From synchronisation to persistent optical turbulence in laser arrays

We define and study synchronisation in a linear array of nearest-neighbour coupled lasers. Our focus is on possible synchronisation types and the stability of their corresponding synchronisation manifolds with dependence on the coupling strength, the laser frequency detuning, the amount of shear (amplitude–phase coupling) in a single laser, and the array size. We classify, and give analytical conditions for the existence of complete synchronisation solutions, where all the lasers emit light with the same intensity and frequency. Furthermore, we derive stability criteria for two special cases where all the lasers oscillate (i) in-phase with each other and (ii) in anti-phase with their nearest neighbour(s). We then explain transitions from complete synchronisation, to partial synchronisation (where only a subset of the lasers synchronises), to persistent optical turbulence (where no lasers synchronise and each laser is chaotic) in terms of bifurcations including blowouts of chaotic attractors. Finally, we quantify properties of optical turbulence using Lyapunov spectrum and dimension, which highlights differences in chaos generated by nearest-neighbour and globally coupled oscillators.