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An optical circuit-switched network core has the potential to overcome the inherent challenges of a conventional electrical packet-switched core of today's compute clusters. As optical circuit switches (OCS) directly handle the photon beams without any optical-electrical-optical (O/E/O) conversion and packet processing, OCS-based network cores have the following desirable properties: a) agnostic to data-rate, b) negligible/zero power consumption, c) no need of transceivers, d) negligible forwarding latency, and e) no need for frequent upgrade. Unfortunately, OCS can only provide point-to-point (unicast) circuits. They do not have built-in support for one-to-many (multicast) communication, yet multicast is fundamental to a plethora of data-intensive applications running on compute clusters nowadays. In this paper, we propose Shufflecast, a novel optical network architecture for next-generation compute clusters that can support high-performance multicast satisfying all the properties of an OCS-based network core. Shufflecast leverages small fanout, inexpensive, passive optical splitters to connect the Top-of-rack (ToR) switch ports, ensuring data-rate agnostic, low-power, physical-layer multicast. We thoroughly analyze Shufflecast's highly scalable data plane, light-weight control plane, and graceful failure handling. Further, we implement a complete prototype of Shufflecast in our testbed and extensively evaluate the network. Shufflecast is more power-efficient than the state-of-the-art multicast mechanisms. Also, Shufflecast is more cost-efficient than a conventional packet-switched network. By adding Shufflecast alongside an OCS-based unicast network, an all-optical network core with the aforementioned desirable properties supporting both unicast and multicast can be realized.