Transition rules and optical properties of armchair graphene nanoribbons embedded in hexagonal boron nitride lattices are studied for the first time. Based on tight binding calculations considering first and second nearest neighbors, we show that the optical transition rules of such structures are completely different from that of conventional graphene nanoribbons. These rules are explained by the symmetry properties of the subband wave functions. The optical spectrum, the quantum efficiency, and the photoresponsivity of different nanoribbons are evaluated and their application in photodetector devices is investigated. The results are verified with first principles calculations.

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