Excitation of Mesoscopic Plasmonic Tapers by Relativistic Electrons: Phase Matching versus Eigenmode Resonances

We investigate the optical modes in three-dimensional single-crystalline gold tapers by means of electron energy-loss spectroscopy. At the very proximity to the apex, a broad-band excitation at all photon energies from 0.75 to 2 eV, which is the onset for interband transitions, is detected. At large distances from the apex, though, we observe distinct resonances with energy dispersions roughly proportional to the inverse local radius. The nature of these phenomena is unraveled by finite difference time-domain simulations of the taper and an analytical treatment of the energy loss in fibers. Our calculations and the perfect agreement with our experimental results demonstrate the importance of phase-matching between electron field and radiative taper modes in mesoscopic structures. The local taper radius at the electron impact location determines the selective excitation of radiative modes with discrete angular momenta.