  We consider a generation and an amplification of THz radiation in
semiconductor superlattices under the action of microwave pump field. Electrons
belonging to a single miniband of the superlattice interact quasistatically
with the pump field and dynamically with a signal THz field. Within this
semiquasistic approach we derive elegant difference formulas describing
absorption (gain) of the weak THz signal. We present an instructive geometric
interpretation of the absorption formulas which allows a search of optimum
conditions for the gain employing only a simple qualitative analysis. Our
theoretical findings contribute to the development of sources and detectors of
THz radiation that are using nonlinear electric properties of semiconductor
superlattices.
