**4. Conclusions**

In summary, to estimate the optical gain in the SA-QCL design, the high-lying subbands need to be included, and the optical gain and absorption arising from any coupled pairs of subbands should be calculated, especially when the SA-QCL design is based on a simple quantum structure. Notably, as shown in this work, for SA-QCLs with two wells, population inversion increases when additional high-lying subbands are included, owing to the activation of more depopulation channels. However, an increase in the optical gain does not correspondingly occur if the lasing frequency exceeds 3 THz; instead, the peak gain undergoes a significant decrease, even below zero. The strong decoupling between population inversion and optical gain is ascribed to the emergence of parasitic absorption, which is caused by transitions between the desired subband and high-lying subband. Owing to the engineering limit permitted in the simple quantum structure, this parasitic absorption unavoidably overlaps with the optical gain, resulting in a reduction in the peak gain intensity. This overlap is more severe when the lasing frequency exceeds 3 THz. This finding reinforces the need for engineering the specific high-lying subbands to suppress the overlaps, thus realizing the two-well SA-QCL design experimentally. Here in the final part of this work, the feasibility by employing AlGaAs ternary alloys instead of GaAs for upper well is shown, and the small Al composition can dramatically enlarge the energy of parasitic absorption, thus almost removing the overlaps.

*Terahertz, Ultrafast Lasers and Their Medical and Industrial Applications*
