Real-time surface plasmon polariton propagation in silver nanowires

Electron microscopy techniques such as electron energy-loss spectroscopy (EELS) facilitate the spatio-spectral characterization of plasmonic nanostructures. In this work, a time-dependent perspective is presented, which significantly enhances the utility of EELS. Specifically, silver nanowires offer the material and geometric features for various high-quality plasmonic excitations. This provides an ideal illustrative system for combined experimental-theoretical analyses of the different plasmonic excitations and their real-time dynamics. It is demonstrated how the plasmonic excitations propagating inside the wire repeatedly interact with the swift electrons in an EELS configuration. In addition, the role of azimuthal modes, often overlooked for very thin wires, is observed and analyzed in both the energy-loss spectrum and the dynamical perspective. Such a complete understanding of the interaction of electrons and plasmonic excitation is key for the design of efficient plasmonic sensors, the study of hot electron dynamics in metals, and applications in the context of electron quantum optics, where full control of the spatial and temporal characteristics of the fields at the nanometer and femtosecond scales is highly desirable.

💡 Research Summary

In this work the authors introduce a time‑domain perspective to electron energy‑loss spectroscopy (EELS) that enables the direct observation of surface plasmon polariton (SPP) propagation in silver nanowires with nanometer spatial and femtosecond temporal resolution. Silver nanowires, owing to their low intrinsic losses and smooth surfaces, serve as an ideal platform for studying long‑range SPPs and higher‑order azimuthal modes that are often neglected in thicker structures.

The theoretical foundation starts from the conventional loss probability Γ_EELS(ω), which quantifies the energy transferred from a swift electron to the induced electromagnetic field. By applying a Fourier transform to Γ_EELS(ω) the authors obtain ˜Γ_EELS(t), a dimensionless quantity that directly maps the excitation probability of plasmonic modes as a function of time. This transformation effectively converts the static spectral information into a real‑time picture of how the electron’s field excites, drives, and interacts with SPPs while the electron approaches, traverses, and departs from the nanowire.

Experimentally, a 200 keV (≈0.7 c) electron beam is rastered across a 2.6 µm long, 30 nm radius silver nanowire deposited on a thin Si₃N₄ membrane. High‑angle annular dark‑field (HAADF) imaging defines the geometry, and line‑scan EELS maps are recorded with an impact parameter of ~5 nm. Spatial Fourier transforms of these maps yield (k, ω) dispersion relations that match the analytical dispersion of an infinite silver cylinder calculated from measured optical constants. Both the fundamental azimuthal mode (n = 0) and higher‑order modes (n = 1, 2) are clearly resolved; additional peaks near the wire caps are identified as localized Mie resonances.

To complement the measurements, the authors perform full‑wave time‑domain simulations using a Discontinuous‑Galerkin Time‑Domain (DGTD) finite‑element solver. The material response is modeled with a Drude permittivity (ℏω_p = 9.17 eV, ℏγ = 21 meV). Simulations are carried out for wires of 15 nm and 30 nm radius, with electron velocities ranging from 0.4 c (≈47 keV) to 0.7 c, reproducing the experimental EELS maps, dispersion curves, and, crucially, the temporal evolution ˜Γ_EELS(t). The simulated propagation speed of the dominant SPP feature (≈0.25 c) agrees with the experimentally extracted value (≈0.35 c), confirming that the observed slope corresponds to the SPP group velocity rather than the electron velocity.

The temporal maps reveal that, as the electron passes the point of closest approach (t = 0), a plasmonic wave packet is launched and travels bidirectionally along the wire. The amplitude of ˜Γ_EELS(t) decays as the wave propagates, reflecting radiative and material losses. By varying the electron trajectory, the authors demonstrate how different azimuthal modes are preferentially excited at specific positions and times, providing a direct visualization of mode selectivity that is inaccessible to conventional static EELS.

The study highlights several broader implications. First, the FT‑EELS approach extracts dynamical information from standard EELS datasets without requiring ultrafast pump‑probe setups, opening a new avenue for time‑resolved plasmonics. Second, the clear identification of azimuthal modes in thin wires informs the design of plasmonic sensors and waveguides where mode confinement and propagation length must be balanced. Third, the detailed knowledge of electron‑plasmon interaction dynamics is essential for understanding hot‑electron generation, energy transfer processes in photocatalysis, and the development of electron‑based quantum optics platforms where single‑electron control of nanophotonic fields is required.

In summary, by marrying high‑resolution STEM‑EELS with Fourier‑domain analysis and rigorous time‑domain simulations, the authors deliver the first real‑time “movie” of SPP propagation in silver nanowires, elucidate the role of higher‑order azimuthal modes, and establish a versatile framework for probing ultrafast light‑matter interactions at the nanoscale.