show that if the coupling topology is chosen appropriately, the laser array exhibits robust phase synchrony (including chaotic and non-chaotic phase synchrony). Furthermore, one can define coupling topologies that lead to chaotic anti-phase synchronization. To the best of our knowledge, chaotic anti-phase synchronization has not been observed in large arrays of coupled nonlinear oscillators. When diodes are coupled via a decayed non-local coupling scheme, the leading spatial mode can be stable. This leads to an almost-perfect phase synchronous state where the phases are synchronized, but the system is not set exactly on the synchronization manifold. This almost-perfect phase synchronous state is robust to noise and frequency disorder and can be realized under periodic (fixed-intensity limit cycle) continuous-wave and chaotic behavior. The presented result is an example of the broader phenomenon of linear transverse mode selection taking place in a coupled oscillator system with nonlinear dynamics.