Coherent control at gold needle tips approaching the strong-field regime

The resonant enhancement of local optical fields and waveguide-like delivery of optical excitation energy make plasmonic structures ideal platforms for light–matter interaction [1, 2] resulting in unique sensing capabilities from detecting single-molecule Raman-scattering [3] to scanning-nearfield microscopy [4].

Plasmonics also gained more and more interest in the realm of strong-field physics as field-driven phenomena such as high-harmonic generation (HHG), attosecond pulse generation, and electron rescattering were explored for dielectrics and metals [5–9]. The solid-state nature of plasmonic structures and their strong enhancement of incident fields resulted in on-chip structures sensitive to the waveform of light [10, 11], ultrafast electron emitters [12–18], and hybrid devices providing nearfield-enhanced HHG from solids [19].

Apart from specially designed targets, using tailored waveforms has proven extremely successful in coherently controlling and probing ultrafast processes [20] initially demonstrated for semiconductors [21, 22]. The idea of symmetry-breaking with light fields [23] has since been realized for atomic, molecular, and solid-state systems by shaping the polarization and spectral phase of laser pulses [24, 25] or superimposing multiple fields of different colors [22, 26], [27], [28], [29]. Coherent control at plasmonic nanostructures applies to the nearfield distribution [30, 31] and as recently shown to govern the emitted photocurrent in the perturbative regime [32]. Here, the total yield emitted from a gold tip can be modulated with visibilities in excess of 95% and being comparable to tungsten [33–35] using a two-color laser field.

In this letter we demonstrate that two-color coherent control of the emitted current maintains a high visibility even for intense broadband excitation pulses and approaching the strong-field regime. To verify the presence of field-driven dynamics we show electron energy spectra with clear rescattering signatures.

In the experiment few-cycle fundamental pulses centered on 1560 nm with 9 fs duration and their phase-locked second harmonic centered on 780 nm with 8 fs duration are tightly focused onto the apex of a gold needle tip as sketched in Figure 1. The tip with an apex radius of curvature around 20 nm emits electrons, which are counted by a multichannel plate (MCP) detector as a function of the delay τ between both laser fields. The polarization of both fields is matched to the symmetry axis of the tip. A retarding field spectrometer can be moved in front of the tip instead of the MCP detector to provide energy-resolved electron spectra. A static bias voltage of U _DC = −980 V is applied to the tip for measurements conducted with the grounded MCP. For spectrally resolved measurements the spectrometer is biased with +50 V against the grounded tip.

Figure 1:

Experimental setup. Few-cycle two-color laser pulses emit electrons from a nanometer sharp gold needle tip. The emitted yield is recorded by a multi-channel plate detector as a function of the delay τ between the fundamental field and its second harmonic. Alternatively, energy-resolved spectra are obtained by a retarding field analyzer.

Figure 2(a) shows the electron count rate as a function of the optical delay, which is strongly modulated when both few-cycle fields are close to perfect temporal overlap. This coherent control scheme allows us to either suppress or strongly enhance the electron emission. The visibility defined by

with maximum count rate N _max and minimum count rate N _min obtained from a fit curve reaches values of V = (80 ± 4)% as shown in the left inset of Figure 1(a). The visibility does not reach the 96.5% level as in the case of multi-cycle driving fields [32], most likely due to the complex temporal shapes and broad spectral bandwidths of the involved pulses. The remaining high-order chirp after the pulse compression and second harmonic generation stage is causing the side structure in the delay scan around ±40 fs. The temporally more confined coherent signal results in broad frequency components centered around the DC and second harmonic frequency 2ω/(2π) in the Fourier spectrum of the delay scan (right inset). A 4ω component with a peak height around one magnitude below the 2ω component was observed for long and weak driving pulses and can be explained by an additional quantum pathway, which is the exchange of two 2ω photons with four ω photons. The increased height of the 4ω peak in the case of gold compared to tungsten could be attributed to the different effective barrier heights of the two materials using simulations based on the time-dependent Schrödinger equation [32]. Here, however, the reduced signal-to-noise level of the broad components likely conceals the 4ω component.

