The recent progresses in single crystalline wide bandgap hexagonal disk have stimulated intense research attention on pursuing ultraviolet (UV) laser diodes with low thresholds. While whispering-gallery modes based UV lasers have been successfully obtained in GaN, ZnO nanorods, and nanopillars, the reported thresholds are still very high, due to the low-quality ($Q$) factors of the hexagonal resonances. Here we demonstrate resonances whose $Q$ factors can be more than two orders of magnitude higher than the hexagonal modes, promising the reduction of the energy consumption. The key to our finding is the avoided resonance crossing between superscar states along two sets of nearly degenerated triangle orbits, which leads to the formation of hexagram modes. The mode couplings suppress the field distributions at the corners and the deviations from triangle orbits simultaneously and therefore enhance the $Q$ factors significantly.

• Received 16 June 2013

DOI:https://doi.org/10.1103/PhysRevA.88.023834