Quenching of material dependence in few-cycle driven electron acceleration from nanoparticles under many-particle charge interaction

Abstract The excitation of nanoscale near-fields with ultrashort and intense laser pulses of well-defined waveform enables strongly spatially and temporally localized electron emission, opening up the possibility for the generation of attosecond electron pulses. Here, we investigate the electron photoemission from isolated nanoparticles of different materials in few-cycle laser fields at intensities where the Coulomb field of the ionized electrons and residual ions significantly contribute to the electron acceleration process. The dependences of the electron cut-off energy on the material’s dielectric properties and electron binding energy are investigated systematically in both experiments and semi-classical simulations. We find that for sufficiently high near-field intensities the material dependence of the acceleration in the enhanced near-fields is quenched by many-particle charge-interaction.


Introduction
Intense laser pulses with well-defined waveform have proven to be a powerful tool for the creation, control and observation of sub-cycle electron dynamics in various systems ranging from atoms to solids. Ultrashort laser fields have been applied to drive and monitor attosecond controlled electric currents (1) and ultrafast, reversible modification of the bandstructure in dielectrics (2), bandgap dynamics in semiconductors (3), ultrafast metallization of dielectric materials (4), and are key to the realization of ultrafast dielectric electronics (5). Furthermore, attosecond light pulses have been used to probe electron transport in metals (6) and adlayer-metal systems (7). When intense fields are applied to nanostructured materials, enhanced and well-controlled near-fields can be excited, permitting tailoring optical fields on sub-wavelength spatial and attosecond temporal timescales (8)(9)(10)(11)(12)(13)(14).
The acceleration of photoelectrons emitted into intense tailored near-fields has been investigated for a variety of systems including isolated nanoparticles (14)(15)(16), metal nanotips (12,(17)(18)(19)(20) and surface-based nanostructures (21,22). Similar to atomic strong-field electron emission (23), the process in nanoscopic materials may be described by the Simple-Man's-Model (SMM) (24) as a three-step process that is driven by the enhanced localized fields (see e.g. (12,16)). The three steps involve (i) the multi-photon or tunnelling electron emission, (ii) its driven acceleration in the laser field and iii) a recollision process that can lead to further energy gain. At laser intensities where the ionization rate is relatively low, the near-field dynamics is mostly determined by the linear dielectric response of the nanosystem (12). For higher laser intensities, many-particle charge interaction of liberated electrons and residual ions can significantly modify the electron acceleration process and lead to quenching of the direct electron emission and extension of the cut-off energies beyond prediction of the SMM (14). The sub-cycle electron emission dynamics in the relevant intensity regime is largely unexplored as it remains an experimental challenge since charge generation from laser-induced damage beam, the particles were brought into a gas stream of N 2 from suspension in ethanol by aerosol techniques (27), dried and focused with an aerodynamic lens, after which most of the residual gas was removed through differential pumping. For each laser shot, the projected momentum distribution of the electron emission from the nanoparticles (see Figure 1(a)) was detected with the VMI and the CEP of the few-cycle laser pulses was measured with a phase metre (28,29). The single-shot detection allowed efficient suppression of background signal by neglecting electron momentum images that do not contain any nanoparticle signal (see (30) for more details). To determine the parameters of the laser field in the interaction volume (intensity and absolute CEP), above-threshold ionization (ATI) of Xe atoms was measured as a reference. The peak laser intensity was derived from the ATI spectral cut-off assuming the cut-off energy law E c = 10.007U p + 0.538I p , (31) where U p = e 2 E 2 ∕(4m 2 ) is the ponderomotive potential of an electron in the driving electric field E, and I p is the ionization potential of the gas atoms. The nanoparticle samples were prepared by wet chemistry synthesis. Transmission electron microscopy (TEM) images of the samples were taken (see Figure 1(b)) to determine their shape and size distributions.

Nanoparticle synthesis and properties
The SiO 2 nanoparticle batches with 80, 92 and 110 nm diameter were prepared by wet chemistry methods based on the Stöber procedure and a seeded growth process (32). The polystyrene (PS) particles were prepared according to reference (33). In brief, the polymerization of a small amount of freshly distilled styrene in a deionized water of the sample occurring on longer timescales obscures the observation of the laser-driven dynamics. Using few-cycle laser fields with controlled carrier-envelope phase (CEP) opens a route to isolate the ultrafast electron dynamics from slower processes (15) and extends the range of intensities that can be explored before the target is damaged (see e.g. (25)).
Here, we present results of our studies of the influence of the material properties, in particular permittivity and electron binding energy, on the laser-induced electron acceleration in nanolocalized fields at intensities where many-particle charge interaction is important. For this purpose, the waveform controlled electron emission from isolated, chemically synthesized SiO 2 , polystyrene (PS), ZnS and Fe 3 O 4 nanoparticles was studied at incident laser intensities of (1-5) × 10 13 W/cm 2 . The experimental results are compared to semi-classical Mean-field Mie Monte-Carlo (M 3 C) simulations (16,26), which have shown to provide accurate results for SiO 2 nanoparticles in earlier work. We find that for a sufficiently high dielectrically enhanced surface intensity the contribution from many-particle charge interaction quenches the material dependence in the electron acceleration.