Figure 2:

Coherent control and strong-field rescattering signatures. (a) Electron count rate as a function of the delay between fundamental and second harmonic field for a gold tip. Left inset shows the center of the temporal overlap with a sinusoidal fit (red line) used to determine the visibility at a fundamental nearfield intensity of I _ω = 3.8 TW/cm² and second harmonic intensity of I _2ω = 440 GW/cm². Right inset: Frequency spectrum obtained via Fourier transform from the ω − 2ω delay trace shown. Broadband components centered around the DC and 2ω/(2π) frequencies are labeled as regions of interest ROI_DC and ROI_2ω . (b) Envelope peak heights B _DC and B _2ω of individually back-transformed regions ROI_DC and ROI_2ω together with the measured visibility as a function of the second harmonic intensity. Inset shows B _DC and B _2ω in a double-logarithmic scale with corresponding slopes. The three lowest second harmonic intensities (indicated by brackets) are excluded from the linear fits. (c) Electron energy spectra using few-cycle fundamental pulses or multi-cycle driving pulses as previously used in [32–34]. Above-threshold photoionization peaks spaced with ΔE = 0.8 eV are visible for long driving pulses. Rescattering plateaus are formed for strong few-cycle pulses with high-energy cutoff positions indicated by spheres. 10 U _p cutoff law is matched if incident intensity I _ω,inc is converted into nearfield intensity by I _ω,NF = FE² I _ω,inc using a field-enhancement factor of FE = 6.5.

The inverse Fourier transform of the regions of interest ROI_DC and ROI_2ω with an additional Hilbert transform applied to ROI_2ω provides the envelopes of the DC and 2ω components as function of the delay. Fitting Gaussian functions to the central peaks of these envelopes gives access to the peak heights B _DC and B _2ω of the respective components (for details of the analysis see [32–34]). The peak heights together with the visibility are plotted as a function of the second harmonic intensity in Figure 2(b). We apply the fitting model from [32]

which describes the data well. Analyzing the average order by linear fits in the double-logarithmic representation displayed in the inset, shows that the peak height B _DC scales almost linearly with the second harmonic intensity and B _2ω slightly sub-linearly. Both, the good match of the fitting model and the average order of B _2ω deviating from a pure square root dependence was also observed in the perturbative regime and could be attributed to the existence of a third quantum-pathway in the emission process [32]. The visibility increases quickly before it saturates for an intensity admixture of around 7%. Although similar in shape, the visibility curve increases more slowly than in the case of long and weak pulses [35]. As the emission by the fundamental field alone increases faster than the pathway involving the second harmonic field, a higher second harmonic admixture is needed to account for an overall higher fundamental intensity.

In Figure 2(c) the energy distribution of electrons emitted by the fundamental field is shown. For long pulses with a duration of 74 fs corresponding to the ω − 2ω date in [33] we can resolve multiphoton above-threshold peaks with an energy separation of 0.8 eV matching the photon energy of the driving field. In the case of short pulses (as discussed in the panels (a) and (b) of Figure 2) a clear plateau is formed indicating elastic rescattering of the field-driven electrons at the gold surface. The plateau is followed by a high energy cutoff which shifts with increasing incident intensity I _ω,inc. The cutoff defines the famous 10 U _p law [36], where U _p is the ponderomotive energy of the electrons in the nearfield of the tip [37].

Optical fields at the tip apex are enhanced with a field enhancement factor FE. The measured cutoff positions can be matched with the expected 10 U _p law by scaling the incident intensity with FE². Turning this argument around, we obtain FE = 6.5 ± 0.6 from the cutoff position measurement, which is in good agreement with simulations of the optical nearfields [38]. Hence, we can infer the local nearfield intensity at the tip apex directly from the clean strong-field plateau in the measurement and the 10 U _p law.

Intriguingly, the ω − 2ω delay trace shown in Figure 2(a) is recorded at an incident intensity of I _ω,inc = 91 GW/cm² similar to the turquoise curve in Figure 2 showing a clear plateau with a deduced nearfield intensity of I _ω = 6.5² I _ω,inc = 3.8 TW/cm². This shows that the ω − 2ω quantum-path interference survives when going to the strong-field regime.

To conclude we have shown that the emitted electron yield can be controlled with high visibility for strong and broadband driving pulses and contains the signatures of quantum-pathway interference. Above-threshold ionization peaks are present and prove that the temporal coherence between consecutive laser cycles is maintained for a plasmonic material. Finally, we observe that ω − 2ω quantum path way interference is maintained at local optical intensities driving the system into the strong-field regime.

Our results are crucial requirements for strong-field control of both ionization and trajectories [39] at plasmonic nanostructures, which would benefit from the strong nearfield enhancement at resonant plasmonic structures [40]. If two-color coherent control is maintained for spatially separated optical excitation and electron emission mitigated by traveling surface plasmons [17, 41], plasmonic nanostructures could probe samples with tailored broadband electron beams or nearfields without interfering interactions caused by the driving pulses, thus combining pioneering theoretical ideas of Mark Stockman from nanoplasmonics, coherent control, and strong-field physics.