Theoretical study of the Fourier-transform analysis of heterodyne comb-emission measurements

Enforcing stable phase relations among all laser comb modes is a powerful way to control broad-band emitted radiation with only two actuators. This is an established technique for pulsed mode-locked lasers covering even more than an octave with several thousand modes. Recently, generation of combs has been demonstrated in miniaturized sources, like microresonators for the near-infrared and quantum cascade lasers for the mid- and far-infrared region. Despite the lack of a thorough theoretical background, these sources have been recently characterized by a Fourier-transform analysis of comb emission (FACE). This technique is suitable for comb characterization in any spectral region and regardless of the temporal emission profile. Here we provide a comprehensive and complete FACE theoretical framework, clarifying the details of the data analysis, giving access to more detailed results, and improving the overall reach of the technique itself. This will foster a widespread use of this approach for a full characterization of any comb emission.