We investigate ultrashort laser pulse filamentation within the framework of spontaneous X Wave formation. After a brief overview of the filamentation process we study the case of an intense filament co-propagating with a weaker seed pulse. The filament is shown to induce strong Cross-Phase-Modulation (XPM) effects on the weak seed pulse: driven by the pump, the seed pulse undergoes pulse splitting with the daughter pulses slaved to their pump counterparts. They undergo strong spatio-temporal reshaping and are transformed into XWaves traveling at the same group velocities as the pump split-off pulses. In the presence of a gain mechanism such as Four-Wave-Mixing or Stimulated Raman Scattering, energy is then transferred from the pump filament leading to amplification of the seed X Wave and formation of a temporally compressed intensity peak.
The description of ultrashort laser pulse filamentation in condensed media as a spontaneous formation of X waves is shown to apply also to filaments generated in air. Within this framework, a simple explanation is brought for several features of the filament such as the subdiffractive propagation and the energy flux from the weakly localized tails of the X-waves to the intense core.
Ultrashort laser pulse filaments in dispersive nonlinear Kerr media induce a moving refractive index perturbation which modifies the space-time geometry as seen by co-propagating light rays. We study the analogue geometry induced by the filament and show that one of the most evident features of filamentation, namely conical emission, may be precisely reconstructed from the geodesics. We highlight the existence of favorable conditions for the study of analogue black hole kinematics and Hawking type radiation.
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