Nonlinear beam control via amplitude and phase locking in multimode GRIN fibers

Spatial beam self-cleaning in graded-index multimode fibers involves a nonlinear transfer of power among the fiber modes, which leads to robust bell-shaped output beams. The resulting output mode power distribution can be described by statistical mechanics arguments. Although the spatial coherence of the output beam was experimentally demonstrated, there is no direct study of modal phase evolution. Based on a holographic mode decomposition method, we reveal that nonlinear spatial phase-locking occurs between the fundamental and its neighboring low-order modes, in good quantitative agreement with theoretical predictions