Ionization of Clusters in Intense Laser Pulses through Collective Electron Dynamics

The motion of electrons and ions in medium-sized rare gas clusters ($\sim 1000$ atoms) exposed to intense laser pulses is studied microscopically by means of classical molecular dynamics using a hierarchical tree code. Pulse parameters for optimum ionization are found to be wavelength dependent. This resonant behavior is traced back to a collective electron oscillation inside the charged cluster. It is shown that this dynamics can be well described by a driven and damped harmonic oscillator allowing for a clear discrimination against other energy absorption mechanisms.

Figure 1

Average charge per atom from ${\mathrm{X}\mathrm{e}}_{561}$ clusters after laser impact according to Eq. (1) as a function of the pulse length $T$ or the peak intensity $I$, respectively, for three different laser wavelengths $\lambda$. The energy of the pulse, i.e., the product $I\times T$, is kept constant.

Figure 2

Dynamics of ${\mathrm{X}\mathrm{e}}_{923}$ in a strong laser pulse ($\lambda =780\mathrm{n}\mathrm{m}$, $I=9\times {10}^{14}\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$, rise and fall time 20 fs, plateau for $t=-80\dots +80\mathrm{f}\mathrm{s}$). All quantities are shown as a function of time $t$. (a) Average charge per atom (circles and fit from Eq. (2), left axis) and corresponding rate (gray filled line, right axis). (b) Radii $R$ of all cluster shells in units of their initial radii $R_0$. (c) Center-of-mass velocity $v_{\mathrm{C}\mathrm{M}}$ of the electronic cloud inside the cluster volume. Note that the oscillations are spatially along the linear polarization of the laser, whereas the electron velocity perpendicular to the laser polarization is very small and hard to see in the figure. (d) Phase shift ${\varphi }_t$ of the collective oscillation in the laser direction with respect to the driving laser; see text.

Figure 3

Driven and damped harmonic oscillator: amplitude $A$ and phase shift $\varphi$ as a function of the ratio of eigenfrequency $\Omega$ and driving frequency $\omega$ according to Eqs. (4) for different damping strengths $\Gamma$.

Figure 4

Parameters of the harmonic oscillator model (3) as calculated from the ${\mathrm{X}\mathrm{e}}_{923}$ dynamics in Fig. 2. Solid line: eigenfrequency for a spherical, uniformly charged cluster ${\Omega }_t=\sqrt{Q_{\mathrm{i}\mathrm{o}\mathrm{n}}(t)/R(t{)}^3}$. Circles: eigenfrequency ${\Omega }_t$ (6a). Diamonds: damping rate ${\Gamma }_t$ (6b). Dotted line: laser frequency $\omega$.