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

Nanophotonics 2021; 10(14): 3717–3721

Research article

Philip Dienstbier*, Timo Paschen and Peter Hommelhoff

Coherent control at gold needle tips approaching
the strong-field regime
https://doi.org/10.1515/nanoph-2021-0242 interaction [1, 2] resulting in unique sensing capabilities
Received May 15, 2021; accepted June 22, 2021; from detecting single-molecule Raman-scattering [3] to
published online July 6, 2021
 scanning-nearfield microscopy [4].
Abstract: We demonstrate coherent control in photoemis- Plasmonics also gained more and more interest in
sion from a gold needle tip using an − 2 field composed the realm of strong-field physics as field-driven phenom-
of strong few-cycle laser pulses with a nearfield inten- ena such as high-harmonic generation (HHG), attosecond
sity of ∼ 4 TW/cm2 . We obtain the nearfield intensity pulse generation, and electron rescattering were explored
from electron energy spectra, showing the tell-tale plateau for dielectrics and metals [5–9]. The solid-state nature
of field-driven electron rescattering at the metal surface of plasmonic structures and their strong enhancement of
induced by the fundamental field. Changing the relative incident fields resulted in on-chip structures sensitive to
phase between the fundamental field centered at 1560 nm the waveform of light [10, 11], ultrafast electron emitters
and its second harmonic modulates the total emitted pho- [12–18], and hybrid devices providing nearfield-enhanced
tocurrent with visibilities of up to 80% despite the strong HHG from solids [19].
and broadband excitation of the plasmonic material. Our Apart from specially designed targets, using tailored
work combines a two-color coherent control scheme and waveforms has proven extremely successful in coherently
strong-field physics enabled by a nanoplasmonic emitter. controlling and probing ultrafast processes [20] initially
 demonstrated for semiconductors [21, 22]. The idea of
Keywords: electron emission; gold needle tips; strong-field
physics; two-color coherent control. symmetry-breaking with light fields [23] has since been
 realized for atomic, molecular, and solid-state systems by
Dedicated to: Professor Mark Stockman, pioneer of plasmonics and shaping the polarization and spectral phase of laser pulses
strongfield physics. [24, 25] or superimposing multiple fields of different colors
 [22, 26–29]. Coherent control at plasmonic nanostructures
 applies to the nearfield distribution [30, 31] and as recently
The resonant enhancement of local optical fields and
 shown to govern the emitted photocurrent in the perturba-
waveguide-like delivery of optical excitation energy make
 tive regime [32]. Here, the total yield emitted from a gold
plasmonic structures ideal platforms for light–matter
 tip can be modulated with visibilities in excess of 95% and
 being comparable to tungsten [33–35] using a two-color
 laser field.
Timo Paschen, Now with: Korrelative Mikroskopie und Material- In this letter we demonstrate that two-color coher-
daten, Fraunhofer-Institut für Keramische Technologien und Systeme ent control of the emitted current maintains a high vis-
IKTS, Äußere Nürnberger Straße 62, 91301 Forchheim, Germany, EU.
 ibility even for intense broadband excitation pulses and
*Corresponding author: Philip Dienstbier, Department of approaching the strong-field regime. To verify the presence
Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), of field-driven dynamics we show electron energy spectra
Staudtstraße 1, Erlangen 91058, Germany,
 with clear rescattering signatures.
E-mail: philip.pd.dienstbier@studium.uni-erlangen.de. https://
orcid.org/0000-0001-8765-8208
 In the experiment few-cycle fundamental pulses cen-
Timo Paschen and Peter Hommelhoff, Department of tered on 1560 nm with 9 fs duration and their phase-locked
Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), second harmonic centered on 780 nm with 8 fs duration
Staudtstraße1, Erlangen 91058, Germany, are tightly focused onto the apex of a gold needle tip as
E-mail: timo.paschen@ikts.fraunhofer.de (T. Paschen),
 sketched in Figure 1. The tip with an apex radius of cur-
peter.hommelhoff@physik.uni-erlangen.de (P. Hommelhoff).
https://orcid.org/0000-0002-6588-3567 (T. Paschen). https://orcid vature around 20 nm emits electrons, which are counted
.org/0000-0003-4757-5410 (P. Hommelhoff) by a multichannel plate (MCP) detector as a function
 Open Access. © 2021 Philip Dienstbier et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0
International License.

