We carry out a stability analysis on the STRS process in two (frequency-detuned) mode fiber amplifiers, in the presence of delayed thermal nonlinearity. We show for the first time that the standard two-wave STRS process is stable against small modal perturbations, and as such it does not describe adequately the TMI process. We further show that inclusion of FWM effects and three-wave interaction, through the addition of an anti-Stokes LP11 wave, is required to describe modal instabilities above a power threshold, and a previously derived TMI power threshold formula is recovered. This work sheds new light on the standard STRS process and adds new insight into its connection with TMI effects in high power fiber amplifiers.
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