Relativistic electron energy loss spectroscopy of solid and core-shell nanowires

Near-field optical spectroscopy with nanometer spatial resolution using transition radiation from a focused, relativistic electron beam is demonstrated for Ge nanowires. The excitation of the waveguide modes is absent in theoretical treatments that neglect retardation because the coupling of the swift electron to the optical modes of the nanowire is a consequence of its relativistic nature. Here, relativistic energy loss probabilities for aloof electron trajectories near a perpendicularly oriented single nanowire are analytically calculated using a local dielectric theory. Multimode and zero-mode Ge nanowires are experimentally measured in this geometry with a ∼2-nm-size electron probe. Observations fall in excellent agreement with the retarded calculations. Optical eigenmodes are identified from comparison of the experimental electron energy loss spectra to theoretical dispersion maps. Adding a Drude-type metallic shell to a dielectric nanowire provides surface-plasmon modes in the same energy range as the dielectric waveguide, leading to strongly coupled hybrid modes that can be efficiently excited by the incident electron. Such results demonstrate a powerful solution for optical studies of nanosystems with nanometer spatial resolution over a broadband energy range.