The optical technology in data center networks (DCNs) has long-term advantages, including higher bandwidth, longer transmission distances, lower power consumption, and reduced cooling costs compared to electrical solutions. As optical networking advances, its role in communication research grows increasingly critical. Meanwhile, modern cloud applications often rely on multicast traffic, a dominant communication mode in data centers. In this paper, we study the multicast communication scheduling problem based on all-optical fat-tree networks. Three non-preemptive scheduling strategies with different performance advantages are proposed to optimize the total task completion time and the average completion time. Compared with the existing non-preemptive scheduling algorithms, the Hybrid-Processing-Time-based (HPT) strategy proposed in this paper reduces the total task completion time by 39.94% and the average task completion time by 49.49%.