Single-shot velocity map imaging of electron emission from isolated nanoparticles
The experimental setup is described in detail in (15). Briefly, intense laser pulses of 5 fs (intensity full-width-athalf-maximum) duration centred at 720 nm were focused into a nanoparticle beam inside a velocity-map imaging (VMI) spectrometer. In order to prepare the nanoparticle emulsion acted as seed particles for the further growth process. More styrene was added over a period of 3 h. The resulting dispersion was further diluted with deionized water and the particle concentration was set to 2 g/l. The ZnS particles were prepared as previously described (34). The reaction of thioacetamide and Zn(NO 3 ) 2 ·6H 2 O was carried out in deionized water. After 4 h of reaction time, the ZnS particles were purified by centrifuging and redispersing first in H 2 O and then in ethanol for several times. The resulting dispersion was further diluted with ethanol and the particle concentration was set to 2 g/l. The Fe 3 O 4 particles were prepared as follows. Ferric chloride hexahydrate (FeCl 3 ·6H 2 O) (0.12 M), sodium citrate dihydrate (0.01 M) and urea (1.0 M) were completely dissolved in ethylene glycol (30 ml). The solution was sealed in a Teflon lined stainless-steel autoclave (50 ml capacity) and then heated at 200 °C for 6 h. After cooling down to room temperature, the black sediment was separated magnetically, washed with ethanol and deionized water several times, and was then dried (35). Table 1 lists the main properties of the studied samples. To avoid significant influence of field propagation effects (see e.g. (16,26)), we used nanoparticles of diameters much smaller than the central wavelength of the laser pulses (16).

Trajectory simulations
The trajectory-based Mean-field Mie Monte-Carlo (M 3 C) model (16,26) was employed to describe the experimental results. In brief, the initial ionization step was approximated by the instantaneous atomic Ammosov-Delone-Krainov (ADK) tunnel ionization in the surface layer (42). In the simulations, we used the binding energy BE as the ionization potential as listed in Table 1 (see also (43)). After their ionization, electrons are propagated classically in the local near-fields, composed of the linear dielectric response of the sphere and taking into account charge interaction of the free electrons and the residual ions, cf. Figure 1(a). The linear near-field of the nanoparticle was calculated via the Mie solution of the Maxwell's equation for a sphere assuming constant relative permittivity of the respective bulk material. The charge interaction is approximated as an effective self-consistent mean-field and calculated via high-order multipole expansion. Electron scattering inside the nanoparticle was calculated assuming isotropic elastic scattering with the scattering parameters (cross section, mean free path) retrieved from quantum mechanical atomic scattering calculations. The elastic mean free path for the investigated energy range is similar for all materials. The inelastic mean free path was modelled with a simplified Lotz formula (44), which uses the binding energy BE as an input parameter. It should be noted that we did not invert the images for our further analysis since this was not required for the comparison to the simulations and determination of the cut-off energies. The frames with nanoparticle signal are identified by a higher number of electron hits (see Figure 2(a)) compared to frames with signal from the background gas only (Figure 2(b)). Figure 2(c) and (d) shows the CEP-averaged images acquired over more than 1 million laser shots for nanoparticles and background gas, respectively. Note that the images have been corrected for a nonhomogeneous Microchannel Plate (MCP)-sensitivity and are left-right symmetrized for a better signal-to-noise ratio. We focus on the high-energy region and in particular the cut-off in the momentum spectra. The momentum distribution at high momenta in Figure 2(c) exhibits a dipolar character and is aligned along the laser polarization direction, in agreement with the previous work on SiO 2 nanoparticles (14). Inspection of Figure 2(c) and (d) already indicates a much higher cut-off for the nanoparticle signal when compared to the residual gas for otherwise identical laser parameters.

