Investigating optical complexity of the phase transition in the intensity of a fibre laser radiation

Fibre lasers have been shown to manifest a laminar-to-turbulent transition when increasing its pump power. In order to study the dynamical complexity of this transition we use advanced statistical tools of time-series analysis. We apply ordinal analysis and the horizontal visibility graph to the experimentally measured laser output intensity. This reveal the presence of temporal correlations during the transition from the laminar to the turbulent lasing regimes. Both methods allow us to unveil coherent structures with well defined time-scales and strong correlations both, in the timing of the laser pulses and in their peak intensities.