"Synthetic gain for electron-beam spectroscopy"

There exist significant challenges in resolving spectral features in electron-beam spectroscopy. These challenges include low signal-to-noise ratios, spectral overlap, and low probability of detecting spontaneous multi-photon events. Recent developments in the synthetic complex-frequency wave (CFW) approach have demonstrated notable improvements in optical microscopy and spectroscopy. Building on this foundation, the present work extends the synthetic CFW methodology to the realm of electron-beam spectroscopy and microscopy, aiming to address analogous challenges in electron-based measurements.

To demonstrate the experimental capabilities of the CFW technique, we present measurements on several representative systems. We first investigate a suspended silver nanoparticle (∼20 nm diameter) positioned within a TEM grid hole, where a 200-keV electron beam is scanned across the particle and electron energy-loss spectroscopy (EELS) spectra are acquired at three representative positions. After CFW processing, the dipolar Mie resonance becomes pronounced at positions A and C, while the bulk plasmon remains absent due to the aloof interaction geometry; notably, CFW enhances both surface and bulk plasmon features at position B, where they are otherwise weak. We further apply the CFW method to cathodoluminescence in a film-coupled nanoantenna system, consisting of silver nanoparticles (∼100 nm diameter) placed on a 100-nm-thick gold film and excited by a 10-keV electron beam. Hyperspectral CL imaging along a scan line across a nanoparticle reveals, in the unprocessed data, a dominant mode at 2.3 eV and a faint mode near 3.4 eV; however, following CFW processing, four distinct optical modes (labeled M1–M4 in ascending energy) emerge, with simulations attributing M1 and M2 to gap-plasmon modes at lower energies and M3 and M4 to Mie resonances at higher energies.

Finally, in the quantum regime, we simulate an EELS spectrum using a Poisson statistics model at strong quantum coupling, enabling spontaneous multiphoton processes; after CFW processing, not only does the four-photon peak become clearly identifiable, but the lower-order photon peaks are also significantly enhanced. These results collectively demonstrate that the CFW technique substantially improves spectral feature recovery and resolution in both classical and quantum regimes of free-electron–matter interactions.