Figure 1

Isolated self-steepening: the simulated propagation of coupled FF and SHF, as obtained from Eqs. (3) (solid lines) and from the corresponding CLLE, Eq. (5) (dotted lines). Initial conditions (dashed lines) correspond to a FF Gaussian pulse at $800\mathrm{nm}$, with a temporal width of $120\mathrm{fs}$ and intensity of $200\mathrm{GW}∕{\mathrm{cm}}^2$. Propagation parameters correspond to a $6\text{−}\mathrm{cm}$-long BBO crystal. In Eqs. (3), $\Delta k$ is set so as to cancel the ${\chi }^{\left(2\right)}$ and ${\chi }^{\left(3\right)}$ nonlinear phase shifts (see text), and the GVD is artificially set to zero. (a) The FF temporal profile; (b) temporal phase; (c) power spectrum; (d) spectral phase.Reuse & Permissions

Figure 2

Cross-correlations as predicted by the simulations (a) versus experimentally observed cross-correlations (b) for $110\mathrm{fs}$ Gaussian pulses after passing $8\mathrm{mm}$ in BBO at $\Delta k=-31\pi ∕\mathrm{mm}$ and at various intensities. (c), (d) The first derivative of (a) and (b), respectively. (e), (f) Spectra; (g) simulated temporal profiles that were used to generate (a). (h) The experimental autocorrelations of the input pulse and $50\mathrm{fs}$ cross-correlation reference pulse.Reuse & Permissions

Figure 3

Simulations corresponding to the case of $1.2\mathrm{TW}∕{\mathrm{cm}}^2$ intensity in Fig. 2, using the coupled two-field equations, Eq. (3) (solid line), CLLE, Eq. (5) (dotted line), and the CLLE with the extra quintic term, $i{\mid a\mid }^{4}a$ (dash-dotted line). Dashed line is input. (a) Temporal profiles, (b) power spectra, and (c) temporal phase profiles.Reuse & Permissions