Nonadiabatic ponderomotive effects in photoemission from nanotips in intense midinfrared laser fields

Transient near fields around metallic nanotips drive many applications, including the generation of ultrafast electron pulses and their use in electron microscopy. We have investigated the electron emission from a gold nanotip driven by midinfrared few-cycle laser pulses. We identify a low-energy peak in the kinetic energy spectrum and study its shift to higher energies with increasing laser intensities from 1.7 to $8.9\times {10}^{11}\mathrm{W}/{\mathrm{cm}}^2$. The experimental observation of the upshift of the low-energy peak is compared to a simple model and numerical simulations, which show that the decay of the near field on a nanometer scale results in nonadiabatic transfer of the ponderomotive potential to the kinetic energy of emitted electrons and in turn to a shift of the peak. We derive an analytic expression for the nonadiabatic ponderomotive shift, which, after the previously found quenching of the quiver motion, completes the understanding of the role of inhomogeneous fields in strong-field photoemission from nanostructures.

Figure 1

Experimental setup. (a) NOPA DFG setup, which is seeded by a multipass chirped-pulse amplification Innoslab amplifier. (b) Vacuum chamber hosting the experimental setup for the photoemission experiments along with an imaging setup used for coarse optimization of tip position and focus size. (c) Spectrum of the laser pulses used in the experiments.

Figure 2

(a) Experimental spectra from a gold nanotip under irradiation for the indicated incident intensities. (b) Low-energy region of the above spectra; dots indicate LEP positions $E_{\mathrm{LEP}}$. (c) Low-energy peak position versus incident intensity. For low intensities an approximately linear dependence with a slope of $15.5U_p$ is found (solid line).

Figure 3

(a) Final kinetic energy for different values of the adiabaticity parameter for a cw laser in terms of the oscillation period $T_0$ and $U_p$. Direct (rescattered) electrons are indicated as solid (dashed) lines. The gray area shows the emission probability according to Fowler-Nordheim tunneling (work function 5.5 eV, intensity $3\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$) on a linear scale from 0 to 1. (b) Electron spectra resulting from weighting the final energies with the emission probability. Clear low-energy peaks appear, whose position is given by the minima in the left plot. (c) Trajectory of a direct electron illustrating the definition of the quiver amplitude $l_q$ and field decay length $l_f$. (d) Positions $E_{\mathrm{LEP}}$ normalized by the ponderomotive potential against the inverse quiver amplitude (proportional to $\delta$) together with the expectations from the analytic expression (shaded area) for a field decay length of $4.5\pm 0.5\mathrm{nm}$ and a field enhancement factor of $5.5\pm 0.5$. (e) Dependence of the lowest final kinetic energy of electrons emitted during the central cycle of a Gaussian pulse on the adiabaticity parameter for different pulse lengths for all CEPs (shaded areas) together with $E_{\mathrm{shift},p}/U_p$ (dashed lines), the heuristic fit to the cw curve (dotted line), and the analytic expression (solid lines) as described in the text.

Figure 4

(a) Simulated energy spectra of electron emission from a gold nanotip with an assumed near-field decay length of approximately $4.5\mathrm{nm}$ for the indicated input intensities. (b) Extended view of the low-energy region, illustrating the shift of low-energy peaks. (c) Electric field $\mathcal{E}$ of the laser pulse (solid line) used to simulate electron trajectories along with their half-cycle emission probability (shaded areas). (d)–(f) Final kinetic energies attained by each electron emitted from the tip surface at different half cycles of the laser pulse (only shown for $I=8.3\times {10}^{11}\mathrm{W}/{\mathrm{cm}}^2$). The turning points (marked above the dotted lines) contribute to the low-energy peaks in the spectra and are indicated in (b).