Rate equations analysis of a dual-wavelength quantum cascade laser

Based on a four-level rate equations model, we carry out a detailed analysis of the two modes of a mid-infrared quantum cascade laser operating simultaneously on two laser lines having a common upper level. Analytical solutions are obtained for the steady-states and the stability analysis of these predicts that, depending on the injected current, the device lases on either one of the two modes or on both wavelengths simultaneously. We also show through numerical simulations that the injected current influences significantly the population inversions and photon numbers dynamics trajectory of a two mode laser where the higher the current the shorter the time needed to reach saturation and therefore steady state operation.