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Silicon photonic microrings have the capability of handling two wavelengths simultaneously and this capability does not exist in other types of photonic switching technologies, such as directional couplers or MEMS. Exploiting this two-wavelength switching capability has not been done before. In this paper, we use this capability to construct a new type of microring-based non-blocking optical interconnects. For a 4×4 network, the new architecture only needs four rings. In contrast, the conventional crossbar-based architecture requires 16 rings. For medium size switches, such as 8 ports or 16 ports, the new architecture also requires significantly fewer rings than conventional crossbar switches of the same sizes.