Far-infrared quantum cascade lasers operating in AlAs phonon Reststrahlen band

We report on the operation of a double metal waveguide far-infrared quantum cascade laser emitting at 28 $\mu$m, corresponding to the AlAs-like phonon Reststrahlen band. To avoid absorption by AlAs-like optical phonons, the Al-free group-V alloy GaAs$_{0.51}$Sb$_{0.49}$ is used as a barrier layer in the bound-to-continuum based active region. Lasing occurs at a wavelength of 28.3 $\mu$m, which is the longest wavelength among the quantum cascade lasers operating from mid-infrared to far-infrared. The threshold current density at 50 K is 5.5 kA/cm$^{2}$ and maximum operation temperature is 175 K. We also discuss the feasibility that operation wavelength cover the whole spectral range bridging between mid-infrared and terahertz by choosing suited group III-V materials.