  Multimode fibres (MMFs) are attracting interest for complex spatiotemporal
dynamics, and for ultrafast fibre sources, imaging and telecommunications. This
new interest is based on three key properties: their high spatiotemporal
complexity (information capacity), the important role of disorder, and complex
intermodal interactions. To date, phenomena in MMFs have been studied only in
limiting cases where one or more of these properties can be neglected. Here we
study MMFs in a regime in which all these elements are integral. We observe a
spatial beam-cleaning process preceding spatiotemporal modulation instability.
We show that the origin of these processes is a universal unstable attractor in
graded-index MMFs. Both the self-organization of the attractor, as well as its
instability, are caused by intermodal interactions characterized by cooperating
disorder, nonlinearity and dissipation. The demonstration of a
disorder-enhanced nonlinear process in MMF has important implications for
telecommunications, and the multifaceted complexity of the dynamics showcases
MM waveguides as ideal laboratories for many topics and applications in
complexity science.
