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In this work we present an all-optical hypercube architecture and a systolic routing protocol for it. An r-dimensional optical hypercube network (OHC) consists of N = 2r processing nodes and r2r optical links. We study a systolic routing protocol that is based on cyclic changes of states of routers and scheduled sendings of packets. The protocol ensures that no electro-optical conversions are needed in the intermediate routing nodes and all the packets injected into the routing machinery reach their targets without collisions. A work-optimal routing of an h-relation is achieved with a reasonable size of h in omega(NlogN).