A comprehensive model of gain recovery due to unipolar electron transport after a short optical pulse in quantum cascade lasers

Abstract

We have developed a comprehensive model of gain recovery due to unipolar electron transport after a short optical pulse in quantum cascade lasers (QCLs) that takes into account all the participating energy levels, including the continuum, in a device. This work takes into account the incoherent scattering of electrons from one energy level to another and quantum coherent tunneling from an injector level to an active region level or vice versa. In contrast to the prior work that only considered transitions to and from a limited number of bound levels, this work include transitions between all bound levels and between the bound energy levels and the continuum. We simulated an experiment of S. Liu et al., in which 438-pJ femtosecond optical pulses at the device's lasing wavelength were injected into an In₀.₆₅₃Ga₀.₃₄₈As/In₀.₃₁₀Al₀.₆₉₀As QCL structure; we found that approximately 1% of the electrons in the bound energy levels will be excited into the continuum by a pulse and that the probability that these electrons will be scattered back into bound energy levels is negligible, ∼10⁻⁴. The gain recovery that is predicted is not consistent with the experiments, indicating that one or more phenomena besides unipolar electron transport in response to a short optical pulse play an important role in the observed gain recovery.