Theoretical and numerical investigation of the interaction between phase-shaped electron probes and plasmonic modes

Electron energy loss spectroscopy (EELS) in the low-loss region has attracted a large interest due to its efficiency in resolving plasmonic resonance at the nanometer scale. However, standard low-loss EELS remained intrinsically unable to detect plasmonic optical activity. Nevertheless, phase shaped electron probes constitute a perfect candidate to overcome this limitation and measure the dichroic behavior of plasmons in an electron microscope. Moreover, it has been recently demonstrated that such probes can be created in an electron microscope by tailoring the phase of the beam. In the present work, we developed a semiclassical formalism describing the interaction between an electron probe with an arbitrary phase profile and a plasmonic mode. We showed that the equation ruling this interaction takes the elegant form of a transition matrix between two electron states mediated by the eigenpotentials of the plasmon modes. In this contribution, we will present the theoretical formalism and a wide variety of numerical studies of interactions between different nano-structures (e.g. helix, rod) and phase shaped electron probes (e.g. vortex beams, HG-like beams...), with a special emphasis on the experimental feasibility of the proposed geometries.