The link between the gain of quantum cascade structures and the gain in periodic superlattices is presented. The proposed theoretical model based on the density matrix formalism is able to treat the gain mechanism of the Bloch oscillator and quantum cascade laser on the same footing by taking into account in-plane momentum relaxation. The model predicts a dispersive contribution in addition to the (usual) population-inversion-dependent intersubband gain in quantum cascade structures and—in the absence of inversion—provides the quantum-mechanical description for the dispersive gain in superlattices. It corroborates the predictions of the semiclassical miniband picture, according to which gain is predicted for photon energies lower than the Bloch oscillation frequency, whereas net absorption is expected at higher photon energies, as a description which is valid in the high-temperature limit. A redshift of the amplified emission with respect to the resonant transition energy results from the dispersive gain contribution in any intersubband transition, for which the population inversion is small.

• Received 15 May 2002

DOI:https://doi.org/10.1103/PhysRevB.67.085315