Multimode optical fibres are enjoying a renewed attention, boosted by the urgent need to overcome the current capacity crunch of single-mode fibre systems and by recent advances in multimode complex nonlinear optics [1][2][3][4][5][6][7][8][9][10][11][12][13]. In this work, we demonstrate that standard multimode fibres can be used as ultrafast all-optical tool for transverse beam manipulation of high power laser pulses. Our experimental data show that the Kerr effect in a graded-index multimode fibre is the driving mechanism for overcoming speckle distortions, leading to a somewhat counter-intuitive effect resulting in a spatially clean output beam robust against fibre bending. Our observations demonstrate that nonlinear beam reshaping into the fundamental mode of a multimode fibre can be achieved even in the absence of a dissipative process such as stimulated scattering (Raman or Brillouin) [14,15].Beam propagation in multimode fibres (MMFs) is subject to a complex interplay of spatio-temporal processes. However, only few studies addressed nonlinear pulse propagation in MMFs, leaving this field largely untapped for the past thirty years. Very recently, there has been a resurgence of interest in MMFs for both fundamental and applied research. MMFs could provide a solution to meet increasing demands of new breakthrough technologies for light control and manipulation in communications, high-power fibre lasers and metrology [1,2,16]. In fundamental physics, MMFs may provide a natural tool for investigating spatiotemporal soliton dynamics [5,6], and for unveiling new, exciting nonlinear phenomena [3,4,9,13].It is well known that light experiences an inherent randomization when propagating along MMFs, whereby input laser beams of high spatial quality fade into irregular granularities called speckles. Fibre stress or bending, as well as technological irregularities of the fibre, couple different guided modes and introduce supplementary randomization of the transmission features. For this reason, MMFs are not ideally suited for beam delivery and were replaced by single-mode fibres (SMFs) since the early days of optical communications. Recent works demonstrated that specific signal-processing algorithms could be used to predict or manage the beam shape at the output of a MMF by controlling its input field [17][18][19]. In particular, the application of multiple-input, multiple-output (MIMO) digital signal processing techniques enables the use of spatial-division multiplexing based on MMFs [2]. For high-power beam delivery applications, the spontaneous recovery of spatial beam quality in MMFs has so far been experimentally achieved exclusively through nonlinear dissipative processes such as stimulated Raman scattering (SRS) [14] or stimulated Brillouin scattering (SBS) [20]. However, these techniques do not lead to any self-cleaning of the input laser beam. It is now known that for powers above a critical level (few MWs) self-phase modulation (SPM) may overcome diffraction for any size of the beam, and this may in turn c...

Real-time access to the internal ultrafast dynamics of complex dissipative optical systems opens new explorations of pulse-pulse interactions and dynamic patterns. We present the first direct experimental evidence of the internal motion of a dissipative optical soliton molecule generated in a passively modelocked erbium-doped fiber laser. We map the internal motions of a soliton pair molecule by using a dispersive Fourier-transform imaging technique, revealing different categories of internal pulsations, including vibration-like and phase drifting dynamics. Our experiments agree well with numerical predictions and bring insights to the analogy between self-organized states of lights and states of the matter.