Few-cycle laser-pulse collapse in Kerr media: The role of group-velocity dispersion and X-wave formation

We study ultrashort laser-pulse propagation and filamentation dynamics in dispersive Kerr media. We identify the regime for which the filamentation threshold (P(th)) is considerably higher than the critical power (P(cr)) for monochromatic beam collapse in pure Kerr media. In particular, we compare the threshold for the formation of filaments with that for the formation of X-waves. At powers P(cr) < P < P(th), self-focusing is arrested by group-velocity dispersion, and no filaments or X-waves are formed. At P >= P(th), we observe X-wave formation and a weak filamentation regime. At P >> P(th), we observe both X-waves and fully formed filaments.