One of the most promising solutions to the problem of limited flight time of unmanned aerial vehicles (UAVs), is providing the UAVs with power through laser beams emitted from Laser Beam Directors (LBDs) deployed on the ground. In this letter, we study the performance of a laser-powered UAV-enabled communication system using tools from stochastic geometry. We first derive the energy coverage probability, which is defined as the probability of the UAV receiving enough energy to ensure successful operation (hovering and communication). Our results show that to ensure energy coverage, the distance between the UAV and its dedicated LBD must be below a certain threshold, for which we derive an expression as a function of the system parameters. Considering simultaneous information and power transmission through the laser beam using power splitting technique, we also derive the joint energy and the Signal-to-noise Ratio (SNR) coverage probability. The analytical and simulation results reveal some interesting insights. For instance, our results show that we need at least 6 LBDs/10km2 to ensure a reliable performance in terms of energy coverage probability.