{'fraction_non_alphanumeric': 0.022962112514351322, 'fraction_numerical': 0.001148105625717566, 'mean_word_length': 5.364963503649635, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Numerical studies of modal instabilities in high-power fiber amplifiers

We present a detailed time-dependent numerical model of the modal instability phenomenon observed in Yb-doped fiber amplifiers. The thermal effects are captured by solving the heat equation in polar coordinate using a 2D, second-order, time-dependent, alternating direction implicit (ADI) method. The model captures the three power-dependent regions that are characteristic of the transfer of energy between the fundamental mode and the higherorder mode as a function of time. It is also shown that for the fiber configuration investigated, the modal instability threshold scales linearly over a wide range with the seed power. Furthermore, we present numerical results indicating that gain tailoring can increase the threshold. Two different gain-tailored fiber designs are simulated and compared.