Electron rescattering at metal nanotips induced by ultrashort laser pulses

We investigate plateau and cutoff structures in photoelectron spectra from nanoscale metal tips interacting with few-cycle near-infrared laser pulses. These hallmarks of electron rescattering, well-known from atom-laser interaction in the strong-field regime, appear at remarkably low laser intensities with nominal Keldysh parameters of the order of $\gtrsim 10$. Quantum and quasiclassical simulations reveal that a large field enhancement near the tip and the increased backscattering probability at a solid-state target play a key role. Plateau electrons are by an order of magnitude more abundant than in comparable atomic spectra, reflecting the high density of target atoms at the surface. The position of the cutoff serves as an in situ probe for the locally enhanced electric field at the tip apex.

Figure 1

Energy spectra of electrons emitted from a tungsten nanotip (radius about 6 nm) interacting with moderately intense laser pulses. Plateau and cutoff regions have been highlighted with lines. The energy axis is referenced to the Fermi level. The electronic kinetic energy is reduced by the work function of the tip ($W_{\mathrm{W}}\left(310\right)=4.35$ eV). The black dots show the cutoff energies $E_{\mathrm{cut}}$ determined from the intersection points of the lines as a function of intensity. The solid black line fit shows the linear increase of $E_{\mathrm{cut}}$ with increasing intensity. The inset shows the orientation of tip and laser beam.

Figure 2

Close-up of tip apex (200 $\times$ 200 nm${}^2$) (inset: overview with 1200 $\times$ 1200 nm${}^2$): cut through the distribution of field strengths $F_z$ along the direction of the tip axis with a tip radius of 10 nm. To visualize the phase shift, the distance in $\vec{k}$ direction is given in units of $\lambda$. The presence of the tip visibly distorts the electric field. While the exciting field has a zero crossing near $x=0$ in $\vec{k}$ direction (black dotted line) the electric field at the apex is near its maximum [purple (dark shaded)]. Here, the field is enhanced by about a factor of 5, $\Delta {\phi }_{\mathrm{CEP}}\approx 0.45\pi$, and falls off to the nominal field amplitude within 15 nm (narrow dotted line $z\sim 15$ nm from tip apex, $z$ much larger than the quiver amplitude in the enhanced field $a_q<0.5$ nm).

Figure 3

Time-dependent change in electron density $\left|\delta n\right(z,t\left)\right|=\left|n\right(z,t)-n(z,-\infty \left)\right|$ on a logarithmic scale for a one-dimensional metal slab irradiated by a 6.5-fs laser pulse. The slope of equally colored lines signifies the momentum of emitted electrons. The color scale changes from logarithmic ($z>0$) to linear ($z<0$) at the surface. Electrons emitted near the field maxima (white solid line indicates $F+F_{\mathrm{dc}}$) are in part driven back to the surface leading to rescattering, wave packets from subsequent cycles interfere (stripes visible for $z>50$ a.u., maxima indicated by arrows).

Figure 4

Comparison of experimental and CEP averaged simulated spectra for a 6.5-fs laser pulse impinging on a tungsten tip. TDDFT results (solid lines) for different intensities are compared with an experimental spectrum (symbols) for $I_0=1.7\times {10}^{11}$ W/cm${}^2$ ($F_0\approx 2.2\times {10}^{-3}$ a.u.) and a classical simulation (green dotted line) for an intensity of $I_{\mathrm{eff}}={10}^{13}$ W/cm${}^2$ ($F_0\approx 1.7\times {10}^{-2}$ a.u.). The classical simulation has been scaled to match the plateau height of the TDDFT result with identical intensity.