A DPG Maxwell approach for studying nonlinear thermal effects in active gain fiber amplifiers

Multi-mode fiber lasers in high-power operation can suffer from undesired thermal coupling effects such as the transverse mode instability (TMI). Indeed, the TMI is a major obstacle in power-scaling of continuous wave, weakly-guided, large mode area, active gain, silica fiber amplifiers. A better understanding of these nonlinear coupling effects is beneficial in the design of new fibers. To that end, we are extending the capabilities of our three-dimensional discontinuous Petrov-Galerkin (DPG) finite element simulation of a nonlinear full vectorial Maxwell model. The model now incorporates both amplification via an active dopant and thermal effects via coupling with the heat equation. To make the computation feasible, the model is scaled in length, using artificial material parameters with the goal of preserving certain quantities of interest. Our numerical studies show the applicability of the scaled model in the simulation of an ytterbium-doped, step-index fiber amplifier that experiences laser amplification and heating.