Strong-field electron emission from gold needle tips

Tungsten and gold needle tips are the most commonly used nanostructures for studying the light-matter interaction in the strong-field regime.^1,2 Both metals can be easily brought into a tip shape with a radius of only a few nanometers. This small tip radius leads to an enhanced optical near-field at the tip apex.³ Plasmonic effects at the surface in the near-infrared to infrared range may further increase the field enhancement. Here, the field enhancement factor is defined as the ratio $ξ=| E nf|/| E in|$ with the optical near-field $E nf$ present at the tip apex and the incident light field $E in$⁠. Over the past two decades, a plethora of experiments have been performed that extracted fundamental key parameters of electron emission and dynamics in these model systems.^2,4–17 In the perturbative (weak field) regime, multiphoton physics can be studied, where the electron energy spectra show effects like above-threshold photoemission (ATP).^12,18 At higher intensities, where the ponderomotive energy of the light field becomes important, strong-field phenomena appear, initially known from atoms.¹⁹ Many experiments around tungsten tips have shown the full variety of these effects.^{8,12,16,18,20} With gold, ATP peaks have so far been shown at flat substrates^21–23 and at gold needle tips.²⁴ Here, we show strong-field emission spectra from gold tips triggered by two different femtosecond laser sources, delivering 170 fs (full width at half maximum, FWHM) pulses at 1550 nm central wavelength and 12 fs (FWHM) pulses at 800 nm wavelength. For both wavelengths, we observe spectra that are clearly modulated by multiphoton peaks and show a plateau in the high-energy part. The presence of multiphoton peaks implies an electronic coherence time of the emitted electrons larger than one optical cycle.

In the experiment, we use gold tips, which we fabricate in a two-step process. Gold wires are etched in a lamellae-drop-off technique with 90% saturated aqueous solution of potassium chloride. Afterward, they are polished in a solution with acetone, calcium chloride dihydrate, and distilled water by applying an alternating potential up to 10 V with a frequency of 2 kHz for 6 s (see also Ref. 25). We achieve clean surfaces and attain typical radii of 15–50 nm, which we determine using a scanning electron microscope.

The metal needle tips are placed inside an ultrahigh vacuum chamber with a base pressure of $p< 10 − 9$ hPa. To remove remnants of the etching process from the tip surface, we use field evaporation in field ion microscopy (FIM) mode by applying a high static positive voltage together with argon as imaging gas. For tungsten tips, FIM represents a well established method to determine the tip radius.²⁶ For gold tips, this is harder without cooling the sample, but cooling is not available in our setup. Nevertheless, evaporation of remnants still takes place thus cleaning the tip's surface.

We use two different laser systems (see Fig. 1). The first system is based on an erbium fiber oscillator with fiber amplifier, which has a central wavelength of 1550 nm and a pulse duration of 170 fs (IR-system). This system is passively carrier-envelope phase-stable. We use a Pockels cell to reduce the repetition rate of the erbium laser from 80 MHz down to 200 kHz. The second system is an amplified titanium sapphire laser at a central wavelength of 800 nm with 12 fs pulse duration also operating at a repetition rate of 200 kHz (NIR-system). The laser pulses are focused on the respective tip by an off-axis parabolic mirror with a focal length of 15 mm. The typical beam waist in the focus is $∼2 μ m$ for 800 nm and $∼5 μ m$ for 1550 nm (⁠ $1/ e 2$-intensity radius). We use a variable neutral density wheel to adjust the intensity in the experiment.

For the electron photoemission experiments, we apply a negative bias at the tip of around a few tens of Volts. When triggered by the laser pulses, the electrons are accelerated toward a DLD. With it, we measure the position and the time of flight of each electron for every laser pulse. From this information, we can calculate the energy of every electron individually (for more details, see Ref. 14). The energy resolution of our detector is $∼0.3$ eV for the highest observed kinetic energies of 40 eV, and for smaller energies even better. (Furthermore, our detector is capable of measuring multiple electrons per laser pulse; however, we do not exploit this capability here. Multielectron effects will be the subject of future research.) The high repetition rate of our laser systems compared to standard amplified kHz laser systems and the shot-to-shot resolution of the detector allow us to measure electron spectra with a high dynamic range on the minute time scale. Our system is, therefore, highly advantageous for measuring any kind of energy-resolved parameter sweep, e.g., as a function of the pulse energy, the carrier-envelope phase,⁸ or in a pump-probe configuration.

