  We introduce the concept of spatial and spectral control of nonlinear
parametric sidebands in multimode optical fibers by tailoring their linear
refractive index profile. In all cases, the pump experiences Kerr
self-cleaning, leading to a bell-shaped profile close to the fundamental mode.
Geometric parametric instability, owing to quasi-phase-matching from the
grating generated via the Kerr effect by pump self-imaging, leads to frequency
multicasting of beam self-cleaning across a wideband array of sidebands. Our
experiments show that introducing a gaussian dip in the refractive index
profile of a graded index fiber permits to dramatically change the spatial
content of spectral sidebands into higher-order modes. This is due to the
breaking of oscillation synchronism among fundamental and higher-order modes.
Hence modal-four-wave mixing prevails over geometric parametric instability as
the main sideband generation mechanism. Observations agree well with
theoretical predictions based on a perturbative analysis, and with full
numerical solutions of the (3D + 1) nonlinear Schrodinger equation.
