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

## TL;DR

This paper introduces a dual-comb detection method to analyze the phase relation and emission profile of quantum cascade laser frequency combs, demonstrating their coherence and stability in mid-infrared and terahertz regimes.

## Contribution

It presents a novel technique combining dual-comb detection and Fourier analysis for comprehensive characterization of quantum cascade laser frequency combs.

## Key findings

- High coherence and long-term stability of quantum cascade laser combs confirmed.
- Simultaneous monitoring of phase patterns over multiple timescales achieved.
- Reconstruction of electric field, intensity, and frequency profiles demonstrated.

## Abstract

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.