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[en] Simple formulas describing terahertz absorption and gain in a semiconductor superlattice irradiated by a microwave pump field are derived for the case when the signal frequency is a half harmonic of the pump. A simple qualitative analysis provides a geometric interpretation of the derived formulas, which can be used to determine if gain is feasible
[en] Generation of direct current in a semiconductor superlattice under the action of an ac bichromatic field is considered in the most general case of an arbitrary ratio of the frequencies of the fields being mixed. It is shown that this effect is of parametric origin associated with oscillations of the electron effective mass in the miniband of the superlattice.