The increasing gap between the growth of datacenter traffic and electrical switch capacity is expected to worsen due to the slowdown of Moore's law, motivating the need for a new switching technology for the post-Moore's law era that can meet the increasingly stringent requirements of hardware-driven cloud workloads. We propose Sirius, an optically-switched network for datacenters providing the abstraction of a single, high-radix switch that can connect thousands of nodes---racks or servers---in a datacenter while achieving nanosecond-granularity reconfiguration. At its core, Sirius uses a combination of tunable lasers and simple, passive gratings that route light based on its wavelength. Sirius' switching technology and topology is tightly codesigned with its routing and scheduling and with novel congestion-control and time-synchronization mechanisms to achieve a scalable yet flat network that can offer high bandwidth and very low end-to-end latency. Through a small-scale prototype using a custom tunable laser chip that can tune in less than 912 ps, we demonstrate 3.84 ns end-to-end reconfiguration atop 50 Gbps channels. Through large-scale simulations, we show that Sirius can approximate the performance of an ideal, electrically-switched non-blocking network with up to 74-77% lower power.