Multislit interference patterns in high-order harmonic generation in ${\mathrm{C}}_{60}$

We study high-order harmonic generation in ${\mathrm{C}}_{60}$ molecules interacting with a linearly polarized intense short laser pulse at near- and mid-infrared wavelengths, using an extension of the so-called three-step or Lewenstein model to the molecular case. The results exhibit modulations in the plateaus of the spectra at the longer wavelengths, which are present for ensembles of aligned as well as randomly oriented fullerenes. The analysis of the results show that the minima can be explained by a multislit interference effect arising from the contributions of the 60 atomic centers to the dipole moment. Good agreement between the positions of the minima in the spectra obtained in the length gauge are found with those of the recombination matrix element, but not for those in the velocity gauge calculations. We further use a simple spherical model to analyze how geometrical information, such as the radius of the fullerene cage, can be obtained from the interference pattern in the harmonic spectra.

Figure 1

HHG spectra for an ensemble of aligned ${\mathrm{C}}_{60}$ molecules at $\lambda =\left(\text{a}\right)800$ and (b) $1800\mathrm{nm}$ and a peak laser intensity of $I_0=5\times {10}^{13}\mathrm{W}∕{\mathrm{cm}}^2$, a pulse duration of $30\mathrm{fs}$, and a ${\sin }^2$ pulse shape. The spectra are obtained for the $h_u$ HOMO in length gauge; the arrows indicate the cutoff of the plateau as predicted from the semiclassical model [35]. (c) Recombination matrix element as obtained from the full calculation (solid line), the incoherent sum of the contributions from the atomic centers (dotted line), and the spherical model (dashed line). For the presentation of the recombination matrix element as a function of the harmonic order $n$, we have used the relation $n{\omega }_{1800}=k^2∕2+I_p$ with frequency ${\omega }_{1800}=0.0253\mathrm{a.u.}$ $(\lambda =1800\mathrm{nm})$ and $I_p=0.272\mathrm{a.u.}$

Figure 2

HHG spectra at $\lambda =\left(\mathrm{a}\right)$ 800 and (b) $1800\mathrm{nm}$ using the velocity gauge. The other parameters are as in Fig. 1. (c) Ionization matrix element as a function of the harmonic order. Solid line, full calculation; dotted line, incoherent sum of the partial contributions.

Figure 3

High-harmonic spectrum for an ensemble of randomly oriented ${\mathrm{C}}_{60}$ molecules ($h_u$ HOMO) using (a) the velocity and (b) the length gauge. Laser parameters are as in Fig. 1b. (c) Comparison of the corresponding recombination matrix elements obtained from the full calculation (solid line) and from the spherical model (dashed line).

Figure 4

Same as Fig. 3 but for the $h_g$ $\mathrm{HOMO}-1$.

Figure 5

Same as Fig. 3 but for the $g_g$ $\mathrm{HOMO}-2$.