Plasmonic nanostar photocathodes for optically-controlled directional currents

The study addresses how to generate and steer ultrafast, nanoscale photocurrents using plasmonic structures and to directly measure their angular (momentum-space) distributions. Ultrafast optically controlled currents underpin applications in electron diffraction/microscopy, x‑ray free-electron lasers, and THz nanoelectronics. In plasmonic nanostructures, geometry dictates localized near-field hot spots that determine where and in which directions electrons are emitted, and multi-resonant asymmetric particles (e.g., gold nanostars) enable spectral and polarization selectivity of distinct tips. While spatial hot spots have been mapped by PEEM, direct, angle-resolved momentum characterization from single nanoparticles has been limited. The authors aim to (i) directly measure momentum-space distributions from single nanostar tips in the multiphoton regime and (ii) demonstrate all-optical directional control by selectively exciting different tips via frequency and polarization, thereby enabling current switching/steering on femtosecond timescales.

Prior work established the importance of plasmonic nanostructures as bright photocathodes, femtosecond photodiodes, and CEP-sensitive detectors. Spatial mapping of hot spots by PEEM correlated with plasmon resonances has shown tip-localized emission (~20 nm resolution), and pulse shaping has enabled coherent spatial control. Angle- and momentum-resolved measurements were achieved for nanorods and bow-tie antennas using momentum-PEEM (Lehr et al.), clarifying angular emission and strong-field transitions; angular steering was also shown for metallic nanotips in strong-field regimes. However, comprehensive momentum-space observation and control in the multiphoton photoemission (MPPE) regime from multi-resonant, single nanoparticles like nanostars remained incomplete, particularly regarding surface vs volume contributions and tip-selective steering via optical parameters.

• Nanostar synthesis and selection: Gold nanostars synthesized via seedless growth using HEPES (pH 7.38) as nucleation and shape-directing agent. Growth: 0.2 mM HAuCl4 in 110 mM HEPES, vortex 1 min, then 24 h in dark. Size sorting by density gradient centrifugation (50–60% sucrose gradient; 4400×g, 4 h); fractions cleaned and dialyzed; TEM used to select fraction with desired dimensions; final population exhibits sharp tips with radius 3.4±0.4 nm and typically ~3 in-plane tips.
• Sample preparation: Glass coverslips coated with 10 nm ITO (conductive, transparent). A 50 nm Au alphanumeric grid patterned for correlated SEM-SPIM localization. Substrates UV-ozone cleaned; nanostars spin-coated (1500 rpm, 5 min) for sparse coverage (~0.05 μm−2).
• SPIM and VMI setup: Femtosecond Ti:sapphire oscillator (700–1000 nm, ~50–200 fs at sample due to GVD, 75 MHz). Additional SHG (350–500 nm) and OPO (510–780 nm) for wider tunability. Normal-incidence back-illumination with NA 0.65 reflective objective; diffraction-limited spot ~500 nm. High vacuum (<5×10−7 Torr). ITO-coated sample and scanning copper stage at −4500 V act as repeller. VMI electrostatic lens maps transverse velocities (vx, vy) to detector (chevron MCP → P47 phosphor → CCD, 20 fps). Single-event centroiding with calibration 4150 m s−1 px−1. Piezo stages for 30×30 μm2 scans; long-term stability for hours-days. Pre-cleaning by brief ~1 GW cm−2, 400 nm SHG exposure to remove adsorbates.
• Measurement protocol: Locate single nanostars via SPIM; acquire photoemission rates vs laser wavelength, polarization angle, and intensity. Determine MPPE process order from log–log intensity dependence. Record 2D velocity maps (vx, vy) under resonance conditions and as a function of optical parameters (frequency, polarization). Reconstruct 3D distributions using BASEX (assuming approximate cylindrical symmetry around resonant tip axis).
• Finite element simulations: SEM-correlated geometries built (subtract 3 nm Pt coating thickness used for SEM imaging). Include measured arm angles/lengths/widths, tip radius (3.4 nm), ITO substrate, and ~1 nm HEPES ligand layer. Compute local fields and surface-normal enhancements; on-resonance fields show |E|/|E0|≈50 at dominant tip; nonlinear enhancement for 4PPE scales as |E⊥|8, strongly localizing at the apex.
• Photoemission theory: Surface-mediated coherent MPPE based on Yalunin et al. Implemented on full nanostar surface mesh. Assumes excitation by evanescent external field (neglecting field penetration); emission from heated Fermi-Dirac distribution (pulse-averaged electron temperature ~2500 K from two-temperature model) into Volkov states, including direct and surface-rescattered amplitudes. Energy conservation includes ponderomotive energy Up=e2E2/(4mω2); for input I≈(1–2)×10^8 W cm−2 and field enhancement ~50, Up≈0.03 eV. Compute differential current density at each surface element wrt local surface normal; rotate to lab frame and sum over surface to obtain 3D momentum distributions.
• Intensity regime and diagnostics: MPPE confirmed by power laws with process order n transitioning from 3 to 4 as photon energy decreases; Keldysh parameter γ>3 (weak-field). Peak pulse intensities <3×10^8 W cm−2; average emission ~10−5 electrons per pulse (75 MHz rep rate), avoiding space charge. Tip work function inferred ~4.5 eV from 3PPE→4PPE crossover near 830 nm.
• Data analysis: Angular distributions and kinetic energy spectra extracted from 3D reconstructions; comparison to theory; directionality vectors obtained via Gaussian fits to angular peaks. Stability, heating, and coherence assessed via supplementary calculations (two-temperature model; spatial coherence estimates).

