  The major development recently undergone by quantum cascade lasers has
effectively extended frequency comb emission to longer-wavelength spectral
regions, i.e. the mid and far infrared. Unlike classical pulsed frequency
combs, their mode-locking mechanism relies on four-wave mixing nonlinear
processes, with a temporal intensity profile different from conventional
short-pulses trains. Measuring the absolute phase pattern of the modes in these
combs enables a thorough characterization of the onset of mode-locking in
absence of short-pulses emission, as well as of the coherence properties. 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 frequency comb. The technique is
applied to characterize 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 electric field, intensity profile and instantaneous
frequency of the emission.
