Attosecond physics in optical near fields

Abstract

Attosecond science, the electron control by the field of ultrashort laser pulses, is maturing into lightfield-driven electronics, called petahertz electronics. Based on optical field-driven nanostructures, elements for petahertz electronics have been demonstrated. These hinge on the understanding of the electron dynamics in the optical near field of the nanostructure. Here we show near field-induced low energy stripes (NILES) in carrier-envelope phase-dependent electron spectra, a new spectral feature appearing in the direct electrons emitted from a strongly driven nanostructure, i.e., in the easily accessible energy region between 0 and a few electron volts. NILES emerge due to the sub-cycle sensitivity of ponderomotive acceleration of electrons injected into a strong near field gradient by a few-cycle optical waveform. NILES enables us to track the emission of direct and re-scattered electrons down to sub-cycle time-scales and to infer the electron momentum width at emission. Because NILES shows up in the direct part of the electrons, a large fraction of the emitted electrons can now be steered in new ways, facilitating the isolation of individual electron bursts with high charge density of 430 attosecond duration. These results not only substantially advance the understanding of attosecond physics in optical near fields, but also provide new ways of electron control for the nascent field of petahertz electronics.

Figures (15)

• Figure 1: Near field-induced low energy stripes, NILES: a Electrons are photo-emitted by a two-cycle laser pulse and propagate in the steeply decaying ponderomotive potential resulting from the optical near field (red in zoom-in) at the apex of a sharp tungsten tip. With just $\sim$2 emission events per laser pulse, this leads to NILES (see text). b Measured electron energy spectra for two selected carrier-envelope phases (as indicated) shown on linear scale (orange, left axis) and logarithmic scale (gray, right axis). c CEP-resolved spectra. The high energy electrons show the well-known CEP-dependent energy modulation in the plateau ($\sim$10 to 40 eV) and the cut-off ($\sim$40 to 50 eV). In the low-energy region between $-2$ eV and 5 eV new spectral stripes appear prominently: NILES. d Zoom-in on the low-energy region of direct electrons showing NILES, on a linear yield scale. The large modulation depth of the integrated yield with CEP, reaching up to $33\,\%$ is noteworthy (see Methods). Lineouts of the low-energy region are shown in Extended Data Fig. \ref{['fig:lineouts_experiment']}. The energy of 30 eV resulting from the static voltage of $-30$ V applied to the tip is subtracted from the energy axis in c and d.
• Figure 1: Experimental setup.a Laser and ultra-high vacuum (UHV) system. PP: Pulse picker based on a Pockels cell. HNLF: highly non-linear fibre. FS: fused silica glass for dispersion compensation. OAP: off-axis parabolic mirror, mounted inside of the UHV chamber. DLD: delay-line detector with micro-channel plate in front, allowing single electron detection. CFD: constant fraction discriminator. TDC: time-to-digital converter. Electrons (blue) laser-emitted from the tungsten needle tip are accelerated to the electron detector. b Scanning electron micrograph of tip after FIB milling with close-up of the tip apex. The inner solid circle corresponds to a radius of curvature of $R =10nm$ and the outer one to $R = 20nm$. For more details see text.
• Figure 2: Origin of NILES: a,c Position- and time-dependent ponderomotive potential $U_\mathrm{P}(x,t)$ of (a) a homogeneous optical field profile and (c) an optical near field with decay length $\zeta=10nm$ as in the experiment. The projections (blue curves) indicate the respective spatial enhancement profiles and temporal intensity envelopes. The spatial gradient of this potential $\mathrm{d}U_\mathrm{P}(x,t)/\mathrm{d}x$ leads to a force acting on emitted electrons (surface color). Red curves show trajectories of electrons liberated at instants of vanishing vector potential in the dominant field half cycles and resulting from the ponderomotive (cycle-averaged) force acting on the electrons. These trajectories are called drift trajectories, resulting in the drift momentum. The grey curves, by contrast, show the corresponding trajectories obtained when the full field is taken into account. Importantly, they result in the same final momentum, the drift momentum. b,d Projections of the trajectories in position and time. The lowest possible drift momentum and respective minimum final energy is realized for electrons liberated at vector potentials $A(t)=0$ and becomes zero for a vanishing ponderomotive force, while additional ponderomotive acceleration results in non-vanishing minimum energies (compare red dots in b,d). The blue curve connecting the red spheres represents the minimum energy determined from full trajectories when varying the CEP. e Zoom-in to panel d: For increasing CEP the minimum energies shift continuously as indicated by the arrows. This results in two almost identical minimum energy curves for the full trajectories and the drift trajectories (compare blue and dashed red curves). Clearly, the drift trajectories contain already the full physics. Importantly, the separated stripes of NILES result from the fact that the red dots are sparse on this curve and hence display a large energy difference exceeding $\sim1.2eV$. The orange curve shows the analytical upper estimate for the minimum energy curve (MEC) as detailed in the main text.
• Figure 2: FROG measurement.a Experimental second-harmonic FROG trace (upper panel) with close-up (lower panel). b Reconstructed FROG trace. c Retrieved temporal intensity with a $\tau_\mathrm{FWHM} = 11.5fs$
• Figure 3: Decay length dependence of NILES: a-c Semi-classical simulations of electron spectra for three near field decay lengths as indicated above each panel and corresponding to (a) a planar surface, (b) a medium-sharp tip and (c) a sharp tip as used in the experiment. The near field peak intensity was fixed at $2e13W/cm^2$. Clearly, NILES appear only for inhomogeneous near field profiles (b,c) and extend up to 2 eV for the experimental parameters (c). The slope of NILES sampled in the central region increases from $0.76$ eV/$(2\pi)$ in (b) to $1.5$ eV/$(2\pi)$ in (c). We note that the slope scales indirectly proportional to the pulse duration, resulting in vanishing NILES features for long pulses (see Methods). The circles labeled 1 to 4 indicate different emission times within a selected half cycle. d Tracking of the emission time by modulating the CEP. With respect to the homogeneous field case (energy $E=0$, black line), emission before the center of the pulse (1, 2) leads to an energy up-shift, while a later emission (4) results in an energy down-shift (indicated by the colored arrows). This behavior is given mainly by the MEC (cf. Fig. \ref{['fig:explanation_NILES_Rostock']}e); the shift to energies below $E=0$ is due to the fact that we now included the DC bias voltage applied to the tip (see Methods). The labels 1-4 relate directly to the corresponding one in panel c. We stress the excellent overall agreement of the numerical results in panel c with the experimental NILES data of Fig. \ref{['fig:experiment_NILES']}. We have applied a Gaussian blurring filter of 0.3 eV (FWHM) to the semi-classical simulation results to account for the finite energy resolution of the detector in the experiment. As in Fig. \ref{['fig:experiment_NILES']}, the energy resulting from the tip bias voltage is subtracted from the energy axis (see Methods).