This article reports on the development and application of quantum-cascade lasers (QCL) based on GaAs/AlxGa1- xAs heterostructures with a hybrid design combining bound-to-continuum (BTC) and resonant phonon (RP) designs. A Fourier transform-based model is applied as a design tool for the active regions to simulate heterostructures with gradual interfaces. Single-plasmon waveguide Fabry-Pérot (FP) quantum-cascade lasers with continue-wave (CW) output powers up to 10 mW and emission frequencies from 2.6 to 4.7 THz are fabricated. Short cavities are generally shown to result in single-mode operation. Applications include table-top systems, local oscillators for heterodyne spectroscopy in astronomy, and absorption spectroscopy for the density determination of atomic oxygen in plasmas.