Temperature Dependence of Optical Gain and Loss in $\lambda \approx$ 8.2–10.2 $\mu$m Quantum-Cascade Lasers

Temperature-dependent optical gain and waveguide loss have been measured for continuous-wave operated quantum-cascade lasers with wavelengths between 8.2 and 10.2 mum up to room temperature using the Hakki-Paoli method. The gain coefficient decreases with increasing temperature, and is close to the designed value for vertical transition lasers, but smaller than the designed value for diagonal transition lasers. The waveguide loss, however, is two to three times higher than calculated from free carrier absorption, and can be nearly constant, increase or decrease with temperature depending on sample design, which indicates that it is dominated by another mechanism other than plain free carrier absorption. One likely factor resulting in high waveguide loss is intersubband resonant absorption into higher lying states.