  Plasmon-exciton polaritons provide exciting possibilities to control
light-matter interactions at the nanoscale by enabling closer investigation of
quantum optical effects and facilitating novel technologies based, for
instance, on Bose-Einstein condensation and polaritonic lasing. Nevertheless,
observing and visualising polaritons is challenging, and traditional optical
microscopy techniques often lead to ambiguities regarding the emergence and
strength of the plasmon-exciton coupling. Electron microscopy offers a more
robust means to study and verify the nature of plexcitons, but is still
hindered by instrument limitations and resolution. A simple theoretical
description of electron beam-excited plexcitons is therefore vital to
complement ongoing experimental efforts. Here we apply analytic solutions for
the electron-loss and photon-emission probabilities to evaluate plasmon-exciton
coupling studied either with the recently adopted technique of electron
energy-loss spectroscopy, or with the so-far unexplored in this context
cathodoluminescence spectroscopy. Foreseeing the necessity to account for
quantum corrections in the plasmonic response, we extend these solutions within
the framework of general nonlocal hydrodynamic descriptions. As a specific
example we study core-shell spherical emitter-molecule hybrids, going beyond
the standard local-response approximation through the hydrodynamic Drude model
for screening and the generalised nonlocal optical response theory for nonlocal
damping. We show that electron microscopies are extremely powerful in
describing the interaction of emitters with the otherwise weakly excited by
optical means higher-order plasmonic multipoles, a response that survives when
quantum-informed models are considered.
