Nonlinear Resonance Absorption in the Laser-Cluster Interaction

Rare-gas or metal clusters are known to absorb laser energy very efficiently. Upon cluster expansion, the Mie plasma frequency may become equal to the laser frequency. This linear resonance has been well studied both experimentally and theoretically employing pump probe schemes. In this work, we focus on the few-cycle regime or the early stage of the cluster dynamics, where linear resonance is not met but, nevertheless, efficient absorption of laser energy persists. By retrieving time-dependent oscillator frequencies from particle-in-cell simulation results, we show that nonlinear resonance is the dominant mechanism behind outer ionization and energy absorption in near infrared laser-driven clusters.

Figure 1

Laser absorption vs driver amplitude in the rigid sphere model (2) for ${\omega }_{\mathrm{Mie}}/{\omega }_{\mathrm{l}}=2.7$, $E(\tau )=-E_0{sin}^2(\tau /2n)\cos (\tau )$, $n=10$. The nonlinear resonance is passed once the threshold driver amplitude $\simeq 3.0$ is reached.

Figure 2

Typical behavior of $[{\omega }_{\mathrm{eff}}(\tau )/{\omega }_{\mathrm{l}}{]}^2$ (red, upper curve) vs time above the threshold driver strength in Fig. 1 (actual value was $E_0/R{\omega }_{\mathrm{l}}^2=3.3$). Excursion $z/R$ (black, middle curve) and energy of the electron sphere $E_{\mathrm{tot}}/R^2{\omega }_{\mathrm{l}}^2$ (green, lower curve) are included in the plot. Outer ionization (i.e., $E_{\mathrm{tot}}/R^2{\omega }_{\mathrm{l}}^2\ge 0$) and occurrence of nonlinear resonance $[{\omega }_{\mathrm{eff}}(\tau )/{\omega }_{\mathrm{l}}{]}^2=1$ (dashed-dotted line) always coincide (vertical line).

Figure 3

PIC results for a ${\mathrm{Xe}}_{1600}$ cluster ($R=3.2\mathrm{nm}$). Total absorbed energy per electron in units of $U_{\mathrm{p}}$ vs laser intensity for charge densities between 20 and 100 times the critical density, corresponding to average charge states between 1.6 and 8. The prediction of the RSM for $\rho /{\rho }_{\mathrm{c}}=40$ is included in the plot (dashed line).

Figure 4

Snapshot of PIC electrons in the frequency vs energy plane at times (a) $t=2.5$, (b) $t=3.0$, (c) $t=3.5$, and (d) $t=4.0$ laser cycles. The laser intensity was $2.5\times {10}^{16}\mathrm{W}{\mathrm{cm}}^{-2}$ and $({\omega }_{\mathrm{Mie}}/{\omega }_{\mathrm{l}}{)}^2=40/3$. Other parameters as in Fig. 3. The radial positions (in units of $R$) are color-coded. Electrons become free upon crossing the nonlinear resonance, i.e., $({\omega }_{\mathrm{eff}}^2/{\omega }_{\mathrm{l}}^2,E_{\mathrm{tot}}/U_{\mathrm{p}})=(1,0)$. At that time, the radial position is $r\simeq 2$.