Electron-Energy Dependent Excitation and Directional Far-Field Radiation of Resonant Mie Modes in Single Si Nanospheres.

High-energy electron beams with energies in the 15-30 keV range are used to excite optical Mie modes in crystalline Si nanospheres with radius 80-100 nm. Cathodoluminescence (CL) spectra show emission from resonant electric and magnetic dipole and quadrupole modes, with relative intensities that depend strongly on electron energy and impact parameter. The measured trends are explained by a coupling model in which the electron-energy dependent CL excitation probability-and thus the CL emission-is proportional to the Fourier transform of the modal electric field at a spatial frequency determined by the electron velocity. As a result, the coupling to a specific resonant mode is strongly dependent on the electron energy and the impact parameter of the electron beam. This enables the selective enhancement of CL emission from a resonant mode by phase-matching with the electron velocity. A systematic study of spatial excitation probability for the electric dipole mode as a function of electron energy further confirms the validity of the coupling model. Angle-resolved cathodoluminescence measurements show strong directional emission due to far-field interference of coherently excited Mie modes. By varying the electron energy and impact parameter the intensity and interference of these modes can be controlled and the angular distribution tailored. The insights in the localized deep-subwavelength coherent excitation of resonant Mie modes explored here are important for studies in light-emitting nanostructures, sensors, and photovoltaics, in which the interplay of local modes and far-field directional emission must be controlled.