$μ$eV electron spectromicroscopy using free-space light

Abstract: The synergy between free electrons and light has recently been leveraged to reach an impressive degree of simultaneous spatial and spectral resolution, enabling applications in microscopy and quantum optics. However, the required combination of electron optics and light injection into the spectrally narrow modes of arbitrary specimens remains a challenge. Here, we demonstrate microelectronvolt spectral resolution in the nanoscale mapping of photonic modes with quality factors as high as 10$^4$. We rely on mode-matching of a tightly focused laser beam to whispering gallery modes to achieve a 10$^8$-fold increase in light-electron coupling efficiency. By adapting the shape and size of free-space optical beams to address specific physical questions, our approach allows us to interrogate any type of photonic structure with unprecedented spectral and spatial detail