Suppression and splitting of modulational instability sidebands in periodically tapered optical fibers because of 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 because of fourth-order dispersion, which in turn is suppressed by the oscillations of dispersion. Moreover, isolated unstable regions appear in the space of parameters because of imperfect phase matching. This confirms the dramatic effect of periodic tapering in the control and shaping of MI sidebands in optical fibers.