We present a mathematical model of the process of laser-induced fluorescence of phosphorus oxide (PO) molecules. Based on the model, the dependences of the fluorescence intensity of PO molecules on the energy and time parameters of exciting laser radiation are derived. It is ascertained that the dependence of the PO fluorescence signal on the energy density of the exciting radiation is a saturation curve, and the dependence on the pulse duration under real atmospheric conditions has a local maximum. It is shown that the optimal pulse duration decreases with the exciting radiation energy density.