Strong-field effects in the photoemission spectrum of the ${\mathrm{C}}_{60}$ fullerene

Considering ${\text{C}}_{60}$ as a model system for describing field emission from the extremity of a carbon nanotip, we explore electron emission from this fullerene excited by an intense, near-infrared, few-cycle laser pulse (${10}^{13}–{10}^{14}\text{W}/{\text{cm}}^2$, 912 nm, 8-cycle). To this end, we use time-dependent density functional theory augmented by a self-interaction correction. The ionic background of ${\text{C}}_{60}$ is described by a soft jellium model. Particular attention is paid to the high-energy electrons. Comparing the spectra at different emission angles, we find that, as a major result of this study, the photoelectrons are strongly peaked along the laser polarization axis forming a highly collimated electron beam in the forward direction, especially for the high-energy electrons. Moreover, the high-energy plateau cutoff found in the simulations agrees well with estimates from the classical three-step model. We also investigate the buildup of the high-energy part of a photoelectron spectrum by a time-resolved analysis. In particular, the modulation on the plateau can be interpreted as contributions from intracycle and intercycle interferences.

Figure 1

(a) Color map of angle-resolved photoelectron spectra (ARPES) as a function of kinetic energy and emission angle, in logarithmic scale for the yield, from ${\text{C}}_{60}$ excited by a laser pulse with following parameters: ${\omega }_{\text{las}}=1.36$ eV, $T_{\mathrm{pulse}}=24$ fs, $I_{\mathrm{las}}=1.6\times {10}^{14}\text{W}/{\text{cm}}^2$. (b) PAD obtained from integration of the ARPES over the high-energy range of 50–160 eV, normalized to 1 at $0^{\circ }$. The dashed line marks the cone angle at full width at half maximum. (c) PES for emission angles at $\theta =0^{\circ },{30}^{\circ },{60}^{\circ },\mathrm{and}{90}^{\circ }$ (in logarithmic scale), with an arrow indicating the $10U_p$ cutoff energy.

Figure 2

Samples of photoelectron spectra in forward direction in ${\text{C}}_{60}$ irradiated by laser pulses with ${\omega }_{\text{las}}=1.36$ eV (912 nm), $T_{\mathrm{pulse}}=24$ fs, and four intensities as indicated $\left(I_0=2\times {10}^{13}\text{W}/{\text{cm}}^2\right)$. The curves are vertically shifted for a better graphical discrimination. Inset: zoom-in the region $0<E_{\mathrm{kin}}<13$ eV contributed by direct emissions.

Figure 3

Cutoff energies of the high-energy plateau in the PES as functions of the laser intensity, from TDLDA calculations compared with the estimate (8) deduced from the strong-field approximation (SFA).

Figure 4

Electronic dipole moment $D_z$ as a function of time (top row), and current density $j_z$ as a function of time and $z$ coordinate (bottom row, 2D density map) of ${\mathrm{C}}_{60}$ along laser polarization axis ($z$ direction), after irradiation by a laser pulse with ${\omega }_{\text{las}}=1.36$ eV, $T_{\mathrm{pulse}}=24$ fs, and with two different intensities $I_{\text{las}}=2.0\times {10}^{13}\text{W}/{\text{cm}}^2$ (left column) and $I_{\text{las}}=9.2\times {10}^{13}\text{W}/{\text{cm}}^2$ (right column). Positive $j_z$ are depicted in red (or gray), and negative $j_z$ are in green (or light gray). For a given color (or type of gray), the brighter the shade, the smaller the absolute value of $j_z$. The inset in the left bottom panel magnifies the map between 10 and 20 fs with a scale in current density divided by 100.

Figure 5

Time-resolved analysis of photoemission from ${\text{C}}_{60}$ irradiated by a laser pulse polarized in the $z$ direction, with ${\omega }_{\text{las}}=1.36$ eV, $T_{\mathrm{pulse}}=24$ fs, and $I_{\mathrm{las}}=1.6\times {10}^{14}\text{W}/{\text{cm}}^2$. (a) Time evolution of the force $F$ acting on electrons, with three “birth” times indicated by arrows (see text for details). (b) Time evolution of the total ionization $N_{\text{esc}}$, with three “final” times indicated by arrows and defined in Eqs. (10). (c) Full PES (black) and PES from data accumulated up to the three different final times.