Momentum distribution of multiply charged ions produced by intense $(50–70\text{‐}\mathrm{PW}∕{\mathrm{cm}}^2)$ lasers

We investigate both theoretically and experimentally the momentum distribution of multiply charged ions ionized by an intense multicycle laser field with a maximum intensity of $\sim (50–70)\mathrm{PW}∕{\mathrm{cm}}^2$. Ions with different charge states are produced during a single laser shot due to a spatial variation of the laser intensity within the beam focus. The measurements show approximately a simple linear relation between the width of the momentum distributions and the ionization potential of the ions. Such a power law scaling appears to be universal for various rare gas atoms used (He, Ne, Ar). We analyze this ionization dynamics using a quasiclassical tunneling theory for a single active electron model assuming that the interaction between electrons is negligible in such a strong field limit. We show that for the relatively long pulses used in the present work ($\sim 200\mathrm{fs}$ or $\sim 80\text{cycles}$) the effect of the laser envelope plays an important role in the ionization process.

Figure 1

A schematic drawing of the time-of-flight analyzer.

Figure 2

Cross section of the laser beam in the focal plane (schematic picture). Intensity distribution is depicted as colored contour plot in log scale. The region where the corresponding ions are produced is indicated.

Figure 3

Longitudinal momentum distributions of ${\mathrm{Ne}}^{+}$. Solid line: measured distribution, dashed line: CTMC-T, and dotted line: ADK. For the CTMC, the number of equivalent electrons is set to $\alpha \left(1\right)=6$.

Figure 4

(Color online) Width (FWHM) of the ion momentum distribution as a function of $E_{\text{ion}}\left(q\right)$. The atoms are subject to a $200\mathrm{fs}$ laser pulse with a wavelength of $775\mathrm{nm}$ and a peak intensity of $50–70\mathrm{PW}∕{\mathrm{cm}}^2$. (a) Measured results (squares), (b) the results simulated by the CTMC-T (circles), and (c) the ADK estimates (triangles) are plotted. In (d) and (e) the different atomic species are plotted separately and the definition of the symbols is the same as in (a)–(c). The results are fitted to a power law $\Delta p\propto E_{\text{ion}}^{\gamma }$ and depicted by the dashed lines. In (c) a power-law behavior $\Delta p\propto E_{\text{ion}}^{9∕4}$ estimated by the ADK theory (see the text in detail) is also plotted (dotted line).

Figure 5

Momentum distribution width of the ${\mathrm{H}}^{+}$ ion driven by laser with a wavelength of $775\mathrm{nm}$ and pulse durations (25, 100, and $200\mathrm{fs}$). The width is plotted as a function of the peak intensity of the laser. (No intensity averaging is done.) In the ADK estimate the momentum width is evaluated using the peak intensity and independent of the pulse duration.