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

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.