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We introduce the concept of spatial and spectral control of nonlinearparametric sidebands in multimode optical fibers by tailoring their linearrefractive index profile. In all cases, the pump experiences Kerrself-cleaning, leading to a bell-shaped profile close to the fundamental mode.Geometric parametric instability, owing to quasi-phase-matching from thegrating generated via the Kerr effect by pump self-imaging, leads to frequencymulticasting of beam self-cleaning across a wideband array of sidebands. Ourexperiments show that introducing a gaussian dip in the refractive indexprofile of a graded index fiber permits to dramatically change the spatialcontent of spectral sidebands into higher-order modes. This is due to thebreaking of oscillation synchronism among fundamental and higher-order modes.Hence modal-four-wave mixing prevails over geometric parametric instability asthe main sideband generation mechanism. Observations agree well withtheoretical predictions based on a perturbative analysis, and with fullnumerical solutions of the (3D + 1) nonlinear Schrodinger equation.

Refractive index profile tailoring of multimode optical fibers for the spatial and spectral shaping of parametric sidebands