Continuous-wave multiphoton photoemission from plasmonic nanostars

Highly nonlinear optical processes require high intensities, typically achieved with ultrashort laser pulses, and hence, they were first observed with the advent of picosecond laser technology. An alternative approach for reaching the required field intensities is offered by localized optical resonances in tailored plasmonic nanostructures, enabling the enhancement of a multitude of nonlinear phenomena. However, so far, plasmon-enhanced high-order nonlinear effects have been restricted to experiments involving short-pulsed and ultrafast laser sources. Here, we demonstrate localized three-photon photoemission from chemically synthesized plasmonic gold nanostars under continuous-wave illumination at sub-MWcm−2 incident intensities. Intensity- and polarization-dependent measurements confirm the nonlinearity of the photoemission process and agree with quantum mechanical calculations of the electron yield from nanostar tips with features smaller than 5 nm, which facilitate local intensity enhancement factors exceeding 1000. Our results open up new avenues for the design of accessible nanoscale coherent electron sources, with potential applications in microscopy, spectroscopy, sensing, and signal processing. Photoemission from nanostructures has raised considerable interest in recent years. The authors propose a low-budget scheme for multiphoton photemission with a continuous-wave laser that may inspire design of accessible nanoscale coherent electron sources.

In general, nonlinear optical signals can be enhanced by confining a given incident average power in time and/or space. While temporal confinement is ubiquitous in the use of ultrashort laser pulses, additional spatial confinement is realized in optical nanostructures, defining the field of ultrafast nano-optics 35,36 . In particular, extensive theoretical and experimental work has led to a growing level of control over the near-field localization associated with resonant modes in optimized nanostructure geometries 37,38 . Exceedingly large-field enhancements in plasmonic nanostructures suggest the observation of highly nonlinear processes even under continuous-wave (CW) illumination conditions.
Here, we study nonlinear photoelectron emission from individual resonant gold nanostars under CW excitation at incident intensities below 1 MWcm −2 , using a 660-nm low-power (60 mW) laser diode. We characterize the CW multiphoton photoemission yield as a function of incident intensity and polarization, and further provide spatial scans to identify emission from individual nanostars. These findings are compared with photoemission measurements using 10 fs laser pulses at 800 nm central wavelength. Additionally, we present simulations of the electromagnetic near-field distributions and the resulting photoelectron yield that further support the nanoscale plasmonic origin of CW nonlinear photoemission at the single-particle level. Our results illustrate the potential of plasmonic field confinement in tailored resonant nanostructures to widely proliferate nonlinear nanooptics beyond ultrafast science.

Results
Nanostar sample preparation and optical properties. The nanostars used in our experiments are grown by a seed-mediated approach 2 protuberances terminating in sharp tips, with radii as small as 4 nm (insets to Fig. 1a, b). Despite the particle-to-particle variability in the detailed nanostar morphology, the controlled growth conditions used in the synthesis allow us to tune their plasmonic response close to the laser operation wavelengths of either 660 nm (CW) or 800 nm (fs-pulses with 190 nm full-width-athalf-maximum (FWHM) spectral bandwidth). Figure 1c shows the measured ensemble optical extinction spectra for both sets of nanostars deposited on glass slides (solid curves). Electromagnetic simulations of individual nanostars (Fig. 1d) from each sample batch, with structural feature sizes extracted from the transmission electron microscope (TEM) images in Fig. 1a, b, yield spectra (dashed curves) agreeing well with the central wavelength of measured response function. The simulated spectra are essentially dominated by one of the protruding tips of the particle, and therefore, notably narrowed compared to the experimental ensemble spectra. The calculated local intensity enhancement (square of the field enhancement) exceeds 1000 at the tip region a few nanometers in diameter, as presented in Fig. 1d for a single 3D nanostar. Figure 1d plots the magnitude squared of the optical field component, which is locally perpendicular to the surface, as the surface-parallel component does not contribute significantly to photoemission due to low quantum efficiency 40 . For an analysis of star ensemble effects, we refer to the study presented in ref. 2 , resulting essentially in broadened resonance feature.
