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This paper presents a new packet scheduling scheme, called frame-based exhaustive matching (FEM), to efficiently resolve the contention in a 3-stage Clos-network photonic switch. Using extended frames to aggregate cells from different incoming lines, the extended frame relaxes the stringent arbitration time constraint at the ultrafast port speed achievable in the photonic switch fabric. We also evaluate and analyze system performances, including throughput and packet delay, under various traffic conditions. At the expense of a moderate internal speedup of 1.5, throughput close to 100% under various traffic conditions can be achieved in a 3-stage Clos-network switch without expansion.