Modulational instability in fractional nonlinear Schrodinger equation

Fractional calculus is entering the field of nonlinear optics to describe unconventional regimes, as disorder biological media and soft-matter. Here we investigate spatiotemporal modulational instability (MI) in a fractional nonlinear Schr�dinger equation. We derive the MI gain spectrum in terms of the L�vy indexes and a varying number of spatial dimensions. We show theoretically and numerically that the L�vy indexes affect fastest growth frequencies and MI bandwidth and gain. Our results unveil a very rich scenario that may occur in the propagation of ultrashort pulses in random media and metamaterials, and may sustain novel kinds of propagation invariant optical bullets.