Influence of signal bandwidth on mode instability threshold of fiber amplifiers

We show how signal linewidth affects the gain of stimulated thermal Rayleigh scattering (STRS) which is responsible for mode instability in fiber amplifiers. The gain is reduced if the coherence time of the signal is less than the group velocity induced walk off between modes LP$_{01}$ and LP$_{11}$. We derive equations for short pulses, linear chirps, and general periodic cases.