We have fabricated three-dimensional (3D) photonic quantum ring lasers with an equilateral triangle microcavity. Their spectra were well explained by combining the off-normal resonance and hexagonally bounced in-plane whispering-gallery-mode condition. The angular distribution of the emission modes and their discrete wavelengths were shown to be in excellent agreement with a 3D Rayleigh Fabry-Perot model. We confirmed that the allowed modes in the equilateral triangle microcavity decrease by decreasing the length of equilateral triangle side, L, and the spectral mode spacing linearly increases with the mode index m and is inversely proportional to L~(2).
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