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We investigate an optically pumped electrically driven laser scheme as an approach for terahertz (THz) quantum cascade lasers. The scheme keeps the advantages of optical conversion, and increases the efficiency by recycling the pump photons. Using a microscopic theory based on the Maxwell-semiconductor Bloch equations, we demonstrate that the approach offers a path to room-temperature THz generation. Furthermore, we show how successful recovery of the pump intensity can yield optical conversion efficiencies exceeding the Manley-Rowe limit.