Power Fluctuations and Random Lasing in Multi-Wavelength Brillouin Erbium-Doped Fiber Lasers

We experimentally and theoretically investigate the power fluctuations of the temporal interference signal produced by up to 5 Stokes orders generated by cascaded stimulated Brillouin scattering in a multiwavelength Brillouin erbium-doped fiber laser system with a 2.5-km-long intracavity fiber and erbium-doped fiber amplifier. Power fluctuations in such a system are due to the existence of several modes within the SBS gain bandwidth with the possibility of random hopping resulting in a chaotic temporal evolution of the pump and Stokes-wave powers and consequently the output signal power. Our simulations and statistical analyses show that at the threshold power resulting in the initial Stokes wave generation over round trips, the output signals have the maximum correlation over replicas; however, by increasing the power and producing more stokes waves, the correlation fades out leading to replica symmetry breaking and the system emits in a disordered manner and shows the signatures of a random laser.