3718 | P. Dienstbier et al.: Coherent control at gold needle tips

 in broad frequency components centered around the DC
 and second harmonic frequency 2 ∕(2 ) in the Fourier
 spectrum of the delay scan (right inset). A 4 component
 with a peak height around one magnitude below the 2 
 component was observed for long and weak driving pulses
 and can be explained by an additional quantum pathway,
 which is the exchange of two 2 photons with four pho-
 tons. The increased height of the 4 peak in the case of
 gold compared to tungsten could be attributed to the dif-
 ferent 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 4 
 component.
 The inverse Fourier transform of the regions of inter-
Figure 1: Experimental setup. Few-cycle two-color laser pulses emit est ROIDC and ROI2 with an additional Hilbert transform
electrons from a nanometer sharp gold needle tip. The emitted yield applied to ROI2 provides the envelopes of the DC and 2 
is recorded by a multi-channel plate detector as a function of the components as function of the delay. Fitting Gaussian func-
delay between the fundamental field and its second harmonic. tions to the central peaks of these envelopes gives access to
Alternatively, energy-resolved spectra are obtained by a retarding
 the peak heights BDC and B2 of the respective components
field analyzer.
 (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
of the delay between both laser fields. The polariza- fitting model from [32]
tion of both fields is matched to the symmetry axis of
 BDC = FDC I2 (2)
the tip. A retarding field spectrometer can be moved in
front of the tip instead of the MCP detector to provide √ √ 3
 B2 = F2 ,1 I2 + F2 ,2 I2 , (3)
energy-resolved electron spectra. A static bias voltage of
U DC = −980 V is applied to the tip for measurements con- which describes the data well. Analyzing the average order
ducted with the grounded MCP. For spectrally resolved by linear fits in the double-logarithmic representation dis-
measurements the spectrometer is biased with +50 V played in the inset, shows that the peak height BDC scales
against the grounded tip. almost linearly with the second harmonic intensity and
 Figure 2(a) shows the electron count rate as a function B2 slightly sub-linearly. Both, the good match of the fit-
of the optical delay, which is strongly modulated when ting model and the average order of B2 deviating from
both few-cycle fields are close to perfect temporal overlap. a pure square root dependence was also observed in the
This coherent control scheme allows us to either suppress perturbative regime and could be attributed to the exis-
or strongly enhance the electron emission. The visibility tence of a third quantum-pathway in the emission process
defined by [32]. The visibility increases quickly before it saturates for
 an intensity admixture of around 7%. Although similar in
 V = (Nmax − Nmin ) ∕ (Nmax + Nmin ) (1) shape, the visibility curve increases more slowly than in
 the case of long and weak pulses [35]. As the emission by
with maximum count rate N max and minimum count the fundamental field alone increases faster than the path-
rate N min obtained from a fit curve reaches values of way involving the second harmonic field, a higher second
V = (80 ± 4)% as shown in the left inset of Figure 1(a). harmonic admixture is needed to account for an overall
The visibility does not reach the 96.5% level as in the case higher fundamental intensity.
of multi-cycle driving fields [32], most likely due to the com- In Figure 2(c) the energy distribution of electrons emit-
plex temporal shapes and broad spectral bandwidths of the ted by the fundamental field is shown. For long pulses with
involved pulses. The remaining high-order chirp after the a duration of 74 fs corresponding to the − 2 date in [33]
pulse compression and second harmonic generation stage we can resolve multiphoton above-threshold peaks with an
is causing the side structure in the delay scan around ±40 energy separation of 0.8 eV matching the photon energy of
fs. The temporally more confined coherent signal results the driving field. In the case of short pulses (as discussed in

P. Dienstbier et al.: Coherent control at gold needle tips | 3719

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 = 3.8 TW/cm2 and second harmonic intensity of I2 = 440 GW/cm2 . Right inset:
Frequency spectrum obtained via Fourier transform from the − 2 delay trace shown. Broadband components centered around the DC and
2 /(2 ) frequencies are labeled as regions of interest ROIDC and ROI2 . (b) Envelope peak heights BDC and B2 of individually
back-transformed regions ROIDC and ROI2 together with the measured visibility as a function of the second harmonic intensity. Inset shows
BDC and B2 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 Up cutoff law is matched if incident
intensity I ,inc is converted into nearfield intensity by I ,NF = FE2 I ,inc using a field-enhancement factor of FE = 6.5.

the panels (a) and (b) of Figure 2) a clear plateau is formed around, we obtain FE = 6.5 ± 0.6 from the cutoff position
indicating elastic rescattering of the field-driven electrons measurement, which is in good agreement with simula-
at the gold surface. The plateau is followed by a high energy tions of the optical nearfields [38]. Hence, we can infer
cutoff which shifts with increasing incident intensity I ,inc . the local nearfield intensity at the tip apex directly from
The cutoff defines the famous 10 U p law [36], where U p is the clean strong-field plateau in the measurement and the
the ponderomotive energy of the electrons in the nearfield 10 U p law.
of the tip [37]. Intriguingly, the − 2 delay trace shown in
 Optical fields at the tip apex are enhanced with a field Figure 2(a) is recorded at an incident intensity of I ,inc
enhancement factor FE. The measured cutoff positions = 91 GW/cm2 similar to the turquoise curve in Figure 2
can be matched with the expected 10U p law by scaling showing a clear plateau with a deduced nearfield inten-
the incident intensity with FE2 . Turning this argument sity of I = 6.52 I ,inc = 3.8 TW/cm2 . This shows that the

3720 | P. Dienstbier et al.: Coherent control at gold needle tips

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