  Understanding light-matter interactions using localized surface plasmons
(LSPs) is of fundamental interest in classical and quantum plasmonics and has a
wide range of applications. In order to understand the spatial properties of
LSPs, electron energy loss spectroscopy (EELS) is a common and powerful method
of spatially resolving the extreme localized fields that can be obtained with
metal resonators. However, modelling EELS for general shaped resonators
presents a major challenge in computational electrodynamics, requiring the full
photon Green function as a function of two space points and frequency. Here we
present an intuitive and computationally simple method for computing EELS maps
of plasmonic resonators using a quasinormal mode (QNM) expansion technique. By
separating the contribution of the QNM and the bulk material, we give
closed-form analytical formulas for the plasmonic QNM contribution to the EELS
maps. We exemplify our technique for a split ring resonator, a gold nanorod,
and a nanorod dimer structure. The method is accurate, intuitive, and gives
orders of magnitude improvements over direct dipole simulations that
numerically solve the full 3D Maxwell equations. We also show how the same QNM
Green function can be used to obtain the Purcell factor (and projected local
density of optical states) from quantum dipole emitters or two level atoms, and
we demonstrate how the spectral features differ in general to the EELS
spectrum.

Mesoscale and Nanoscale Physics;Optics