Acoustic band engineering in terahertz quantum-cascade lasers and arbitrary superlattices

We present theoretical methods for the analysis of acoustic phonon modes in superlattice structures, and terahertz-frequency quantum-cascade lasers (THz QCLs). Our generalized numerical solution of the acoustic-wave equation provides good agreement with experimental pump-probe measurements of the acoustic resonances in a THz QCL. We predict that the detailed layer structure in THz QCLs imprints up to ∼2GHz detuning of the acoustic mode spacing, which cannot be seen in analytical models. This effect is strongest in devices with large and abrupt acoustic mismatch between layers. We use an acoustic deformation potential within a density-matrix approach to analyze electron transport induced in a range of the most common THz QCL active-region design schemes. We conclude that acoustic modes up to ∼200GHz are capable of significantly perturbing QCL transport, highlighting their potential for ultrafast modulation of laser emission.