Multiphoton photoemission. In the photoemission experiments, nanostars ( Fig. 1a, b) dispensed on a fused silica substrate with conductive indium-tin-oxide (ITO) coating are illuminated with focused CW or fs-pulsed laser radiation (see "Methods" for details), as depicted in Fig. 1e. The focal spot diameters (FWHM of intensity) are 3.5 μm × 1.1 μm (major × minor axis) and 5 μm for the CW and femtosecond-pulsed illumination, respectively, enabling the excitation of single nanostars for samples with a surface coverage of 0.1 particles/μm². Polarization and intensity control are realized with a broadband half-wave plate and a thinfilm polarizer. The photoemission measurements are conducted in a high-vacuum chamber at background pressures of 10 −7 mbar. Emitted photoelectrons are detected using a phosphor-screen microchannel-plate (MCP), imaged by a charge-coupled device camera for a moderate bias voltage (−10 to −30 V) applied to the sample, drawing emitted electrons toward the grounded detector front plate. Spatial photoemission maps are obtained by scanning the samples relative to the laser focus using a precision 3D translation stage. Figure 1f, g shows a photoemission map (recorded with femtosecond excitation) and a scanning electron micrograph of the scanned region on the nanostar sample (850 nm ± 100 nm resonance wavelength; see Fig. 1b, c), respectively. The photoemission hotspots can be clearly identified as positions of single or multiple nanostars, indicated by the blue circles. Only particles exhibiting nanometric feature sizes (confirmed by scanning electron microscopy, see insets to Fig. 1g) yield photoemission at an incident peak intensity of 100 MWcm −2 . A finer scan of an individual star (see upper-right insets to Fig. 1f, g) reveals that the emission profile is significantly narrowed compared to the intensity FWHM diameter of the focal spot of the incident beam (bright emission region and dashed circle), illustrating the nonlinearity of the emission process.
In the following, by employing the high-field enhancement in the nanostars, we demonstrate multiphoton photoemission under CW illumination with sub-MW cm −2 incident intensities. The nanostar sample that exhibits a resonance at 630 nm ± 75 nm wavelength (see Fig. 1a, c) is excited with the 660-nm CW-line from a laser diode with 60 mW maximum output power.  Photoelectron emission rate (s -1 ) Single star b 10 6 Fig. 2 Continuous-wave multiphoton photoemission. a Light-peak-intensity dependence of the photoelectron emission rate for single and multiple nanostars. For quantitative comparison, the photoemission rate for the femtosecond experiments is normalized to the laser duty cycle (pulse duration times repetition rate). The solid line is the calculated three-photon photoemission rate (see Eq. (1) in the "Methods" section) for a single nanostar under CW illumination, assuming an effective tip area of 5×5 nm 2 (upper tip in Fig. 1d). The photoelectron emission rate for the experimental data is calculated from the electron count rate by assuming 10% detection efficiency of the used MCP detector. b Photoemission map recorded with 45 mW CW excitation, corresponding to an incident intensity of 1.5 MWcm −2 (scale bar: 5 µm) of Fig. 2b. The hotspot extension and shape reflect the nonlinearity of the photoemission process and the oval shape of the focal spot, respectively. For comparison, we also plot in Fig. 2a the light-intensity-dependent photoelectron yield from a single nanostar produced upon femtosecond-pulse excitation (filled black circles). The nonlinear scalings of the photoemission signals ∝I n with incident light intensity I is indicated with dashed red (n = 3) and black (n = 4.5) lines (guides to the eye) for CW and femtosecond excitation, respectively. In order to better understand the nonlinear photoemission process, we carry out perturbative simulations of the photoemission yield from a single nanostar under CW excitation (see solid red curve in Fig. 2a), based upon a description of conduction electrons as independent particles subject to a rectangular step potential to describe the surface barrier (see "Methods" for details). The results are in good quantitative agreement with the experimentally observed electron yield, justifying the employed perturbative treatment.
