  We report on a comprehensive experimental investigation into the
spatial-spectral complexity of the laser beam during Kerr-induced beam
self-cleaning in graded-index multimode fibers. We demonstrate the
self-cleaning of beams using both transform-limited and chirped femtosecond
pulses. By utilizing the spectrally resolved imaging technique, we examine
variations in beam homogeneity during the beam cleanup process and reveal
correlations observed among spatial beam profiles at different wavelengths for
the various cleaned pulses. Our results significantly advance our understanding
of Kerr-induced self-cleaning with chirped ultrafast pulses and offer new
possibilities for diverse applications.
