  A periodic arrangement of 2D conducting planes is known to host a (bulk)
plasmon dispersion that interpolates between the typical, gapped behavior of 3D
metals and a gapless, acoustic regime as a function of the out-of-plane
wavevector. The semi-infinite system -- the configuration relevant to Electron
Energy Loss Spectroscopy (EELS) in a reflection geometry, as in High Resolution
EELS (HREELS) -- is known to host a surface plasmon that ceases to propagate
below a cutoff wavevector. As the f-sum rule requires a finite response whether
or not there exist sharp excitations, we demonstrate that what remains in the
surface loss function -- the material response probed by HREELS -- is the
contribution from the (bulk) plasmon of the infinite system. In particular, we
provide a one-to-one mapping between the plasmon continuum and the spectral
weight in the surface loss function. In light of this result, we suggest that
HREELS be considered a long wavelength probe of the plasmon continuum in
layered materials.
