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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] Partial electron localization in a finite-size superlattice placed in an electric field is considered. The role of electric field in forming of quasilocalized states is investigated. A quantitative criterion for the degree of partial localization is suggested based on analysis of maximal probability density of finding an electron at a given point. It is found that with increase in the electric field the degree of localization does not increase monotonically. Furthermore, the localization is affected stronger by the amplitude of superlattice potential than by the electric field.