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The nonlinear propagation of picosecond or femtosecond optical pulses in multimode fiber amplifiers underlies a variety of intriguing physical phenomena as well as the potential for scaling sources of ultrashort pulses to higher powers. However, existing theoretical models of ultrashort-pulse amplification do not include some critical processes, and, as a result, they fail to capture basic features of experiments. We introduce a numerical model that combines steady-state rate equations with the unidirectional pulse propagation equation, incorporating dispersion, Kerr and Raman nonlinearities, and gain/loss-spectral effects in a mode-resolved treatment that is computationally efficient. This model allows investigation of spatiotemporal processes that are strongly affected by gain dynamics. Its capabilities are illustrated through examinations of amplification in few-mode gain fiber, multimode nonlinear amplification, and beam cleaning in a multimode fiber amplifier.

Kerr beam cleaning is a nonlinear phenomenon in graded-index multimode fiber where power flows toward the fundamental mode, generating bell-shaped output beams. Here we study beam cleaning of femtosecond pulses accompanied by gain in a multimode fiber amplifier. Mode-resolved energy measurements and numerical simulations showed that the amplifier generates beams with high fundamental mode content (greater than 30% of the overall pulse energy) for a wide range of amplification levels. Control experiments using stretched pulses that evolve without strong Kerr nonlinear effects showed a degrading beam profile, in contrast to nonlinear beam cleaning. Temporal measurements showed that seed pulse parameters have a strong effect on the amplified pulse quality. These results may influence the design of future high-performance fiber lasers and amplifiers.