• Direct momentum-space characterization: Single nanostar tips act as point-like, spatially coherent electron sources producing tip-aligned, highly directional MPPE distributions measured by VMI and reconstructed in 3D.
• Optical switching/steering: All-optical control of emission direction achieved by selective excitation of different tips via laser frequency or linear polarization. For a two-resonance nanostar, changing excitation frequency from 725 nm (short tip) to 825 nm (long tip) rotates the emission direction by ~90°, with intermediate frequencies yielding linear combinations and continuous steering.
• Polarization control: At an intermediate frequency where both modes are resonant, rotating linear polarization switches dominant emission between orthogonal tips, rotating the emission direction by 90°. Due to cos(θ−θ_tip) sensitivity and MPPE nonlinearity, only ~±10° polarization tuning around the midway setting changes the tip emission ratio from 50:50 to ~90:10, enabling fine angular control.
• Process order and work function: Intensity-dependent MPPE shows a sigmoidal transition of effective order n from 3.01(3) to 3.99(4) centered around 830 nm (ħω≈1.5 eV), implying a tip work function φ≈3ħω≈4.5 eV. Non-integer slopes (e.g., n≈3.6) reflect simultaneous 3PPE and 4PPE contributions.
• Field enhancements and localization: Finite element modeling gives peak surface-normal field enhancement |E|/|E0|≈50 at resonant tips; nonlinear enhancement for 4PPE (∝E⊥8) localizes excitation to the apex. Tip radius R_tip=3.4±0.4 nm.
• Surface-dominated mechanism: Strongly directional distributions and agreement with surface-mediated theory indicate surface MPPE (rate ∝E⊥2n) dominates over volume-mediated processes (∝E2n) that would yield more isotropic emission.
• Energy distributions: Experimental and theoretical kinetic energy distributions agree, with average electron kinetic energy decreasing with lower excitation photon energy, consistent with m_ev^2 = nħω − φ − Up. Ponderomotive shift is small (Up≈0.03 eV) under present conditions.
• Weak-field regime and stability: Keldysh γ>3 confirms MPPE dominance; peak pulse currents imply ~10−5 electrons per pulse, avoiding space charge. Nanostar tips are stable over hours; lattice heating limited (~200 K per pulse) with full cooling in the 13 ns interpulse interval.
• Spatial coherence: Small source size (~3.4 nm) and broad angular spread (~70°) yield high spatial coherence, comparable to leading femtosecond electron sources in the linear regime.

The results show that in multi-resonant plasmonic nanostars, optical parameters provide a direct and intuitive map to tip-selective hot-spot excitation, enabling deterministic control of the direction of emitted electrons on femtosecond timescales. Frequency and polarization serve as independent control knobs: one can choose polarization to select the emitting tip (thus emission angle) while using frequency to tune kinetic energy and relative enhancement. The strong agreement between measured 2D/3D momentum distributions and surface-mediated MPPE theory, using SEM-correlated geometries and simulated fields, demonstrates that surface processes at sharp tips govern emission in the weak-field MPPE regime. The observed 3PPE→4PPE crossover defines an effective tip work function (~4.5 eV) and provides a quantitative framework to predict emission energies and angular distributions. Because the control mechanism is rooted in field enhancement and mode selectivity rather than absolute intensity, it should extend into stronger-field regimes (optical field emission), with additional dynamics (tunneling, sub-cycle acceleration) possible. The MPPE nonlinearity affords high contrast for tip selection, enabling large directional changes with small polarization adjustments and suggesting scalability to higher tip densities for fine angular control. Switching times are ultimately limited by plasmon dephasing (T2 ≲10 fs) and optical cycles (1–3 fs), implying potential for attosecond-scale spatiotemporal current control.

This work establishes gold nanostars as prototypical plasmonic photocathodes that enable all-optical switching and steering of directional multiphoton photoemission. By directly measuring and reconstructing momentum-space distributions from single tips and correlating with plasmonic simulations and surface-mediated quantum photoemission theory, the study demonstrates tip-aligned emission, frequency/polarization-selective tip excitation, and 90° rotation of emission direction through optical control. Quantitative insights include a 3PPE→4PPE transition around 830 nm (φ≈4.5 eV), field enhancements ~50 at tips, and operation in a weak-field, space-charge-free regime with high spatial coherence and stability. These capabilities suggest applications in ultrafast electron imaging/diffraction, polarization-sensitive detection, site-selective photocatalysis, and THz nanoelectronics. Future work could extend to strong-field regimes to explore tunneling and sub-cycle control, incorporate trajectory effects in highly inhomogeneous fields, engineer higher-density tip arrays for continuous angular steering, and systematically investigate substrate gap modes and volume-mediated contributions.

• Modeling emphasizes surface-mediated MPPE and neglects volume-mediated excitation; while justified by directionality, volume effects may contribute in other geometries or conditions.
• Finite element fields are sensitive to exact tip radius, geometry, and dielectric environment (e.g., HEPES layer); uncertainties can affect quantitative rates (agreement within ~order of magnitude reported).
• Possible substrate gap resonances at the nanostar–ITO interface are difficult to model precisely and were not observed but cannot be completely excluded.
• Theoretical treatment neglects optical field penetration into gold and assumes uniform external evanescent field over the electron’s quiver and decay lengths; trajectory effects in strongly varying fields are not included.
• Concave geometry re-collisions with other surfaces are not accounted for, though expected negligible for tip-like emission.
• 3D reconstruction assumes approximate cylindrical symmetry (BASEX), which may introduce artifacts if symmetry is imperfect.