Abstract
We map the complete plasmonic spectrum of silver nanodisks by electron energy loss spectroscopy and show that the mode which couples strongest to the electron beam has radial symmetry with no net dipole moment. Therefore, this mode does not couple to light and has escaped from observation in optical experiments. This radial breathing mode has the character of an extended two-dimensional surface plasmon with a wavenumber determined by the circular disk confinement. Its strong near fields can impact the hybridization in coupled plasmonic nanoparticles as well as couplings with nearby quantum emitters.