Dependence of the spontaneous luminescence intensity in ZnO nanorods on their length

The influence of the length of ZnO nanorods (500 nm in diameter) on the mode structure and spontaneous luminescence in the ultraviolet spectral region is studied by optical luminescence microscopy. It is shown that individual nanorods with a metal mirror on one face exhibit only two or three laser modes in the case of short nanocavity lengths (8–30 $\mu$m). Different values of the optical losses of the longitudinal and transverse waveguide modes are established for a ZnO nanorod lying on a glassy substrate. The quadratic dependence of the spontaneous luminescence intensity on the rod length can be attributed to improvement of the optical quality factor Q of bound longitudinal modes of light within longer rods (the Purcell effect).