Electron-phonon relaxation rates and optical gain in a quantum cascade laser in a magnetic field

We present a model for calculating the optical gain in a midinfrared GaAs/AlGaAs quantum cascade laser in a magnetic field, based on solving the set of rate equations that describe the carrier density in each level, accounting for the optical- and acoustic-phonon scattering processes. The confinement caused by the magnetic field strongly modifies the lifetimes of electrons in the excited state and results in pronounced oscillations of the optical gain as a function of the field. Numerical results are presented for the structure designed to emit at lambda~11.4 µm, with the magnetic field varying in the range of 10–60 T. The effects of band nonparabolicity are also included. © 2005 American Institute of Physics.