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.