Microscopic density matrix model for optical gain of terahertz quantum cascade lasers: Many-body, nonparabolicity, and resonant tunneling effects

Intersubband semiconductor-Bloch equations are investigated by incorporating many-body Coulomb interaction, nonparabolicity, and coherence of resonant tunneling transport in a quantitative way based on the density matrix theory. The calculations demonstrate the importance of these parameters on optical properties, especially the optical gain spectrum, of terahertz (THz) quantum cascade lasers (QCLs). The results show that the lasing frequency at gain peak calculated by the proposed microscopic density matrix model is closer to the experimentally measured result, compared with that calculated by the existing macroscopic density matrix model. Specifically, both the many-body interaction and nonparabolicity effects red-shift the gain spectrum and reduce the gain peak. In addition, as the injection-coupling strength increases, the gain peak value is enhanced and the spectrum is slightly broadened, while an increase of the extraction-coupling strength reduces the gain peak value and broadens the gain spectrum. The dependence of optical gain of THz QCLs on device parameters such as external electrical bias, dephasing rate, doping density, and temperature is also systematically studied in details. This model provides a more comprehensive picture of the optical properties of THz QCLs from a microscopic point of view and potentially enables a more accurate and faster prediction and calculation of the device performance, e. g., gain spectra, current-voltage characteristics, optical output powers, and nonlinear amplitude-phase coupling. DOI: 10.1103/PhysRevB.86.235306