Competition between phase-matching and stationarity in Kerr-driven optical pulse filamentation

Experiments show that the spatiotemporal spectral broadening of an intense pump pulse in a Kerr medium in the presence of strong higher-order dispersion does not lead to symmetric profiles, and hence cannot be interpreted as standard modulational instability of a plane and monochromatic nonlinear eigenmode. The highly asymmetric features of the generated $(K_{\perp },\Omega )$ spectrum are due to odd-order dispersion terms and are interpreted in terms of spontaneous formation of stationary conical waves.

Figure 1

(Color online) (a) Experimentally measured log-scale spectrum of a filament in $4\mathrm{cm}$ of water, with an input pump centered at $1.055\mu \mathrm{m}$ and with $E_{\mathit{in}}=15\mu \mathrm{J}$. The inset shows the input spectrum on the same scale, but with shifted axis. (b) Same as in (a) but calculated numerically from Eq. (1). White solid lines indicate the stationary fish mode, as described in the text.

Figure 2

(Color online) Experimentally measured spectrum of a filament in $3\mathrm{cm}$ of fused silica with an input pump centered at $1.6\mu \mathrm{m}$ and with $E_{\mathit{in}}=5\mu \mathrm{J}$.

Figure 3

(Color online) Gain profiles for a background white noise with an input Gaussian pump with (a) $r_{\mathit{FWHM}}=1\mathrm{mm}$, $t_{\mathit{FWHM}}=200\mathrm{fs}$, ${\lambda }_0=800\mathrm{nm}$, (b) $r_{\mathit{FWHM}}=1\mathrm{mm}$, $t_{\mathit{FWHM}}=200\mathrm{fs}$, ${\lambda }_0=1055\mathrm{nm}$, and (c) $r_{\mathit{FWHM}}=50\mu \mathrm{m}$, $t_{\mathit{FWHM}}=20\mathrm{fs}$, ${\lambda }_0=1055\mathrm{nm}$. Solid lines are a guide for the eye and qualitatively reproduce curves obtainable from Eq. (3).