Influence of a backward reflection on low-threshold mode instability in Yb³⁺-doped few-mode fiber amplifiers

An influence of backward reflection on spatio-temporal instability of the fundamental mode in Yb³⁺-doped few-mode polarization maintaining fiber amplifiers with a core diameter of 10 μm was studied experimentally and theoretically. The mode instability threshold was registered to decrease dramatically in the presence of a backward reflection of the signal from the output fiber end; an increase of the signal bandwidth or input power resulted in the increase of the threshold. Numerical simulation revealed a self-consistent growth of the higher-order mode LP₁₁ and a traveling index grating accompanying the population grating induced by the mode interference field (due to different polarizability of the excited and unexcited Yb³⁺ ions). The presence of the backward-propagating wave resulted in four-wave mixing on the common index grating induced by the interference field of pairs of the fundamental LP₀₁ and LP₁₁ modes.