Atomiclike Selection Rules in Free Electron Scattering

Phase-shaped electron energy-loss spectroscopy (PSEELS) measures the scattering probability of structured free electron beams by a target. Over the last decade, it was shown that this scheme can be employed to emulate polarized optical spectroscopies with electrons, and therefore to transpose macroscopic optical concepts-such as dichroism-down to the deep subwavelength scale. In this Letter, we theoretically demonstrate that PSEELS can, in fact, go way further than mimicking optics and enables to map a plethora of so far inaccessible nano-optical quantities such as the electric quadrupolar momentum.