This paper studies the joint trajectory and resource allocation problem for a laser-powered unmanned aerial vehicle (UAV) assisted data aggregation framework. The considered system incorporates semi-passive nodes that establish their wireless communication links with the UAV via bistatic backscatter communications enabled by a battery-powered power beacon source. We aim to optimize the UAV trajectory while minimizing the laser energy consumption throughout the whole flight by tuning the laser power and the power beacon radiated temporal power profiles. Towards this aim, we first adopt path discretization to approximate the optimal control problem of interest into a non-linear programming one whilst accounting for the UAV dynamics constraints and available power budget restrictions. Then,  we solve the problem by successive convex approximation (SCA) over the joint set of variables and determine the problem feasibility by a data collection maximization problem. Moreover, we propose a low-complexity solution for the feasibility problem. Finally, the conducted simulations show that the proposed algorithm provides  50% collected data increase  and almost 50%  laser energy reduction  under different operation conditions such as laser station position, maximum laser output power, start and end points of the trajectory, power beacon battery capacity, and the  permissible flight length.