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.

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• Chirality
• Light-matter interaction
• Near-field optics
• Quantum optics
• Electron microscopy
• Spectroscopy