Retrieval of phase relation and emission profile of quantum cascade laser frequency combs

Recently, the field of optical frequency combs experienced a major development of new sources. They are generally much smaller in size (on the scale of millimetres) and can extend frequency comb emission to other spectral regions, in particular towards the mid- and far-infrared regions. Unlike classical pulsed frequency combs, their mode-locking mechanism relies on four-wave-mixing nonlinear processes, yielding a non-trivial phase relation among the modes and an uncommon emission time profile. Here, by combining dual-comb multi-heterodyne detection with Fourier-transform analysis, we show how to simultaneously acquire and monitor over a wide range of timescales the phase pattern of a generic (unknown) frequency comb. The technique is applied to characterize both a mid-infrared and a terahertz quantum cascade laser frequency comb, conclusively proving the high degree of coherence and the remarkable long-term stability of these sources. Moreover, the technique allows also the reconstruction of the electric field, intensity profile and instantaneous frequency of the emission.