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1. Introduction
Since the invention of optical frequency combs (FCs), huge efforts have been spent to extend FCs emission to all spectral regions. In this framework, quantum cascade lasers (QCLs) technology, both in the mid-infrared (MIR) and THz, is exploiting the extraordinary versatility of these sources for developing active regions and waveguides with engineered dispersion able to generate FCs. There are a lot of similarities with ultrashort-pulses lasers, such as the constant spacing between the modes, which results in a very narrow and stable intermodal beatnote. The main difference consist in the temporal profile of the emission. QCLs cannot spontaneously generate short pulses due to the lasing transition lifetime. In this case, the phase locking mechanism is four-wave mixing taking place within the laser waveguide. Evidences that multimode QCLs behave as FCs (QCL-combs) have already been provided [1–3].
Within the NEMO project we found the strongest signature of QCLs FC operation, that is the demonstration of a constant phase relation among the laser modes.
A general experimental approach capable of simultaneously measuring and monitoring the Fourier phases of a QCL-comb has been developed. It is named FACE – Fourier transform analysis of comb emission [4]. The obtained results provide complete answers to the questions above, and give a fundamental contribution to assess the FC operation of QCLs.
2. Experimental setup
Fig.1: frequency comb sources and dual-comb setup for the multiheterodyne detection.
The experiment is based on the frequency-domain analysis of the time-evolving multiheterodyne signal obtained by beating the QCL with a metrological-grade difference-frequency-generated FC (see fig. 1) [4]. Two similar experimental setups have been implemented for the measurement of a MIR QCL-comb emitting at 4.7 μm, and of a THz QCL-comb, emitting at 2.8 THz (107 μm).
Fig.2: RF spectrum of the multi-heterodyne signal obtained by Fourier transform.
The mode spacing of the QCL-combs is electronically locked to an RF reference. The detected signal is processed in order to remove the common frequency noise contribution. The signal is acquired as time traces, then each acquisition is sliced into consecutive frames and the Fourier transform of each frame is computed. In fig. 2 a sample amplitude spectrum is reported. From the generated dual-comb signal it is possible to retrieve the spectrum of the QCL-comb, and to study the time evolution of each mode, in terms of amplitude, frequency and Fourier phase.
3. Results and Discussion
Two examples of the acquired data, for the MIR and THz QCLs, are given in fig. 3 (left and right, respectively), where the FFT phases corresponding to the peaks positions are shown for different frames.
Fig. 3. Fourier phases of the MIR and the THz QCL-combs modes related to 8 (7) acquisitions. The different acquisitions are color-coded according to the starting time. The time interval between two consecutive acquisitions is 37 seconds for the MIR QCL-comb and 100-500 seconds for the THz QCL-comb.
The fact that, during the acquisition time, the phases are well confined, confirms the phase coherence characterizing QCL-combs, and gives an evidence of the FC nature of this kind of sources, both in the mid and the far infrared.
[1] A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, "Mid-infrared frequency comb based on a quantum cascade laser," Nature 492, 229–233 (2012).
[2] J. Faist, G. Villares, G. Scalari, M. Rösch, C. Bonzon, A. Hugi, and M. Beck, "Quantum Cascade Laser Frequency Combs," Nanophoton. 5, 272 (2016).
[3] F. Cappelli, G. Campo, I. Galli, G. Giusfredi, S. Bartalini, D. Mazzotti, P. Cancio, S. Borri, B. Hinkov, J. Faist, and P. De Natale, "Frequency stability characterization of a quantum cascade laser frequency comb," Laser Photonics Rev. 10, 623–630 (2016).
[4] F. Cappelli, L. Consolino, G. Campo, I. Galli, D. Mazzotti, A. Campa, M. Siciliani de Cumis, P. Cancio Pastor, R. Eramo, M. Rösch, M. Beck, G. Scalari, J. Faist, P. De Natale, and S. Bartalini, "Retrieval of phase relation and emission profile of quantum cascade laser frequency combs," Nat. Photon. 13, 562-568 (2019).
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