  We theoretically investigated electron energy loss spectroscopy (EELS) of
ultraviolet surface plasmon modes in aluminum nanodisks. Using full-wave
simulations, we studied the impact of diameter on the resonant modes of the
nanodisks. We found that the mode behavior can be separately classified for two
distinct cases: (1) flat nanodisks where the diameter is much less than the
thickness; and (2) thick nanodisks where the diameter is comparable to the
thickness. While the multipolar edge modes and breathing modes of flat
nanostructures have previously been interpreted using intuitive, analytical
models based on surface plasmon polariton (SPP) modes of a thin-film stack, it
has been found that the true dispersion relation of the multipolar edge modes
deviates significantly from the SPP dispersion relation. Here, we developed a
modified intuitive model that uses effective wavelength theory to accurately
model this dispersion relation with significantly less computational overhead
compared to full-wave electromagnetic simulations. However, for the case of
thick nanodisks, this effective wavelength theory breaks down, and such
intuitive models are no longer viable. We found that this is because some modes
of the thick nanodisks carry a polar (i.e. out of the substrate plane, or along
the electron beam direction) dependence and cannot be simply categorized as
radial breathing modes or angular (azimuthal) multipolar edge modes. This polar
dependence leads to radiative losses, motivating the use of simultaneous EELS
and cathodoluminescence measurements when experimentally investigating the
complex mode behavior of thick nanostructures.