VMI of the CEP-controlled electron emission
The CEP-dependence of the electron emission is analysed as outlined in earlier work on SiO 2 (15). For each (p x ,p y )-momentum, the CEP-dependent electron signal Table 1. overview of parameters for the nanoparticle samples studied in this work. in measurements with sio 2 nanoparticles three different samples of 80, 92, and 110 nm diameters were used, which yielded indistinguishable results. the field enhancement given in the table corresponds to the one obtained at the poles of spherical nanoparticles from the analytic Mie solution. momentum where the amplitude A vanishes, and the phase offset φ 0 loses its well-defined oscillatory behaviour with CEP, is defined as the cut-off p c = √ 2m e E c . A figure eight shape of the amplitude A is clearly visible in Figure 3(a) and (b), indicating that (i) the electron emission is dominated by rescattered electrons (16) and (ii) the highest energy electrons directly follow the direction of the strongest near-field components. In our earlier work on SiO 2 , we found that the loss of direct electrons and dominance of rescattered electrons is a result of charge-interaction and the build-up of a trapping potential near the nanoparticle surface that traps all lower energy electrons (14-16, 26, 46). The rings in the simulations indicate the contributions from different sub-cycles of the laser pulse.
S was fitted with a sine-function with an amplitude A, a phase offset φ 0 (which is sometimes referred to as the 'phase of the phase' (45)), and a constant C 0 which accounts for any CEP-independent contributions: The resulting parameter A as a function of projected momenta p x and p y is shown in Figure 3(a). It is compared to the results from M 3 C simulations in Figure 3(b). We used the CEP-dependent electron emission to determine the cut-off of rescattered electrons in the experiment. The  for these nanoparticles at the lower intensity end might be caused by both limitations in the experiments and in the simulations. Experimentally, low electron emission numbers might favour particles with nano-protrusions, exhibiting higher field enhancement and thus higher photoemission probability. Without intrinsic diagnostics of the nanoparticles that contributed to the ionization signals, such a scenario cannot be excluded. We believe that this will be negligible at higher intensities. Theoretically, the description of the ionization step in the model becomes more challenging for lower intensities, where a transition to multi-photon ionization is expected and thus deviations from using a tunnelling ionization model could be expected. Larger discrepancies in the cut-off energies for the ZnS and Fe 3 O 4 can possibly be ascribed to significant deviation of the nanoparticle shape from a sphere for these samples. The M 3 C simulations are expected to give quantitative results for spherical particles (see e.g. Refs. (16,26)). Using the bulk binding energies for the different materials all major effects can be described, but we found the cutoff energies to be slightly too low at low intensities. The binding energies for nanoparticles can deviate from their bulk values due to the inclusion of impurities, which is known for SiO 2 to lower the binding energy (see Table  1). In cases where the binding energies for nanoparticles were unknown, we adapted their values from the reported bulk values within the same range found for silica (about 20%) for optimal agreement with the experimental data. The curves shown in Figure 4 were obtained assuming the binding energies for nanoparticles as given in Table 1.
Since the experimental low energy region is also affected by residual gas signal, we here concentrate on just the high-energy signal and the cut-off.

