Theoretical backgrounds of nonlinear THz spectroscopy of semiconductor   superlattices
  We consider terahertz absorption and gain in a single miniband of semiconductor superlattice subject to a bichromatic electric field in the most general case of commensurate frequencies of the probe and pump fields. Using an exact solution of Boltzmann transport equation, we show that in the small-signal limit the formulas for absorption always contain two distinct terms related to the parametric and incoherent interactions of miniband electrons with the alternating pump field. It provides a theoretical background for a control of THz gain without switching to the negative differential conductivity state. For pedagogical reasons we present derivations of formulas in detail. 
Alexey V. Shorokhov, Kirill N. Alekseev