Conical Emission, Pulse Splitting, and X-Wave Parametric Amplification in Nonlinear Dynamics of Ultrashort Light Pulses

The precise observation of the angle-frequency spectrum of light filaments in water reveals a scenario incompatible with current models of conical emission (CE). Its description in terms of linear X-wave modes leads us to understand filamentation dynamics requiring a phase- and group-matched, Kerr-driven four-wave-mixing process that involves two highly localized pumps and two X waves. CE and temporal splitting arise naturally as two manifestations of this process.

Figure 1

Contour plot (in logarithmic scale over two decades) of the measured $\theta \mathrm{\text{−}}\lambda$ spectrum for $E_{\mathrm{in}}=2\mu \mathrm{J}$.

Figure 2

(a) Solid circles, $\theta \mathrm{\text{−}}\Omega$ distribution of peak fluence in Fig. 1; black dotted line, best fit of the entire set of experimental data with Eq. (2); red dashed line, best fit of the $\Omega <0$ data with Eq. (3); blue solid line, best fit of the $\Omega >0$ data with Eq. (3). (b) Experimentally measured $\theta \mathrm{\text{−}}\lambda$ spectrum: input energy is increased to $E_{\mathrm{in}}=3\mu \mathrm{J}$ to enhance the visibility of the new tails.

Figure 3

Left axis: Values of ${\tilde{\beta }}_{s,i}$ obtained from X-wave fitting to the numerical $K_{\perp }-\Omega$ spectra for increasing pump intensities $I$ (open squares) and prediction of Eq. (4) (solid curve). Right axis: GVM between the splitting pulses obtained from direct space-time numerical simulation (open circles) and between the X waves as given by $2\sqrt{k_0^{\prime \prime }{\omega }_0{n}_{2}I/c}$ (solid curve).