Intensity dependence of the electron emission from different materials
The intensity-dependent cut-off energy for electrons from nanoparticles of different materials is compared in Figure  4. The measurements with SiO 2 samples show a cut-off energy E c around 50 U p , in agreement with previous studies (14). Electrons from those nanoparticles with the largest permittivity and field enhancement (ZnS, Fe 3 O 4 ) exhibit much higher cut-off energies of about 140 U p . While the permittivity of polystyrene is similar to that of SiO 2 , the cut-off energies measured for PS particles are significantly larger, especially at low intensities, suggesting that both the dielectric polarizability of the particle and the binding energy affect the electron acceleration process. In the experiment, the highest laser intensity was limited by the maximum electron kinetic energy detectable with the VMI spectrometer (~120 eV). The lowest intensity measurements were limited by the number of electrons emitted from the nanoparticles and the signal-to-noise ratio: with the 1-kHz laser source the lowest intensity measurements took 8 h, which is close to the limit of what can realistically be implemented while keeping the laser parameters constant.
The model simulations show overall good agreement with the experimental data, in particular for SiO 2 and PS nanoparticles, especially at higher intensities. Deviations and the dielectrically enhanced intensity at the surface of the particle α 2 I. It should be emphasized that the normalization to the linear field enhancement in this analysis would lead to a constant cut-off energy in terms of U p if the effects of the tunnel exit and charge interaction would be negligible. The results of the simulations, however, reveal a quite complex behaviour. For the lowest dielectrically enhanced surface intensities (α 2 I ≲ 4 × 10 13 W/cm 2 ), the scaled cut-off energy shows a significant dependence on binding energy, where the values decrease with increasing binding energy. This can be explained by a higher ionization rate and correspondingly stronger many-particle Coulomb field for lower binding energies at these intensities. In addition, a closer tunnelling exit in case of lower binding energies can contribute to the observed dependence. As intensity increases, the density of the ionized electrons in the vicinity of the particle reaches a critical value and the mean-field starts screening the driving field. This diminishes the dependence on binding energy because the mean-field limits the total number of created charges and compensates for differences during the ionization process. In this regime, the scaled cut-off energy shows very small intensity dependence with values in the range of 20-25 and the material dependence is effectively quenched.
Having identified the dependence of the scaled cutoff energy on the material parameters, we now examine the relative contributions of the linear field enhancement and the mean-field to the electron acceleration process An increase in the cut-off energy with increasing ɛ r can be intuitively explained by the dependence of the near-field enhancement on the permittivity. For a neutral dielectric sphere in vacuum, Mie theory predicts a monotonous increase in the field enhancement factor with permittivity as illustrated for the four studied materials in Table 1.
The dependence of the electron cut-off energy on the binding energy is more complex and can be related to the influence of the binding energy on the electron tunnelling process. On the one hand, the binding energy determines the position of the electron tunnelling exit. As the electron dynamics is very sensitive to the initial displacement of the tunnelled electron with respect to the parent ion, this change can affect the electron cut-off energies. On the other hand, the binding energy has a direct effect on the ionization rate and thus on the number of the released electrons and residual ions. With increasing binding energy, the density of free charges decreases resulting in reduction of the many-particle field and correspondingly in a lower contribution to the acceleration of electrons.
To explore the general dependence of the photoemission process on the electron binding energy BE of the material, we performed M 3 C simulations for a set of values within the range 4.0eV < BE < 10.0eV covering the spectrum of most dielectrics and semiconductors. The colour map in Figure 5 shows the cut-off energies, scaled to the ponderomotive potential of the enhanced surface field, E c /(α 2 U p ), as a function of the binding energy BE Figure 5. dependence of the scaled electron cut-off energies, E c /(α 2 U p ), on the binding energy BE and dielectrically enhanced surface intensity, α 2 I, obtained from M 3 c simulations. in the simulations 100 nm sio 2 nanoparticle parameters were assumed and the laser intensity was varied in the range of 0.8-6.25 × 10 13 W/cm 2 . the circles represent experimental results from the four investigated materials and are coloured according to the measured scaled cut-off values.
shows that the permittivity and binding energy of the material are the main parameters that determine the material-dependent contribution to the electron acceleration process. Similar to the previous studies, both dielectrically enhanced near field and the fields resulting from the interaction with released electrons and residual ions contribute to the acceleration dynamics. Our results for particles in the size range of 100 nm clearly show the quenching effect that marks the transition from the tunnel-rate driven to purely Coulomb-limited behaviour in the acceleration dynamics. We expect that this conclusion also holds for other materials, providing predictive capability for the cut-off energies that can be obtained in electron acceleration in strong near-fields of nanoscale materials under charge interaction. Our results may also be of relevance in applications of nanosystems for the generation of ultrashort electron bunches.

Disclosure statement
No potential conflict of interest was reported by the authors.

Funding
We are grateful for support by the Max Planck Society and the DFG through SPP1840 (QUTIF), SPP1391 and the Cluster  (2) simulations with the mean-field switched off. To account for the difference in the field enhancement factors of the materials, the scaled cut-off energy was plotted as a function of the dielectrically enhanced surface intensity α 2 I. When neglecting the charge interaction all the materials show quite similar intensity scaling close to the semi-classical atomic cut-off law (cf. Figure 6, dashed lines: E c,no_mf ≈ 10 α 2 U p ). Including charge interaction results in a significant increase in the scaled cut-off energies (solid lines). Though different materials show significant deviation at low intensities they converge as the intensity increases. While the values for PS, ZnS and Fe 3 O 4 already converge at around 8 × 10 13 W/cm 2 , SiO 2 with the highest binding energy lies at this intensity within a 20% range and gets closer with increasing intensity.
The weak intensity and material dependence above an enhanced surface intensity of 8 × 10 13 W/cm 2 can be explained by the build-up of the mean-field from charge interaction and subsequent screening of the driving laser field leading to quenching of additional ionization. In agreement with this explanation, the number of emitted electrons is only linearly increasing with intensity, whereas an exponential increase would be expected without charge interaction.

Conclusions
We have studied electron emission in nanolocalized fields of isolated nanoparticles of different materials. Comparison with trajectory-based M 3 C simulations