Recollision-induced plasmon excitation in strong laser fields

Recolliding electrons are responsible for many of the interesting phenomena observed in the interaction of strong laser fields with atoms and molecules. We show that in multielectron targets such as ${\mathrm{C}}_{60}$ an important recollision pathway opens up: the returning electron may excite collective modes even if the laser frequency is far off-resonant. We formulate a simple analytical theory which predicts that the recollision-induced excitation of collective modes should dominate over the “usual” harmonic generation yield at $800\mathrm{nm}$ wavelength. In this case the tomographic imaging of complex multielectron systems may be obscured. We employ a time-dependent density functional model of ${\mathrm{C}}_{60}$ and show that with increasing laser wavelength the dynamics becomes more and more single-active-electron–like, suggesting that long wavelengths are to be preferred for imaging purposes.

Figure 1

(Color online) Net KS potential (black, squares), total density (red, diamonds), wave functions of the lowest KS orbital and the HOMO (orange, crosses and triangles, respectively). The $\sigma$ and $\pi$ levels are indicated. Density and wave functions are scaled to fit into the plot.

Figure 2

Dipole response of the ${\mathrm{C}}_{60}$ model system. Narrow lines (single-particle transitions) on top of two broad structures (surface or Mie plasmon ${\omega }_{\mathrm{Mie}}\simeq 0.7$ and volume plasmon ${\omega }_{\mathrm{p}}\simeq 1.4$) are observed. The Mie plasmon corresponds to homogeneous dipolelike oscillations of the electron density with respect to the ions. The volume plasmon (in general a breathing mode) is visible in our dipole spectra since it contains a nonvanishing dipole component. The dipole strength is normalized such that its integral equals $N=250$.

Figure 3

(Color online) Harmonic spectra of the ${\mathrm{C}}_{60}$ model for Gaussian laser pulses with ${\omega }_{\mathrm{l}}=0.057$ ($\lambda =800\mathrm{nm}$, upper panel) and ${\omega }_{\mathrm{l}}=0.02$ ($\lambda =2280\mathrm{nm}$, lower panel). The values of $\widehat{E}$ are given in the plots. The linear response profile from Fig. 2 is included (dotted). The field amplitude $\widehat{E}=0.04$ corresponds to the intensity $5.6\times {10}^{13}\mathrm{W}∕{\mathrm{cm}}^2$.

Figure 4

(Color online) Harmonic spectra of the ${\mathrm{C}}_{60}$ model for $\widehat{E}=0.05$, ${\omega }_{\mathrm{l}}=0.057$ $(\lambda =800\mathrm{nm})$, and an eight-cycle trapezoidal laser pulse with two cycles up and down ramps [13]. The full spectrum and the one just from the valence KS electron (“HOMO only”) are shown. The linear dipole response from Fig. 2 is included (shifted vertically). The vertical arrow indicates the standard cutoff $3.17U_{\mathrm{p}}+\mid {ϵ}_{\mathrm{HOMO}}\mid$.

Figure 5

(Color online) Emission for ${\omega }_{\mathrm{l}}=0.02$ $(\lambda =2280\mathrm{nm})$ and $\widehat{E}=0.03$ (other parameters as in Fig. 4). The results from a full TDKS calculation (“full”) and a SAE simulation are shown. The linear dipole response from Fig. 2 is included (shifted vertically). The vertical arrow indicates the standard cutoff.

Figure 6

(Color online) Emission for ${\omega }_{\mathrm{l}}=0.013$ $(\lambda =3508\mathrm{nm})$ and $\widehat{E}=0.02$. The results from a full time-dependent KS calculation (“full”) and a SAE simulation are shown. The bold vertical arrow indicates the standard cutoff, the three thin vertical arrows local minima in the envelope of the full spectrum.

Figure 7

(Color online) The same as in Fig. 3, lower panel, for $\widehat{E}=0.01$ but two different grid sizes (indicated in the plot). The linear response profile from Fig. 2 is included again (dotted).

Figure 8

(Color) Logarithmically scaled contour plot of the time-frequency analyzed dipole emission ${\log }_{10}{\mid d_z(t,\omega )\mid }^2$ for the parameters of Fig. 5. The white lines indicate the classical solutions of returning electrons (see text). The positions of the Mie surface plasmon and the volume plasmon are indicated.

Figure 9

(Color online) Harmonic spectra $S\left(\omega \right)$, calculated from Eq. (12) for $\mathcal{l}=4$, $\mathcal{l}=0$, and $\mathcal{l}=4$ but twice the radius $R$. The laser parameters are the same as in Fig. 6 [${\omega }_{\mathrm{l}}=0.013$ $(\lambda =3508\mathrm{nm})$ and $\widehat{E}=0.02$]. $R=6.7$ and $\Delta =1.4$ was used. The three thin vertical arrows indicate local minima in the envelope of the spectrum for $\mathcal{l}=4$.