Dual-comb spectrometer in the two-micron region using a new design of dispersion-controlled highly nonlinear fibre

. We present here an experimental demonstration of dual-comb spectroscopy performed around 2 µm, with the use of a new design of dispersion-controlled highly nonlinear fibre. The latter allows us to efficiently convert light via a four-wave mixing process from 1.55 µm to 2 µm, which is a spectral region suited for the detection of pollutants such as CO 2 or N 2 O. Experimental measurements have been performed with these two molecules and show an excellent agreement with the HITRAN database.


Introduction
Over the last decades, dual-comb spectroscopy (DCS) has emerged as a powerful tool for high-resolution spectroscopic measurements, with a large variety of applications such as combustion diagnosis, breath analysis, or atmospheric gas measurement to cite a few [1][2][3].Additionally, the maturity of optical components for telecommunication facilitates the development of DCS around 1.55 µm.This spectral window is however not adapted for the detection of pollutants such as CO2 or N2O, whose absorption is much stronger in the twomicron region.In this paper, we propose to convert frequency combs from 1.55 µm to 2 µm, thanks to a degenerate four-wave mixing process.The frequency conversion is optimized thanks to a new design of dispersion-controlled highly nonlinear fibre, allowing us to study ro-vibrational absorptions of CO2 and N2O, and to measure their broadening coefficients.Experimental results are compared with the HITRAN database, to confirm the efficiency of this technique [4].

New design of dispersion-controlled highly nonlinear fibre
Degenerate four-wave mixing corresponds to an energy exchange between a pump wave, a Stokes wave, and an anti-Stokes wave.The efficiency of the conversion process depends on the phase-matching condition, and thus depends on the fibre parameters.Considering the dispersion coefficients up to the fourth order, the maximum conversion occurs at an angular frequency   given by [5]: where  2 and  4 are the second and fourth order dispersion coefficients of the fiber, ϒ its nonlinear coefficient, and  the pump power.In order to efficiently convert light at a desired wavelength, Eq. ( 1) indicates that the ratio  2 / 4 must be controlled precisely.
Based on this observation, a new fibre design has been proposed to control more efficiently this ratio [6].The starting point of this fiber is a W-type fiber design, depicted in Fig. 1 (a), for which the core is surrounded by a low-index layer.This layer has been replaced by inclusions made of the same material, to reduce the constraints imposed on the guided mode of the core.dispersion parameters, which are detrimental for the efficiency of conversion.This discretized highly nonlinear fiber (D-HNLF) allows a thinner control over the mode spreading to the cladding as the wavelength increases.

Experimental results.
We now present the dual-comb spectrometer, depicted in Fig. 2. First, two frequency combs ("Comb 1" and "Comb 2") are generated through electro-optic modulation [7,8].Each comb is then mixed with a 1.3 µm seed with the use of a 1.3/1.5 µm wavelength division multiplexer (WDM), and injected into the D-HNLF with another WDM.The two combs counter-propagate in the D-HNLF, and the signals generated with FWM are isolated with the 2 µm port of the previous WDM.These signals interfere in a 50/50 coupler and are filtered with a band-pass filter (BPF).Finally, another 50/50 coupler is used to split the signal into a reference signal (Ref.) that directly goes to the measurement apparatus, and an absorbed signal (Abs.) that goes through a gas cell before being measured.Experimental measurements of the width Δν of the absorption peaks of CO2 as a function of the pressure are shown in the red curve of Fig. 3.The slope of this curve gives us the self-broadening coefficient, whose value is ϒself= (0.096 ± 0.004) cm -1 atm -1 .This coefficient is compatible to the value given in HITRAN, equal to 0.092 cm -1 .The inset in Fig. 3, corresponding to an absorption peak at 705 mbar, shows the good agreement between the experimental measurement and the simulated peak.The latter corresponds to a Voigt profile whose parameters depends on the pressure and on the considered absorption peak.Other results have been obtained with pure N2O and with a mixture CO2/N2O, and will be presented during the conference.

Conclusion
In this paper, we have presented a dual-comb spectrometer working in the two-micron spectral region, which uses a specially designed dispersion-controlled highly nonlinear fibre.This new fibre design allows us to efficiently convert the frequency combs to the two-micron spectral region, in order to study ro-vibrational absorption of gases such as CO2 or N2O.Experimental measurements show a very good agreement with the HITRAN database, proving the performance of such spectrometer.

Fig. 1
Fig.1 Principle of a W-type commercial fiber (a) and of the proposed fiber design (b).This new design, depicted in Figure 1 (b), also allows us to reduce longitudinal and transverse fluctuations of the