Multimode nonlinear fiber optics in presence of amplification can play a pivotal role in a variety of new interesting phenomena and applications. However, extending the numerical models for light-matter interaction to multimode fields requires careful consideration.

The authors in this publication propose an accurate spatiotemporal numerical modelling based on mode expansion theory to capture several relevant physical mechanisms, such as the pump depletion, the spontaneous emission noise, the spatial saturation, and the related variation of the gain spectrum. The model combines unidirectional pulse propagation equations with rate equations to describe the population inversion.

The authors leverage their model to approach a series of effects such as the differential modal gain, the gain-managed nonlinear evolution, and the beam cleaning - an effect enabling the fiber output beam's shape to be well-defined, with a low multimode field background. About this last effect, the authors underline how the persistence of the gain saturation in the central part of the fiber core can lead to higher losses for high order modes, which in turn can improve the effect of beam cleaning driven by the sole Kerr effect.

By contributing a rigorous presentation, the authors help explain some of the experimental results discussed in the literature, while also providing an important tool for exploring new applications.

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