Multisplitting and collapse of self-focusing anisotropic beams in normal/anomalous dispersive media

Three-dimensional self-focusing light pulses in normal and anomalous dispersive media are investigated by means of a waveguide instability analysis, a Lagrangian approach, and a quasi-self-similar analysis. In the case of normal dispersion for which no localized ground state exists, it is shown that a high-intensity elongated beam cannot self-similarly collapse. Even when the incident beam power widely exceeds the critical power for a two-dimensional self-focusing, the beam is shown to split into multiple cells that ultimately disperse when their individual mass lies below the critical power. The mechanism underlying this fragmentation process is described in terms of a stretching of the self-focusing beam along its propagation axis. The focal point, where the splitting process develops, is identified. Finally, it is shown that the longitudinal dynamical motions of self-focusing elongated pulses also play an important role in an anomalous dispersive medium. In this case, unlike the former one, the beam self-contracts along its propagation axis and reconcentrates its shape back toward the center where it ultimately collapses in a finite time.