Direct and Indirect Pathways in Strong Field Atomic Ionization Dynamics

With the help of a suitably chosen momentum-space analysis, we study some of the basic mechanisms governing the physics of the processes occurring when atoms are submitted to intense infrared laser pulses, with peak intensities ${10}^{14}\mathrm{W}{\mathrm{c}\mathrm{m}}^{-2}\le I_{\mathrm{m}\mathrm{a}\mathrm{x}}\le {10}^{15}\mathrm{W}{\mathrm{c}\mathrm{m}}^{-2}$. This intensity range is especially interesting because two highly nonlinear atomic processes, namely, above threshold ionization and high-order harmonic generation, take place with significant probabilities. Several issues regarding the dynamics of these processes are resolved, with special attention devoted to the mechanism leading to the ejection of the photoelectrons in this intensity range.

Figure 1

Electron probability density as a function of time and $p_z$, for the interaction of H with an eight-cycle pulse with $I_0=2\times {10}^{14}\mathrm{W}{\mathrm{c}\mathrm{m}}^{-2}$ and $\omega =0.057\mathrm{a}\mathrm{.}\mathrm{u}\mathrm{.}$ $p_n=0$ and the solid line represents $A(t)$.

Figure 2

Average instantaneous velocity along $\mathbf{z}$ as a function of $A(t)$ (same pulse shape as in Fig. 1). (a) $I={10}^{14}\mathrm{W}{\mathrm{c}\mathrm{m}}^{-2}$; (b) $I=2\times {10}^{14}\mathrm{W}{\mathrm{c}\mathrm{m}}^{-2}$.

Figure 3

(a) $P(p_n,t)$ as defined by Eq. (8) for a sine square laser pulse of full duration $\Delta t=4T$ (optical cycle), $I_0=5\times {10}^{14}\mathrm{W}{\mathrm{c}\mathrm{m}}^{-2}$, $\omega =0.057\mathrm{a}\mathrm{.}\mathrm{u}\mathrm{.}$ Dashed line is the normalized instantaneous intensity. (b) $P_{\mathrm{i}\mathrm{o}\mathrm{n}}(p_n)$ extracted from our TDSE results, $P_{\mathrm{i}\mathrm{o}\mathrm{n}}^{\mathrm{S}\mathrm{F}\mathrm{A}}(p_n)$ [see Eq. (9)] and the dc tunneling prediction; see [18].

Figure 4

(a) $p_z^{\mathrm{i}\mathrm{o}\mathrm{n}}=-A(t_{\mathrm{i}\mathrm{o}\mathrm{n}})$ [see Eq. (5) and text]. (b) $F_{12}^{(+)/(-)}(t)$ [see Eq. (10)] for two symmetric intervals $0.25<|p_z|<0.5\mathrm{a}\mathrm{.}\mathrm{u}\mathrm{.}$ [same field parameters as in Fig. 3a]. In (a), between brackets, ionization fractions due to (direct, indirect) calculated on a wider interval $|p_z|<1\mathrm{a}\mathrm{.}\mathrm{u}\mathrm{.}$ It reveals that $26/37\approx 70\%$ comes from an indirect process and $11/37\approx 30\%$ from a direct one.