In this paper, we investigate a novel simultaneous lightwave information and power transfer (SLIPT) in visible light communication (VLC) systems, where a photo diode (PD) and a solar panel are utilized as the information receiver and the energy harvester, respectively. By systematically analyzing both the information receiver and the energy harvester, we obtain the explicit expressions to characterize the illumination-rate-energy region. Based on the derived expressions, we investigate the downlink unicast transmission of multi-LED multi-user SLIPT VLC networks, and study the total transmit power minimization problem under the rate requirements, the minimum energy harvesting requirements, and dimming control constraints. To solve such non-convex problem, we exploit the semidefinite relaxation (SDR) technique and relax the problem into a convex problem, which can be efficiently solved via interior-point methods. Moreover, for the sake of users’ fairness, we further investigate the beamformer design to maximize the minimal rate under both minimum energy harvesting and dimming control constraints. Finally, the numerical results are provided to evaluate the proposed SLIPT system.