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Cooperative communication has been widely studied as an effective technique for free-space optical (FSO) systems to combat the effects of atmospheric conditions and beam misalignment. Related works on cooperative FSO communication mostly used a fixed splitter to uniformly distribute optical power for broadcast transmission, which tends to cause the insufficient utilization of optical power when the relay links have different channel statuses. In this paper, we focus on the optical power utilization of cooperative FSO communication, which remains less touched in previous works, while it is a decisive factor in system performance. We propose an elastic optical splitter structure to improve the efficiency of optical power by dynamically adjusting its optical output to the changing atmospheric channels. The elastic optical splitter brings a new chance for the relay selection and power allocation, which will become a different issue from that in traditional cooperative FSO systems. Thus, we further propose an adaptive relay selection and power allocation scheme using a deep reinforcement learning algorithm. Results demonstrate that the proposed elastic optical splitter is superior to the fixed optical splitter for cooperative FSO communication in bit error rate (BER) by a performance improvement of 1 to 2 orders of magnitude. Along with the proposed adaptive relay selection and power allocation scheme, the performance is further improved by more than 25% under different channel conditions.