Figure 1

Time-of-flight (TOF) traces for the interaction of xenon clusters [$⟨N⟩\approx 1.6\times {10}^4$) (a)] with a Fourier-transform-limited $100\mathrm{fs}$, $800\mathrm{nm}$, ${10}^{15}\mathrm{W}{\mathrm{cm}}^{-2}$ laser pulse (N.B. The inset shows the complete TOF trace) (solid line) and the optimal linearly chirped laser pulse (dashed line) for forming highly charged ions derived from the former ($\sim 500\mathrm{fs}$ long); (b) with the optimum pulse shape obtained by means of an 80-parameter unrestricted optimization. As shown in Fig. 2a the optimum pulse consists of a sequence of two $120\mathrm{fs}$ pulses, separated by $500\mathrm{fs}$. The inset in (b) shows the evolution of the fitness value for the 80-parameter optimization (full squares, maximum fitness; open squares, average fitness).Reuse & Permissions

Figure 2

Autocorrelation traces for pulses obtained by (a) an unrestricted 80-parameter optimization for $⟨N⟩\approx 1.6\times {10}^4$ [Fig. 1b], and (b) a restricted 3-parameter optimization with larger clusters $\left(⟨N⟩\approx 2.0\times {10}^6\right)$. In the latter case the 3 parameters in the optimization were the amplitude and period of an oscillatory phase pattern applied to the LCD mask (leading to the formation of a pulse train) and the linear chirp of the pulse.Reuse & Permissions

Figure 3

(a) Optimal pulse shape found in an optimal-control calculation for the ionization of ${\mathrm{Xe}}_{108}$ by a tailored laser pulse derived from a $30\mathrm{fs}$, $3.5\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$ laser pulse. Efficient ionization is achieved by a sequence of two pulses separated by $146\mathrm{fs}$; (b) average ionic charge-state resulting from the interaction of a sequence of two $30\mathrm{fs}$, $1.75\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$ Gaussian pulses with ${\mathrm{Xe}}_n$ clusters, where $n=64$ (solid squares), 108 (open squares), 302 (solid circles), 588 (open circles), 1524 (solid triangles), and 5056 (open triangles). The result of the optimal-control calculation given in (a) is shown as a star. The vertical lines indicate the times where the electron density $n_e$ of the plasma generated by the first pulse falls to $3n_{\mathrm{crit}}$. Very good agreement is observed between this time delay and the optimum delay between the two pulses.Reuse & Permissions