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Multimode optical fibers (MMF) recently attracted a renewed attention, because of their potential for spatial division multiplexing, medical imaging and high-power fiber lasers, thanks to the discovery of new nonlinear optical effects, such as Kerr beam self-cleaning, spatiotemporal mode-locking, and geometric parametric instability, to name a few. The main feature of these effects is that many transverse modes are involved in nonlinear interactions. To advance our understanding, it is necessary to analyse the modal content of beams at the output of MMFs. In this work, based on a computer digital holography method using a phase-only spatial light modulator (SLM) as a correlation filter, we experimentally demonstrate a method of mode decomposition involving a large (≃80) number of fiber modes. To obtain this, we carried out a SLM calibration, and numerically investigated the most critical parameters which affect the fidelity of the decomposition, by comparing experimental and reconstructed beam patterns in both the linear (speckled structures) and in the nonlinear (self-cleaned beams) propagation regime.

We experimentally and theoretically investigate complex temporal pulse reshaping that accompanies Kerr beam self-cleaning in multimode optical fibers. We also study the output beam shape dependence on initial conditions.

We show that Kerr beam self-cleaning results from parametric mode mixing instabilities that generate a number of nonlinearly interacting modes with randomized phases - optical wave turbulence, followed by a direct and inverse cascade towards high mode numbers and condensation into the fundamental mode, respectively. This optical self-organization effect is an analogue to wave condensation that is well known in hydrodynamic 2D turbulence.

The all-fiber all-normal-dispersion cavity length and mode-field diameter have been increased simultaneously up to 40-m and 10-μm. By suppressing Raman effect, highly-chirped pulses with energy >50 nJ at 250 fs compressed duration are generated.