  GaN-based resonators supporting whispering gallery modes are suggested as a
promising approach for fabrication of efficient nanophotonic applications. A
modification of excitonic emission due to coupling with cavity modes is
observed experimentally in the GaN planar hexagonal microcavities grown by a
selective area metal-organic vapor phase epitaxy. Low temperature
cathodoluminescence spectra measured in-situ scanning electron microscope show
two or three emission peaks split by 100 meV or 160 meV for the resonators
formed by double- and single-wall micro-nuts, respectively. The results are
compared with numerical calculations of the cavity mode energies, their
Q-factors and the spatial distribution of the modes intensities. Although most
modes are characterized by a small Purcell coefficient, there are a limited
number of isolated cavity modes with a large Purcell factor. Such modes can
efficiently interact with the bulk exciton in GaN. The results are also
analyzed by diagonalization of Hamiltanion describing the system of interacting
exciton and cavity modes. Theoretically, it is shown that a strong coupling
between the exciton and the cavity modes is possible in such micro-resonators.
