Nonlinear X-wave formation by femtosecond filamentation in Kerr media

We investigate the formation of X waves during filamentation in Kerr media. From the standard model developed for femtosecond filamentation in liquids, solids, and gases, the influence of several physical effects and parameters is numerically studied in the strongly nonlinear regime where group velocity dispersion alone is insufficient to arrest collapse. The collapse is shown to be arrested by multiphoton absorption and plasma defocusing, but not by dispersion. The postcollapse dynamics takes the form of a pulse splitting, which induces large gradients in the near field and seeds the formation of X waves, appearing both in the near and far fields. We discuss the universal features of the X-wave patterns, among which the long arms in the far field that follow the linear dispersive properties of the medium [Conti, Phys. Rev. Lett. 90, 170406 (2003); Kolesik, Phys. Rev. Lett. 92, 253901 (2004)] and are accompanied by a strong modulated axial emission.