Persistence and stochastic periodicity in the intensity dynamics of a fiber laser during the transition to optical turbulence

Many natural systems display transitions among different dynamical regimes, which are difficult to identify when the data are noisy and high dimensional. A technologically relevant example is a fiber laser, which can display complex dynamical behaviors that involve nonlinear interactions of millions of cavity modes. Here we study the laminar-turbulence transition that occurs when the laser pump power is increased. By applying various data analysis tools to empirical intensity time series we characterize their persistence and demonstrate that at the transition temporal correlations can be precisely represented by a surprisingly simple model.