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

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