Coherent Control at Gold Needle Tips Approaching the Strong-Field Regime

Nanophotonics 2021; aop

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 5, 2021 scanning-nearfield microscopy4 [ ]. Abstract: We demonstrate coherent control in photoemis- Plasmonics also gained more and more interest in sion from a gold needle tip using an 𝜔 − 2𝜔 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 ∼ 4TW/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: electronemission;goldneedletips;strong-field physics; two-color coherent control. symmetry-breaking with light fields23 [ ] 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 distribution30 [ , 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: [email protected]. https:// orcid.org/0000-0001-8765-8208 In the experiment few-cycle fundamental pulses cen- Timo Paschen and Peter Hommelhoff, Department of teredon1560nmwith9fsdurationandtheirphase-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: [email protected] (T. Paschen), sketched in Figure 1. The tip with an apex radius of cur- [email protected] (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. 2 | P. Dienstbier et al.: Coherent control at gold needle tips

in broad frequency components centered around the DC andsecondharmonicfrequency2𝜔∕(2𝜋)intheFourier 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. The inverse Fourier transform of the regions of inter-

Figure 1: Experimental setup. Few-cycle two-color laser pulses emit est ROIDC and ROI2𝜔 with an additional Hilbert transform 𝜔 electrons from a nanometer sharp gold needle tip. The emitted yield applied to ROI2𝜔 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 𝜏 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 B and B 𝜔 oftherespectivecomponents field analyzer. DC 2 (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 𝜏 between both laser fields. The polariza- fitting model from32 [ ] tion of both fields is matched to the symmetry axis of B F I (2) the tip. A retarding field spectrometer can be moved in DC = DC 2𝜔 √ √ front of the tip instead of the MCP detector to provide 3, B2𝜔 = F2𝜔,1 I2𝜔 + F2𝜔,2 I2𝜔 (3) energy-resolved electron spectra. A static bias voltage of

UDC =−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 B2𝜔 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 B2𝜔 deviating from both few-cycle fields are close to perfect temporal overlap. apuresquarerootdependencewasalsoobservedinthe 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 Nmax and minimum count the fundamental field alone increases faster than the path- rate Nmin 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 fields32 [ ], 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 𝜔 − 2𝜔 date in [33] pulse compression and second harmonic generation stage wecanresolvemultiphotonabove-thresholdpeakswithan 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 | 3

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 . 2 2 the visibility at a fundamental nearfield intensity of I𝜔 = 3 8TW/cm and second harmonic intensity of I2𝜔 = 440 GW/cm . Right inset: Frequency spectrum obtained via Fourier transform from the 𝜔 − 2𝜔 delay trace shown. Broadband components centered around the DC and 𝜔 𝜋 2 /(2 ) frequencies are labeled as regions of interest ROIDC and ROI2𝜔. (b) Envelope peak heights BDC and B2𝜔 of individually back-transformed regions ROIDC and ROI2𝜔 together with the measured visibility as a function of the second harmonic intensity. Inset shows

BDC and B2𝜔 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 2 . intensity I𝜔,inc is converted into nearfield intensity by I𝜔,NF = FE I𝜔,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 nearfields38 [ ]. Hence, we can infer cutoff which shifts with increasing incident intensity I𝜔,inc. the local nearfield intensity at the tip apex directly from The cutoff defines the famous 10 Up law [36], where Up is the clean strong-field plateau in the measurement and the the ponderomotive energy of the electrons in the nearfield 10 Up law. of the tip [37]. Intriguingly, the 𝜔 − 2𝜔 delay trace shown in

Optical fields at the tip apex are enhanced with afield Figure 2(a) is recorded at an incident intensity of I𝜔,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 10Up law by scaling showing a clear plateau with a deduced nearfield inten- 2 . 2 2 the incident intensity with FE . Turning this argument sity of I𝜔 = 6 5 I𝜔,inc = 3.8 TW/cm . This shows that the 4 | P. Dienstbier et al.: Coherent control at gold needle tips

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