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Abstract

With unrivaled spatial resolution, spectromicroscopy methods using fast electrons can quantitatively evaluate the optical response of excitations. Electron waves, however, are unable to access polarization-related quantities due to their intrinsic scalar nature. To overcome this limitation and based on the developments of the second chapter, the objective of this chapter is to lay the foundation of a phase-shaped electron energy-loss spectroscopy (PSEELS) with special emphasis on its application to nano-optics. Indeed, we will show that playing with the phase of the electron beam enables us to recover information unreachable with conventional EELS such as the polarized electromagnetic local density of states. More specifically, we will show that the PSEEL probability takes the form of a transition matrix leading to the existence of selection rules in strong analogy with atomic physics. In addition, we demonstrate that, by converting concepts originating from singular optics (such as vortex beams), one can define an optical polarization analogue for fast electrons as the optical polarization of the virtual photon exchanged during the scattering between two well-chosen singular electron states. 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.