Free Electron-Plasmon Coupling Strength and Near-Field Retrieval through Electron Energy-Dependent Cathodoluminescence Spectroscopy

Abstract

Tightly confined optical near fields in plasmonic nanostructures play a pivotal role in important applications ranging from optical sensing to light harvesting. Energetic electrons are ideally suited to probing optical near fields by collecting the resulting cathodoluminescence (CL) light emission. Intriguingly, the CL intensity is determined by the near-field profile along the electron propagation direction, but the retrieval of such field from measurements has remained elusive. Furthermore, the conditions for optimum electron near-field coupling in plasmonic systems are critically dependent on such field and remain experimentally unexplored. In this work, we use electron energy-dependent CL spectroscopy to study the tightly confined dipolar mode in plasmonic gold nanoparticles. By systematically studying gold nanoparticles with diameters in the range of 20-100 nm and electron energies from 4 to 30 keV, we determine how the coupling between swift electrons and the optical near fields depends on the energy of the incoming electron. The strongest coupling is achieved when the electron speed equals the mode phase velocity, meeting the so-called phase-matching condition. In aloof experiments, the measured data are well reproduced by electromagnetic simulations, which explain that larger particles and faster electrons favor a stronger electron near-field coupling. For penetrating electron trajectories, scattering at the particle produces severe corrections of the trajectory that defy existing theories based on the assumption of nonrecoil condition. Therefore, we develop a first-order recoil correction model that allows us to account for inelastic electron scattering, rendering better agreement with measured data. Finally, we consider the albedo of the particles and find that, to approach unity coupling, a highly confined electric field and very slow electrons are needed, both representing experimental challenges. Our findings explain how to reach unity-order coupling between free electrons and confined excitations, helping us understand fundamental aspects of light-matter interaction at the nanoscale.

Keywords: cathodoluminescence spectroscopy; confined optical modes; free electron−light interactions; near-field distributions; plasmons; strong light−matter interaction.

Figure 1

(a, b) Electric field of a z-oriented plasmonic dipole induced by a plane wave at 530 nm wavelength in (a) a 100 nm and (b) a 50 nm diameter gold spherical particle, calculated using BEM.^, (c) Real (solid) and imaginary (dashed) parts of the z component of the electric field along the z-axis for x,y = 0 in particles of 100 nm (blue) and 50 nm (red) diameter. (d) Squared modulus of the spatial Fourier transform of the complex z component of the electric field in panel (c), which is proportional to the CL emission probability.

Figure 2

Measured CL emission probability for gold spheres of (a) 100, (b) 50, and (c) 30 nm diameter, excited by 4–30 keV electrons (dark red to blue, respectively), which are passing close to the particle at a distance of 5 ± 2.5 nm.

Figure 3

Measured (dots) and simulated (solid) CL emission probability for aloof excitation of gold nanospheres with a diameter of 100 (green), 50 (purple), and 30 nm (red). Experimental data points are obtained by integrating the emission probability from Figure 2 over a bandwidth of 60 nm around the peak wavelength in each measured spectrum. The bandwidths around the solid lines show the uncertainty of the impact parameter, which is estimated as b = 5 ± 2.5 nm. Figure S2 shows the same data on a logarithmic scale to reveal details in the low-signal data.

Figure 4

Measured (dots) and simulated (solid) CL emission probability for electrons passing through the center of gold nanospheres with a diameter of 100 (green) and 50 nm (purple) in (a), and 30 (red) and 20 nm (blue) in (b). The emission probability is integrated over a 60 nm bandwidth around the peak wavelength. The dashed curves show the CL emission probability calculated using a recoil correction on eq 1, taking into account the penetration depth of the electron, normalized to the analytical nonrecoil calculation (see Methods section).

Figure 5

Simulated coupling probability between the electron and the near field induced in spherical gold nanoparticles with a diameter of 100 (green), 50 (purple), 30 (red), 20 (blue), 10 (turquoise), and 5 nm (orange) for penetrating trajectories (passing near the particle center), calculated using BEM with a fwhm of the e-beam width of 0.1 nm and corrected for the plasmon scattering albedo (see Methods section).