Study of Spatio-Temporal Character of Frequency Combs Generated by Quantum Cascade Lasers

Free-running quantum cascade lasers (QCLs) show a natural tendency to operate in the multimode regime as a result of both spatial and spectral hole burning. While multimode operation by itself is far from unusual, what distinguishes QCLs from other lasers is that the phases of the individual modes in them can be locked in the absence of any additional intracavity elements, thus forming frequency combs (FCs) that have many practical applications. Unlike typical FCs produced in mode-locked lasers or microcavities, the temporal shape of a QCL FC is not a short pulse but rather a combination of frequency and (to a lesser extent) amplitude modulated signals, the origin of which is not obvious. In this paper, we develop a theory aimed at explicating the most recent experimental measurements of temporal characteristics of QCL FCs. We identify spatial hole burning as the root cause of frequency modulation and show that, in addition to previously analyzed rapid, pseudo-random frequency modulation, the experimentally observed long linearly chirped signal can also alleviate spatial hole burning efficiently. We find that in the absence of spectral hole burning, a linearly chirped regime has the lowest threshold. Furthermore, we show that for relatively weak frequency modulation, amplitude modulation should also arise as confirmed experimentally. The result of this paper is a first step toward reliably engineering FCs with specified characteristics in mid IR and THz regions.