Investigations of modal instabilities in fiber amplifiers through detailed numerical simulations

We present detailed numerical simulations of modal instabilities in high-power Yb-doped fiber amplifiers using a time-dependent temperature solver coupled to the optical fields and population inversion equations. The temperature is computed by solving the heat equation in polar coordinates using a 2D second-order alternating direction implicit method. We show that the higher-order modal content rises dramatically in the vicinity of the threshold and we recover the three power-dependent regions that are characteristic of the transfer of energy. We also investigate the dependence of the threshold on the seed power and the modal content ratio of the seed. The latter has a minimal effect on the threshold while it is shown that for the fiber configuration investigated, the modal instability threshold scales linearly over a wide range with the seed power. In addition, two different gain-tailored core designs are investigated and are shown to have higher thresholds than that of a uniformly doped core. Finally, we show that this full time-dependent model which does not assume a frequency offset between the modes a priori, predicts a reduced threshold when the seed is modulated at the KHz level. This is in agreement with the steady-periodic approach to this phenomenon.