Resonant modes of single silicon nanocavities excited by electron irradiation.

High-index dielectric or semiconductor nanoparticles support strong Mie-like geometrical resonances in the visible spectral range. We use 30 keV angle-resolved cathodoluminescence imaging spectroscopy to excite and detect these resonant modes in single silicon nanocylinders with diameters ranging from 60 to 350 nm. Resonances are observed with wavelengths in the range of 400-700 nm, with quality factors in the range Q = 9-77, and show a strong red shift with increasing cylinder diameter. The photonic wave function of all modes is determined at deep-subwavelength resolution and shows good correspondence with numerical simulations. An analytical model is developed that describes the resonant Mie-like optical eigenmodes in the silicon cylinders using an effective index of a slab waveguide mode. It shows good overall agreement with the experimental results and enables qualification of all resonances with azimuthal (m = 0-4) and radial (q = 1-4) quantum numbers. The single resonant Si nanocylinders show characteristic angular radiation distributions in agreement with the modal symmetry.