Theoretical investigations of power fluctuations statistics in Brillouin erbium-doped fiber lasers.

We present theoretical investigations including simulations and statistical analyses on the fluctuations of the temporal output power in a Brillouin erbium-doped fiber laser. The generation of even Stokes waves up to the 5th order is considered by solving coupled-mode equations including SBS and Kerr nonlinearities. It is demonstrated that by increasing the EDFA pump power and generating a few orders of Stokes waves in such a laser, there are strong power fluctuations and rogue events are expected. Transition from Gaussian-like to levy-like regime is described as the power is increased from threshold resulting in the initial Stokes wave generation to well beyond threshold generating 5 effective even Stokes waves. Accordingly, phase portraits confirm increasing fluctuations as a function of the power. It is also shown that at the SBS lasing threshold, the output signals have the maximum correlation over replicas in round trips, nevertheless by enhancing the power, the correlation diminishes, which results in a full symmetry breaking and the system radiates in a chaotic manner and exhibits random laser behavior.