Optical phase locking between two coupled lasers can occur even when the coupling delay time greatly exceeds the coherence time of the lasers themselves[1]. However, for a larger numbers of lasers, the interplay between the topology of the coupled laser networks and synchronization remains an enigma.

We experimentally investigated the dynamics of large coupled laser networks and established the fundamental rules governing their synchronization state[2]. Synchronization is controlled by the network connectivity, where the number of distinct multi-laser synchronized clusters is shown to depend on the greatest common divisor of network loops. This dependence enables remote switching mechanisms to control the optical phase coherence among distant lasers by local network connectivity adjustments. Our findings are generalized to include heterogeneous time delay laser networks schemes.   

[1] M. Nixon, et. al., Opt. Lett., 34, 1864 (2009).

[2] M. Nixon, et. al., Phys. Rev. Lett., 106,  22 (2011).