We study theoretically terahertz (THz) lasing in a system consisting of a quantum well placed inside an optical microcavity and a THz cavity in the regime of two-photon excitation of 2p dark exciton states. The stability of the system with varying parameters of the microcavity under coherent pumping is analyzed. We show that the nonlinearity provided by two-photon absorption can give rise to bistability and hysteresis in the THz output. This offers an opportunity for the realization of ultrafast THz switches.
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