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 GaAsAlGaAs 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 λ~11.4 μm, with the magnetic field varying in the range of 10-60 T. The effects of band nonparabolicity are also included.