Quantum cascade laser with low threshold and high characteristic temperature T$_{0}>$ 300K at $\sim $ 14 $\mu $m

High-performance quantum cascade (QC) lasers with wavelength in 4 $\sim $ 12 $\mu $m range are widely used in trace gas sensing. However, lack of high performance for longer wavelength in the 12 $\sim $ 16 $\mu $m range, where exist the strongest absorption lines of BTEX (benzene, toluene, ethylbenzene, and xylenes) and Uranium Hexafluoride, prohibits QC laser applications in sensing these important gases. The QC laser emitting at $\sim $ 14 $\mu $m we investigate here is based on a diagonal-transition design. The depletion of the lower laser state is achieved by a one-phonon-continuum scheme instead of the widely used ``continuum'' lower mini-bands in existing long-wavelength lasers. This scheme reduces LO scattering from the upper laser state, the leakage from the injector and thermal back-filling to the lower laser state, thus attaining population inversion efficiently. The laser shows low threshold (J$_{th}$ =2.4 kA/cm$^{2}$ for a 1.97-mm-long laser at room temperature), and a high characteristic temperature T$_{0}$ =309K fitted from $\mbox{J}_{\mbox{th}} \mbox{(T) = J}_0 e^{\mbox{T/T}_0 }$ , which is comparable with the record highest characteristic temperature. The peak power is 1.4W at 80K and 0.25W at 300K.