The effect of the azimuthal angle φ of the wave vector k on the propagation characteristics of the superluminous L-O mode waves （together with a case of the R-X mode） during different geomagnetic activities using a three-dimensional （3D） ray-tracing method is investigated. This work is primarily an extension of our previous two-dimensional study in which the wave azimuthal angle was not considered. We present numerical simulations for this mode which is generated in the source cavity along a 70° night geomagnetic field line at the specific altitude of 1.5RE （where RE is the Earth＇s radius）. It is found that, as in the two-dimensional case, the trajectory of L-O mode starting in the source meridian plane （or the wave azimuthal angle φ = 180°） can reach the lowest latitude; whereas it basically stays at relatively higher latitudes starting off the source meridian plane （or φ=180°）. The results reveal that under appropriate conditions, the superluminous L-O mode waves may exist in the radiation belts of the Earth, but this remains to be supplemented by observational data.
