Theory of the intrinsic linewidth of quantum-cascade lasers: Hidden reason for the narrow linewidth and line-broadening by thermal photons

We have developed a theory of the intrinsic linewidths of laser output of single-mode quantum-cascade (QC) lasers in mid-infrared and terahertz (THz) ranges. In the theoretical treatment, the concept of an effective coupling efficiency of spontaneous emission, given by a fractional rate of spontaneous emission coupled into a lasing mode to total nonlasing relaxation, is introduced to clarify a hidden reason for the narrowness of the linewidths. A narrow linewidth (12-kHz) reported with a frequency-stabilized 8.5-mu m distributed-feedback QC laser is successfully interpreted in terms of an extremely small effective coupling efficiency of spontaneous emission, caused by ultrafast nonradiative scatterings. The present theory predicts the presence of a minimum linewidth floor in a high-injection-current region and the independence of linewidth on detuning between gain-peak and emission wavelengths. The theoretical treatment is expanded to derive the further modified Schawlow-Townes formula including the line-broadening by black body radiation in a THz QC laser. The linewidth of a THz QC laser is predicted to be considerably broadened by black body radiation.