Optical polarization analogue in free electron beams

The functionality of electron energy loss spectroscopy can be extended to include a polarization analogue constructed via the dipole transition vector between two electronic states, bringing it closer to its optical counterpart. Spectromicroscopy techniques with fast electrons can quantitatively measure the optical response of excitations with unrivalled spatial resolution. However, owing to their inherently scalar nature, electron waves cannot access the polarization-related quantities. Despite promising attempts based on the conversion of concepts originating from singular optics (such as vortex beams), the definition of an optical polarization analogue for fast electrons has remained an open question. Here we establish such an analogue using the dipole transition vector of the electron between two well-chosen singular wave states. We show that electron energy loss spectroscopy allows the direct measurement of the polarized electromagnetic local density of states. In particular, in the case of circular polarization, it directly measures the local optical spin density. This work establishes electron energy loss spectroscopy as a quantitative technique to tackle fundamental issues in nano-optics, such as super-chirality, local polarization of dark excitations or polarization singularities at the nanoscale.

Automated summary

This research establishes an optical polarization analogue for fast electrons using the dipole transition vector between two selected singular wave states. Electron energy loss spectroscopy allows for the direct measurement of polarized electromagnetic local density of states and local optical spin density, particularly in the case of circular polarization. This work showcases the potential of electron energy loss spectroscopy in tackling fundamental issues in nano-optics.