In Fig. 2(a), we show the electron energy spectra as a function of the incident pulse energy (color coded) on a semilogarithmic scale for the 1550 nm-IR-system. For increasing near-field intensity, the spectra broaden and the integrated count rate increases. The spectra consist of three distinct regions: (1) directly emitted electrons (first linear decay as a function of energy), (2) the strong-field plateau with nearly constant electron count rate, and (3) the drop-off (second linear decay).^1,2,19,27 The strong-field plateau is a consequence of electrons that rescatter after emission with the tip surface and gain additional energy in the laser field.^19,28,29 The transition region between (2) and (3) is known as the 10- $U P$-cutoff and can be used as an intrinsic measure for the near-field intensity directly at the tip apex.³⁰ Here, $U P= e 2 E 0 2/4m ω 2$ is the ponderomotive energy of the electron in the laser field with the peak electric field $E 0$⁠, the mass of the electron $m$⁠, the charge of the electron $e$⁠, and the angular frequency of the laser field $ω$⁠. We use two linear fits (dashed lines) in the semilogarithmic representation to determine this cutoff. The intersection between these fits is indicated by a gray circle in Fig. 2(a). This cut-off scales linearly as a function of the incident ponderomotive energy of the laser field [Fig. 2(b)]. From the slope of this linear fit, we can directly determine the field enhancement factor, which in this case is $ξ=18.1±2.0$⁠. In Fig. 2(c), we show how the mean number of emitted electrons per laser pulse $μ e$ scales as a function of the near-field intensity (extracted from the cutoffs) on a double-logarithmic axis. From the slope, we can extract the nonlinearity of the emission process of $n=3.7$ (see discussion below). Furthermore, our electron spectra show a periodic modulation almost up to the respective cutoff, spaced by the photon energy of 0.8 eV. The inset in (a) shows a zoom of the plateau region for better visibility. Overall, the spectra show a model-like behavior as expected from solving the time-dependent Schrödinger equation (TDSE) and are an ideally suited example to benchmark current and future theory models¹—the main reason for this article. For the TDSE, typically an electron in a box model is assumed, similar to the atomic case. Although this model holds true astonishingly well,¹⁷ it cannot be the full reality for a real metal. For such a solid state system, multielectron effects inside the metal can potentially influence the emission process and the coherence time of the electrons. One potential approach for including such effects could be time-dependent density functional theory.³¹ Finding the difference between such models and the data, for example, can shed more light on the electron emission processes and the electron dynamics of electrons in strong laser fields of real metals.

Figure 3 shows the same measurement as in Fig. 2 but now for the NIR pulses centered at 800 nm wavelength. Note that the two measurements are obtained with two different but comparable tips. We observe a similar behavior of the spectral shape and nonlinear increase of the emission yield as compared to the pulses at 1550 nm. Here, the spectra change from almost completely perturbative distributions (linear decay, nearly no plateau visible) to clear strong-field dominated spectra with the aforementioned three different regions. Again, we extract the field enhancement factor from the scaling between the incident ponderomotive energy of the laser field and the cut-off energy [Fig. 3(b)]. We obtain a field enhancement of $ξ=4.7±0.4$⁠. Furthermore, we observe a nonlinearity of $n=3.1$ of the emission process in Fig. 3(c). The spectra are highly modulated by ATP peaks spaced by the photon energy of 1.6 eV in this case. For higher intensities and higher count rates, these peaks start to wash out. This decrease in contrast likely arises from Coulomb interactions after the emission when more than one electron is emitted within one laser pulse.^14,15,32 How the presence of more than one electron during the emission process affects the coherence time and, therefore, the modulation depth of the ATP peaks will be investigated in future studies.

