Title: Vibrational surface EELS probes confined Fuchs-Kliewer modes,
Abstract: Recently, two reports have demonstrated the amazing possibility to probe
vibrational excitations from nanoparticles with a spatial resolution much
smaller than the corresponding free-space phonon wavelength using electron
energy loss spectroscopy (EELS). While Lagos et al. evidenced a strong spatial
and spectral modulation of the EELS signal over a nanoparticle, Krivanek et al.
did not. Here, we show that discrepancies among different EELS experiments as
well as their relation to optical near- and far-field optical experiments can
be understood by introducing the concept of confined bright and dark
Fuchs-Kliewer modes, whose density of states is probed by EELS. Such a concise
formalism is the vibrational counterpart of the broadly used formalism for
localized surface plasmons; it makes it straightforward to predict or interpret
phenomena already known for localized surface plasmons such as
environment-related energy shifts or the possibility of 3D mapping of the
related surface charge densities.