Effective group dispersion of terahertz quantum-cascade lasers

Terahertz (THz) quantum-cascade lasers (QCLs) are based on complex semiconductor heterostructures, in which the optical gain is generated by intersubband transitions. Using the spacing of the laser modes in the emission spectra, we have determined the effective group refractive index $n_{g,eff}$ for more than one hundred THz QCLs of the hybrid design with Fabry–Pérot resonators based on single-plasmon waveguides. The experimentally obtained values of $n_{g,eff}$ for emission frequencies between 2.5 and 5.6 THz generally follow the trend of $n_{g,eff}$ derived from electromagnetic simulations. However, for a certain number of QCLs, the experimental values of $n_{g,eff}$ exhibit a rather large deviation from the general trend and the simulation results. From a thorough analysis, we conclude that differences in the optical gain/loss spectra are responsible for this deviation, which lead to a modification of the dispersion in the active region and consequently to altered values of $n_{g,eff}$. The analysis also provides evidence that these differences in the gain/loss spectra originate from both, the details of the design and the gain broadening due to interface roughness. (paper)