Optimal input excitations for suppressing nonlinear instabilities in multimode fibers

Wavefront shaping has become a powerful tool for manipulating light propagation in various complex media undergoing linear scattering. Controlling nonlinear optical interactions with spatial degrees of freedom is a relatively recent but fast growing area of research. A wavefront-shaping-based approach can be used to suppress nonlinear stimulated Brillouin scattering (SBS) and transverse mode instability (TMI), which are the two main limitations to power scaling in high-power narrowband fiber amplifiers. Here we formulate both SBS and TMI suppression as optimization problems with respect to coherent multimode input excitation in a given multimode fiber. We develop an efficient method using linear programming for finding the globally optimal input excitation for minimizing SBS and TMI individually or jointly. The theory shows that optimally exciting a standard multimode fiber leads to roughly an order of magnitude enhancement in instability-free output power compared to fundamental-mode-only excitation. We find that the optimal mode content is robust to small perturbations and our approach works even in the presence of mode-dependent loss and gain. When such optimal mode content is excited in real experiments using spatial light modulators, the stable range of ultrahigh-power fiber lasers can be substantially increased, enabling applications in gravitation wave detection, advanced manufacturing, and defense.