Low-order optical whispering-gallery modes in hexagonal nanocavities

We present a detailed numerical analysis of the lowest-order resonant modes of a hexagonal dielectric cavity. Our investigations include resonant wave numbers, linewidths, mode patterns, and their dependency on the refractive index. On the basis of our theoretical results, we are able to simulate the resonance spectra of individual hexagonal zinc oxide nanocavities without a free parameter. A superposition of Lorenzian resonance lines leads to perfect agreement with experimental data obtained from polarization-resolved micro-photoluminescence and cathodoluminescence spectroscopy. Series of radially higher-order modes are theoretically predicted and experimentally observed. Therefore, we present a consistent description of the resonance behavior of a hexagonal dielectric optical cavity on nanoscopic scale.