Fundamental frequency noise and linewidth broadening caused by intrinsic temperature fluctuations in quantum cascade lasers

Abstract

We theoretically investigate fundamental thermal frequency noise and linewidth broadening caused by intrinsic temperature fluctuations in both terahertz (THz) and mid-infrared (IR) quantum cascade lasers (QCLs) for the first time. The analytical derivation is based on the Green function analysis and the Van Vliet-Fassett theory. The results show that the fundamental frequency noise caused by temperature fluctuations is prominent in the low frequency range (below a few kHz) and is sensitive to the temperature, heat conductivity, and the thickness of the active region/substrate. It also shows that this fundamental frequency noise does not show a 1/$f$ trend in the whole frequency spectra for both THz and mid-IR QCLs. For THz QCLs, considering only the refractive-index variation caused by the current-induced device self-heating, we calculate the linewidth broadening to be only around 1 Hz, which is comparable to the value of 3 Hz caused by spontaneous emission, stimulated emission, and blackbody radiation in high power THz QCLs. For mid-IR QCLs this frequency noise leads to the linewidth broadening from 14.74 Hz to 62.02 Hz as the temperature increases from 200 K to 400 K. When the microscopic features of the refractive-index variations associated with the intersub-band gain transition, the self-heating-induced thermal expansion and energy-level broadening in mid-IR QCLs are considered, an estimation shows that the linewidth broadening increases greatly by a factor of at least four times.