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

In this paper, 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 beam profile. Geometric parametric instability, owing to quasi-phase matching from the dynamic 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 into the refractive index profile of a graded index fiber permits us to dramatically change the spatial content of spectral sidebands into higher-order modes. This is due to the breaking of the oscillation synchronism among low-order and higher-order modes. Hence, the inter-modal four-wave mixing approach should be used to describe the sideband generation mechanism. Observations agree well with theoretical predictions based on a perturbative analysis and with full numerical solutions of the (3+1)D nonlinear Schrödinger equation.