Reflection and Phase Matching in Plasmonic Gold Tapers

We investigate different dynamic mechanisms, reflection and phase matching, of surface plasmons in a three-dimensional single-crystalline gold taper excited by relativistic electrons. Plasmonic modes of gold tapers with various opening angles from 5 degrees to 47 degrees are studied both experimentally and theoretically, by means of electron energy-loss spectroscopy and finite difference time-domain numerical calculations, respectively. Distinct resonances along the taper shaft are observed in tapers independent of opening angles. We show that, despite their similarity, the origin of these resonances is different at different opening angles and results from a competition between two coexisting mechanisms. For gold tapers with large opening angles (above similar to 20 degrees), phase matching between the electron field and that of higher-order angular momentum modes of the taper is the dominant contribution to the electron energy-loss because of the increasing interaction length between electron and the taper near-field. In contrast, reflection from the taper apex dominates the EELS contrast in gold tapers with small opening angles (below similar to 10 degrees). For intermediate opening angles, a gradual transition of these two mechanisms was observed.