  Strong nanoscale light-matter interaction is often accompanied by
ultra-confined photonic modes and large momentum polaritons existing far beyond
the light cone. A direct probe of such phenomena is difficult due to the
momentum mismatch of these modes with free space light however, fast electron
probes can reveal the fundamental quantum and spatially dispersive behavior of
these excitations. Here, we use momentum-resolved electron energy loss
spectroscopy (q-EELS) in a transmission electron microscope to explore the
optical response of plasmonic thin films including momentum transfer up to
wavevectors (q) significantly exceeding the light line wave vector. We show
close agreement between experimental q-EELS maps, theoretical simulations of
fast electrons passing through thin films and the momentum-resolved photonic
density of states (q-PDOS) dispersion. Although a direct link between q-EELS
and the q-PDOS exists for an infinite medium, here we show fundamental
differences between q-EELS measurements and the q-PDOS that must be taken into
consideration for realistic finite structures with no translational invariance
along the direction of electron motion. Our work paves the way for using q-EELS
as the preeminent tool for mapping the q-PDOS of exotic phenomena with large
momenta (high-q) such as hyperbolic polaritons and spatially-dispersive
plasmons.
