In large-scale multi-processor computing systems, global communications are typically supported by an auxiliary network (e.g., IBM Blue Gene) or with hardware support in the network (e.g., NEC Earth Simulator). We explore the potential for realizing efficient global communications that can scale beyond a million processors by harnessing the unique parallelism and wavelength routing properties of optical devices. Specifically, we use an arrayed waveguide grating router (AWGR) device as the basic building block in realizing scalable global communication. The AWGR is a passive switch fabric (wavelength router) that uses multiple wavelengths to interconnect outputs and inputs by following a specific cyclic wavelength routing (permutation) pattern. We analyze different network topologies using AWGR devices for barrier synchronization and propose techniques to pick parameters of the network for a given number of processors. We compare the performance and energy consumption for barrier synchronization with what is achievable with state-of-the-art electrical networks.