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Due to ever-increasing throughput demands, the lookup in conventional IP routers based on longest prefix matching is becoming a bottleneck. Additionally, the scalability of current routing protocols is limited by the size of the routing tables. Geometric greedy routing is an alternative to IP routing which replaces longest prefix matching with a simple calculation employing only local information for packet forwarding. For the first time, in this paper we propose a novel and truly all-optical geometric greedy router based on optical logic gates and optical flip-flops. The circuit of the router is constructed through the interconnection of SOAs and directional couplers. The successful functionality of the proposed router is verified through simulation. The circuit enables high data rate throughput.