High-frequency absorption and gain in superlattices: Semiquasistatic   approach
  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. 
A. V. Shorokhov, K. N. Alekseev