  We fabricated GaN based hollow nanowires standing upright on a sapphire
substrate by the sublimation method and found that they exhibit laser
oscillation at room temperature. These very long, hollow, nano-sized structures
cannot be fabricated by other means. Furthermore, we determined the condition
under which the fundamental mode is azimuthally polarized by investigating the
dispersion of the hollow structure. Examination of the measured emission
properties indicates that the hollow nanowire operates as a topological,
vector-beam, light source.