Polarization dependence. In both experiment and simulation, the far-field coupling to the resonant modes of individual nanostars strongly depends on the incident laser polarization. Figure 3a displays the polarization-dependent photoemission yields for three different stars, using either CW (solid red circles) or femtosecond-pulse (open black diamonds and blue circles) illumination. The measurements show a strong polarization dependence of the photoemission yield for each individual nanostar, thus confirming a polarization-dependent mode coupling. We find that (cos α) 2n fits of this polarization dependence (solid curves in Fig. 3a) are generally consistent with the nonlinearity of the photoemission process for both CW (n = 3) and pulsed (n = 4.5) excitation. In the case of fs-excitation, some variation in nonlinearity for different nanostars likely stems from different resonance wavelengths overlapping the broad spectrum of the Titan:Sapphire laser (690-880 nm bandwidth) used, as well as local variations of the gold work function due to substrate effects, crystalline facets, or the nanometric size of the features [44][45][46] . Somewhat higher than expected nonlinear power scalings of photoelectron yields from gold (with n = 4-5) have also been observed previously, for example, at sharp gold tips using 800-nm fs-excitation 15 . For some nanostars, we have also observed photoemission signals for more than just one polarization angle, indicating that multiple protruding tips of the nanostar can emit photoelectrons (see Fig. 3b).

Discussion
In conclusion, we demonstrated three-photon photoemission from individual gold nanoparticles using low-power CW laser radiation at a wavelength of 660 nm (1.88 eV photon energy). This type of nonlinear processes requires large light intensities typically realized by employing ultrafast laser pulses. Instead, by harnessing a 1000-fold optical CW intensity enhancement via localized plasmons at the tips of gold nanostars, we achieve a >10 9 -fold total enhancement of the three-photon electron yield, which agrees with calculations from a perturbative model. The findings suggest the use of very sharp tips (>4 nm radii) as coherent electron sources in future nanoscale free electron devices for quantum electronics. Our study also shows the strong potential of this system for optical near-field enhancement with general applicability to nonlinear optics (e.g., harmonic generation, frequency conversion) and strong electron (or photoelectron) interactions with amplified optical fields for microscopy, spectroscopy, and sensing.

Methods
Photoemission experiment. Two sources are used to illuminate the samples with (i) few-femtosecond, nano-joule laser pulses having a central wavelength of 800 nm at 80 MHz repetition rate, and (ii) continuous-wave radiation at a wavelength of 660 nm from a low-budget (sub-100 €) laser diode.
Synthesis of spherical Au seeds nanoparticles. Spherical Au nanoparticles of 12 nm in diameter were produced by a modification of the well-known Turkevich method [47][48][49][50][51] . Briefly, Milli-Q water (500 mL) was heated to boil. After boiling had commenced, a solution of sodium citrate (11 mL, 0.1 M) was added to achieve a final citrate concentration of 2. Synthesis of Au nanostars with λ max at 850 nm. Au nanostars were prepared by a modification of a previously reported procedure 2 by dissolving 6.99 g of PVP in DMF (25 mL). After its complete dissolution, 10 mL extra of DMF were added, and the mixture was further sonicated for 30 min to assure homogeneity of the polymer in the solution. Followed by the addition of an aqueous solution of HAuCl 4 (77.7 μL, 0.1402 M) under rapid stirring at room temperature. Immediately after, 300 μL of the preformed dispersion of 12 nm, PVP-coated Au seeds in ethanol ([Au] = 16.2 × 10-4 M) was rapidly added. Within 15 min, the color of the solution changed from pink to blue, indicating the formation of Au nanostars. The solution was left under stirring overnight to assure the reduction of all reactants. DMF and excess of PVP was removed by several centrifugation steps, a first one at 7500 rpm for 40 min followed by two more at 7000 rpm for 10 min, in all steps the particles were resuspended in EtOH (35 mL). The obtained Au nanostars, exhibit a maximum absorbance peak at 850 nm.
