Unveiling the temporal dynamics in multi-longitudinal mode ytterbium-doped fiber lasers

In this work, we propose a unified spatio-temporal model to study the temporal dynamics in continuously pumped ytterbium-doped fiber lasers (YDFLs). Different from previously reported theories, this model is capable of obtaining the temporal evolution of an YDFL from relaxation oscillation region to relative stable region in different time scales ranging from sub-nanosecond to millisecond. It reveals that there exists dual time scale characteristics in the temporal evolution of a multi-longitudinal mode YDFL. Specifically, the temporal evolution would experience sharp change during one cavity round-trip while keep relatively stable between adjacent cavity round-trips. Representative cases are simulated to study the influences of structure parameters on the temporal dynamics and the longitudinal mode characteristics in YDFLs. Three types of temporal instabilities, i.e. sustained self-pulsing, self-mode locking, and turbulence-like pulsing, coexist in a multi-longitudinal mode YDFL. The simulation results clarify that the three temporal instabilities are all the reflectors of intrinsic characteristics of longitudinal modes superposition in multi-longitudinal mode YDFLs. In addition, the strength of the irregular sustained self-pulsing is the major issue which impacts the macroscopic temporal fluctuations in YDFLs.