Suppression and splitting of modulational instability sidebands in periodically tapered optical fibers due to fourth-order dispersion

We study the modulational instability induced by periodic variations of group-velocity dispersion in the proximity of the zero dispersion point. Multiple instability peaks originating from parametric resonance coexist with the conventional modulation instability due to fourth order dispersion, which in turn is suppressed by the oscillations of dispersion. Moreover isolated unstable regions appear in the space of parameters due to imperfect phase matching. This confirms the dramatic effect of periodic tapering in the control and shaping of MI sidebands in optical fibers.