Transverse Modulation of Continuous Electron Beams by a Structured Optical Cavity

Compact aberration correction at large semi-angles remains a central challenge in electron microscopy. Here we propose a phase plate for continuous electron beams based on the ponderomotive interaction with an intracavity standing wave in a near-concentric Fabry–Pérot resonator. For electrons propagating along the cavity axis, a standing-wave with Laguerre-Gaussian mode of topological charge $l=1$ imprints an annular phase shift that is opposite in sign to the third-order spherical aberration of a conventional electron lens. For a $5\mathrm{k}\mathrm{e}\mathrm{V}$ beam with a convergence semi-angle of $25\mathrm{m}\mathrm{r}\mathrm{a}\mathrm{d}$, we fully compensate the third-order spherical aberration of an objective lens with $C_{\mathrm{s}}=1\mathrm{m}\mathrm{m}$, yielding the transverse width of the corrected probe in the focus of ${\sigma }_{\mathrm{p}}=1.4\mathring{\mathrm{A}}$. The accessible transverse electron phases are set by the supported resonator modal basis and its coherent superpositions.