Standard strong-field experiments around metal needle tips require typically few femtosecond laser pulses to achieve sufficiently high intensities to observe a clear plateau without damaging the tip, as shown in Fig. 3. Our measurements at 1550 nm are in contrast to this: Relatively long pulses of 170 fs duration suffice to reach model-like strong-field emission spectra. Two key parameters are favorable for obtaining such spectra. First, the ponderomotive energy of the laser field scales quadratically with the wavelength. In this case, doubling the wavelength from 800 to 1550 nm gives an almost four times higher ponderomotive energy for equivalent peak intensity, thus a four times higher cutoff. Second, the field enhancement is higher for the infrared region compared to the near-infrared because of the scaling invariance of Maxwell equations.³³ Furthermore, the dielectric function of gold is $ϵ(800 nm)=−24.1+i⋅1.5$ and $ϵ(1550 nm)=−115+i⋅11.6$ at 1550 nm. Because of the large negative real part and the comparably small imaginary part, plasmonic effects can increase the field enhancement even further.^3,33

Interestingly, these plasmonic effects, present for both wavelengths, do not prevent the appearance of ATP peaks. In the strong-field regime, the presence of multiphoton peaks can be explained by two (or more) emission slits in time, separated by the optical cycle, leading to interference of the electron matter waves in the energy domain.^1,8,34 The more such emission points in time contribute coherently to the spectra, the higher is the contrast of the multiphoton peaks, in analogy to optical multislit experiments. As a consequence, the coherence time of the electrons including the plasmonic effects present at the tip apex must be larger than one optical cycle, i.e., $2.7$ fs (800 nm) and $5.2$ fs (1550 nm). This lower bound is in agreement with experiments measuring the dephasing time of plasmons by Rayleigh scattering from gold needle tips.³⁵ In principle, our spectra allow us to determine the width of the multiphoton peaks as no postprocessing of the spectra is necessary. A future in-depth analysis of the multiphoton peak width will help us to determine the coherence time but is beyond the scope of this work.

Last, let us comment on the observed nonlinearity of the photoemission processes. The work function of gold is approximately $Φ≈5$ eV. Therefore, the nonlinearity $n=3.1$ for 800 nm (1.5 eV photon energy) matches quite well the multiphoton picture, where on average, three photons are required to lift an electron from the Fermi level into vacuum. In this picture, one would expect that the nonlinearity increases by a factor of roughly two when going to 1550 nm. The observed nonlinearity of $n=3.7$ at 1550 nm, however, is much smaller, which can be explained by the Keldysh rate.³⁶ As an example, for a peak intensity of $I=1× 10 13 W / c m 2$⁠, the Keldysh parameter equals $γ=0.96$ for 1550 nm, and $γ=1.9$ for 800 nm. Both values indicate that the emission processes lie in the transition region between the multiphoton $γ≫1$ and the tunneling regime $γ≪1$⁠. Therefore, the lowering of nonlinearity is more pronounced at 1550 nm as emission takes place deeper in the tunneling regime.³⁷ 

In summary, we have shown electron energy spectra from gold needle tips that are triggered by two different pulsed laser beams, one at 1550 nm central wavelength and the other at 800 nm. In both cases, we observe strong-field features like the rescattering plateau together with clearly resolved above-threshold photoemission peaks. These spectra behave as predicted by theory and can serve as a benchmark for theoretical models.

Although small spectral bandwidths are favorable to study the coherence time of electrons related to the ATP width, using a shorter pulse duration at 1550 nm could be highly beneficial in the future. Shorter pulses will allow us to venture further into the strong-field regime. In combination with carrier-envelope phase-dependent or two-color measurements, deep insights into the emission physics can be gained.^16,17 Such measurements could determine how the temporal emission window changes under the presence of plasmons at the tip surface (see supplement of Ref. 17).

This research was supported by the European Research Council (Consolidator Grant NearFieldAtto and Advanced Grant AccelOnChip) and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Project-ID 429529648: TRR 306 QuCoLiMa (“Quantum Cooperativity of Light and Matter”), and SFB 953 (“Synthetic Carbon Allotropes”), Project-ID 182849149. J.H. acknowledges funding from the Max Planck School of Photonics.

The authors have no conflicts to disclose.

Jonas Heimerl and Stefan Meier contributed equally to this paper.

Jonas Heimerl: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Stefan Meier: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Adrian Kirchner: Conceptualization (supporting); Investigation (supporting); Writing – review & editing (supporting). Tobias Weitz: Conceptualization (supporting); Investigation (supporting); Writing – review & editing (supporting). Peter Hommelhoff: Funding acquisition (equal); Investigation (equal); Project administration (equal); Resources (equal); Supervision (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.