  Random fiber laser (RFL) is a complex physical system that arises from the
distributed amplification and the intrinsic stochasticity of the fiber
scattering. There has been widespread interest in analyzing the underlying
lightwave kinetics at steady state. However, the transient state, such as the
RFL build-up and dissipation, is also particularly important for unfolding
lightwave interaction process. Here, we investigate for the first time the RFL
dynamics at transient state, and track the RFL temporal and spectral evolution
theoretically and experimentally. Particularly, with the contribution of
randomly distributed feedback, the build-up of RFL shows continuous Verhulst
logistic growth curves without cavity-related features, which is significantly
different from the step-like growth curve of conventional fiber lasers.
Furthermore, the radiation build-up duration is inversely related to the pump
power, and the spectral evolution of RFL undergoes two phases from spectral
density increase to spectral broadening. From steady-state to pump switch-off
state, the RFL output power dissipates immediately, and the remaining Stokes
lightwave from the Rayleigh scattering will gradually disappear after one
round-trip. This work provides new insights into the transient dynamics
features of the RFL.
