Figure 1

Probe phase shift $\Delta \Phi (x,t)$ measured in neon using single-shot supercontinuum spectral interferometry, for an intensity below (left) and above (right) the onset of ionization.Reuse & Permissions

Figure 2

(a) Ionization rates $w$, $w_9$, $R$, and $R_T$ calculated using the models in 12, 15, 17 for 800 nm light in H. Here $w_k$ is the $k$th order MPI rate applicable for $\gamma \gg 1$ (shown for $k=9$), $w$ is the sum of $w_k$ from $k=2$ to 50, $R_T$ is the rate in the tunneling limit $\gamma \ll 1$ [17], and $R$ is the rate from [15] applicable from the MPI through tunneling regimes. The blue dots are for a TDSE calculation. (b) Calculation of the absorption cross section $N^{-1}\Delta \alpha$ in Hydrogen using $R$ (solid black line) and the $\Delta \alpha$ expression from [12] (dashed red line) for pump intensity $1\mathrm{TW}/{\mathrm{cm}}^2$ and $\hslash \omega =1.55\mathrm{eV}$. (c) Curves of (b) for pump intensity $50\mathrm{TW}/{\mathrm{cm}}^2$. The blue dots show the probe absorption cross section derived from the nondegenerate ionization rate determined by a TDSE calculation [19]. (d) Same as (b) and (c) but in Ar at $50\mathrm{TW}/{\mathrm{cm}}^2$. Vertical dotted lines in (b), (c), and (d) show where $\Omega =\omega$. For $\Omega <\omega$ the KK integrand in Eq. (1) is negative.Reuse & Permissions

Figure 3

The nonlinear refractive index $\Delta n$ of the noble gases experienced by a weak probe pulse as a function of pump laser peak intensity. Blue dots show experimental data points, and the solid line shows a linear fit of the data to $2n_{2}I$. Vertical dotted lines show, for each gas, the measured ionization threshold. Our KK calculation, using the ionization rate $R$, is shown as a dashed black line. The red dashed line is the result from Brée et al. [12], where we have calculated $\Delta n$ for a weak probe by multiplying their self-refractive index coefficients $n_{2k}$ by $k+1$ [18]. The blue dash-dotted line is the self-refractive index plotted in Brée et al. Horizontal error bars denote uncertainty in the intensity calibration and vertical error bars denote uncertainty in the phase extraction.Reuse & Permissions