Geometric parametric instability in periodically modulated GRIN multimode fibers

We present a theoretical and numerical study of light propagation in graded-index (GRIN) multimode fibers where the core diameter has been periodically modulated along the propagation direction. The additional degree of freedom represented by the modulation permits to modify the intrinsic spatiotemporal dynamics which appears in multimode fibers. More precisely, we show that modulating the core diameter at a periodicity close to the self-imaging distance allows to induce a Moir\'{e}-like pattern, which modifies the geometric parametric instability gain observed in homogeneous GRIN fibers.