  We experimentally demonstrate Kerr beam self-cleaning in the anomalous
dispersion regime of graded-index multimode optical fibers. By using 90 ps
duration, highly chirped (2 nm bandwidth at -3dB) optical pulses at 1562 nm, we
demonstrate a 2 decades reduction, with respect to previous experiments in the
normal dispersion regime, of threshold peak power for beam self-cleaning into
the fundamental mode of the fiber, accompanied by more than 65% nonlinear
increase of intensity correlation into the fundamental mode. Highly efficient
self-selection of the LP11 mode is also observed. Self-cleaned beams remain
spatio-temporally stable for more than a decade of variation of the peak pulse
power.
