  Multimode fiber systems are desirable for industrial and scientific
applications. As an interesting effect for the laser beam propagation in a
multimode fiber, nonlinear Kerr beam cleanup has attracted considerable
research interest due to the spatial beam compressing. However, its physical
mechanisms, especially the influences of input conditions on its performances,
remain unclear. Here, we report a new self-organized regime for the multimode
beam propagation in a graded-index multimode fiber: when the input laser has a
dominant mode in which most of the laser energy is concentrated, the beam
profile can be maintaining in a well-defined structure similar to the input
dominant mode in nonlinear regime, while it will evolve to an irregular pattern
in linear regime. The existence and universality of this nonlinear beam
self-maintaining effect have been verified by the experimental and numerical
data. Our results also provide evidence that nonlinear Kerr effects can be the
driving mechanism and nonlinear Kerr beam cleanup is a specific case of this
effect. Further research into this spatial beam shaping effect may provide a
new perspective to understand other multimode fiber nonlinearities.
