Thermally-induced transverse mode instability: Hopf bifurcation in high-power fiber laser

The thermally-induced transverse mode instability (TMI) has become a major challenge for further enhancing the output power of single-mode fiber laser. Even though much work has been done over the past decades, the spontaneous generation process of output spot oscillation has not been well understood yet. Here, we establish a new theoretical model of the thermally-induced TMI in a high-power fiber oscillator and provide a new mechanism explanation from the point of view of nonlinear dynamics. Theoretical analysis shows that the spontaneous oscillation (∼kHz) of the output spot caused by the thermally-induced TMI is a limit-cycle oscillation via Hopf bifurcation, and the oscillation frequency is proportional to square root of the relaxation rate γ1 of thermally-induced refractive index grating (RIG) (νTMI∝γ1) when the thermally-induced TMI is initially triggered. Furthermore, the relationship between the threshold power, together with oscillation frequency and several parameters of fiber laser system was also discussed in detail. This work help us better understand the underlying dynamics of the thermally-induced TMI.