Synthesis of Au nanostars with λ max at 630 nm. The previous synthesis of Au stars with λ max at 850 nm was repeated, and as before, after synthesis, the obtained Au nanostars were cleaned once by centrifugation (7500 rpm, 40 min) and redispersion in EtOH (35 mL Au nanostars deposition on SiN TEM grids. Au nanostars were deposited on a TEM SiN grid via spin coating (5 μL; first ramp at 500 rpm for 10 s; second ramp at 3000 rpm for 30 s with an acceleration rate for both ramps of 500 rpm/s) from two different Au concentrations (8 × 10 −5 M, 4 × 10 −4 M) to achieve particle densities of 0.18 and 0.6 particles/μm 2 .
Au nanostars deposition on glass slides for solid UV-VIS characterization. Solutions of both types of Au nanostars with concentrations of 5 × 10 −4 M were prepared and spin-coated (50 μL, 500 rpm, 60 s) on microscope cover-slip glass slides to achieve a low particle density sufficient to avoid interparticle coupling while enabling UV-vis spectra to be recorded.
Optical characterization. UV-VIS spectroscopy was recorded with a PerkinElmer, Lambda 19. Size, shape, and topographical characterization of the nanoparticles and the substrates were performed with transmission and scanning electron microscopy (TEM, LEO 922 EFTEM operating at 200 kV and LEO 1530 FE-SEM, Zeiss).
Electromagnetic simulations. Extinction spectra and near-field distributions are calculated using a finite-difference method (COMSOL) to solve Maxwell's equations under external plane-wave illumination for characteristic nanostar morphologies (see Fig. 1d). The dielectric function of gold is taken from optical data 52 . We note that we use a local description of the material, in which the plasmon-induced charge is fully placed in an infinitesimally thin layer at the metal surface. We neglect nonlocal effects, essentially quantified by the extension of the induced charge toward the bulk of the material over a distance (<1 nm) because this distance is small with the rounding radius of the star tips (~4 nm).
Multiphoton photoemission calculation. An estimate of the photoemission rate is obtained by considering a flat surface exposed to a normal electric field with an amplitude given by the maximum intensity of the locally normal near-field resulting from the electromagnetic calculations for the nanostars. An effective hotspot area of 5 × 5 nm 2 is assumed (i.e., we multiply the electron emission current density by this area). The flat surface approximation is justified by the small electron wavelength (~1 nm at the Fermi level of gold) compared with the nanostar tip rounding radius (~4 nm). We describe the gold flat surface through a square-step potential (depth V 0 ¼16.3 eV, work function Φ ¼4.5 eV). Available analytical solutions 53 for the initial, intermediate, and final electron states are used (see detailed explicit expressions for orthonormalized wave functions in ref. 53 ), including their plane-wave dependence along the x-y directions parallel to the surface. As the parallel wave vector k || is preserved during the emission process, we study transitions involving the perpendicular wave-function components, starting from an initial state φ n¼0 ðzÞ (energy hε 0 relative to the valence band bottom), and with each of the three absorbed photons (frequency ω) producing a transition from φ nÀ1 ðzÞ (energy hε 0 þ n À 1 ð Þ hω) to φ n ðzÞ (with n ¼ 1 À 3 is the forward electron Green function that satisfies the identity for the square-step potential VðzÞ. Here, A n ¼ Ài k n À k ′ is the electron wave vector along z inside the metal, and k n ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi is the normal wave vector in the vacuum side. Finally, integrating over initial states (i.e., over ε and k || in the range 0<ε þ hk 2 k 2m <E F ¼ V 0 À Φ), the photoelectron current per unit area with n = 3 photons (under the assumption that hnω>Φ) reduces to where k ′ 0 is the initial electron wave vector inside gold, k ′ min ¼ Re Data availability. The data sets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.