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Versatile mid-infrared frequency-comb referenced sub-Doppler spectrometer

We present a mid-IR high-precision spectrometer capable of performing accurate Doppler-free measurements with absolute calibration of the optical axis and high signal-to-noise ratio. The system is based on a widely tunable mid-IR offset-free frequency comb and a Quantum-Cascade-Laser (QCL). The QCL emission frequency is offset locked to one of the comb teeth to provide absolute-frequency calibration, spectral-narrowing, and accurate ﬁne frequency tuning. Both the comb repetition frequency and QCL-comb offset frequency can be modulated to provide, respec-tively, slow- and fast-frequency-calibrated scanning capabilities. The characterisation of the spectrometer is demonstrated by recording sub-Doppler saturated absorption features of the CHF 3 molecule at around 8.6 µ m with a maximum signal-to-noise ratio of ∼ 7 × 10 3 in 10 s integration time, frequency-resolution of 160 kHz, and accuracy of less than 10 kHz.

We present a mid-IR high-precision spectrometer capable of performing accurate Doppler-free measurements with absolute calibration of the optical axis and high signal-to-noise ratio. The system is based on a widely tunable mid-IR offset-free frequency comb and a Quantum-Cascade-Laser (QCL). The QCL emission frequency is offset locked to one of the comb teeth to provide absolute-frequency calibration, spectral-narrowing, and accurate fine frequency tuning. Both the comb repetition frequency and QCL-comb offset frequency can be modulated to provide, respectively, slow-and fast-frequency-calibrated scanning capabilities. The characterisation of the spectrometer is demonstrated by recording sub-Doppler saturated absorption features of the CHF 3 molecule at around 8.6 µm with a maximum signal-to-noise ratio of ∼7 × 10 3 in 10 s integration time, frequency-resolution of 160 kHz, and accuracy of less than 10

I. INTRODUCTION
The accuracy of the absolute optical frequency axis and signal-to-noise level are key parameters for any precision-spectroscopy measurement. The advent of visible and near-infrared optical frequency-combs 1,2 at the beginning of the century gave a tremendous boost to precision spectroscopy systems, allowing for a straightforward and absolute optical frequency calibration potentially reaching the 10 16 -10 18 level of the most accurate atomic and optical frequency standards today available. 3,4 Moreover, the continuous progress in Quantum-Cascade-Laser (QCL) technology recently led to the availability of room-temperature plug-and-play mid-infrared (mid-IR) single-frequency tunable laser sources with an optical power of few tens of mW, 1 MHz emission linewidth, and very high frequency stability [5][6][7] allowing for the detection of strong fundamental absorption lines with a high signal-tonoise ratio (SNR) and resolution. The use of QCLs combined with the more recent availability of mid-IR frequency combs [8][9][10][11][12] has allowed to extend precision spectroscopy to the 3-15 µm spectral window (covering the majority of the fingerprint region) where most molecules exhibit their strongest absorption features, greatly enhancing both accuracy and sensibility of direct-absorption spectroscopy measurements. Several spectroscopic techniques can also be implemented for further increase of system resolution, accuracy, and sensitivity. Non-linear spectroscopy techniques 13  to partially remove the sources of inhomogeneous spectral line-broadening allowing us to observe Doppler-free absorption features few orders of magnitude narrower than the linear-absorption profiles, with a strong benefit for measurement precision. Balanced detection or other well assessed background-removal techniques can also be adopted to account for baseline-related artifacts, such as etalon effects or beam-intensity wavelength dependence, that may also affect the overall accuracy. Modulation-spectroscopy techniques 14 on the other hand allow for both technical-noise and background rejection, therefore enabling for very sensitive detection, which is very important especially in the presence of very crowded absorption spectra typical of heavy molecules or molecular mixtures.
In this work, we present a versatile and relatively simple spectrometer based on a QCL laser frequency-locked to a mid-IR optical frequency comb, capable of Doppler-free precisionspectroscopy measurements with high-accuracy and high-sensitivity in both direct-absorption and modulation-spectroscopy approaches. We tested the system performances by probing narrow spectral features of trifluoromethane, CHF 3 , which is a very important molecule for the emerging field of cold stable molecules 15 and which is very demanding from a spectroscopy point of view due to a very crowded absorption spectrum. With respect to our previous investigations, 16,17 in this work, we focused our attention to the analysis of sub-Doppler spectral features using a novel absolute-calibrated scanning approach which is a powerful method to retrieve several spectroscopic parameters.

II. EXPERIMENTAL SETUP
The experimental setup is sketched in Fig. 1 and is based on a commercial distributed-feedback (DFB) QCL tunable between 8.55 and 8.65 µm with a maximum optical power of ∼40 mW, tightly locked to a mid-IR, difference frequency generation (DFG)-based, optical frequency-comb tunable in the region between 8 and 14 µm having a repetition frequency f r = 250 MHz. Further details on the mid-IR comb generation setup can be found in Ref. 12. The QCL beam acts as the actual spectroscopic laser source, while the mid-IR comb serves for stabilisation and calibration purposes. The QCL output beam is collimated by a 20-cm focal length anti-reflection (AR) coated ZnSe plano-convex lens (not shown in Fig. 1) to a beam waist of 2.1 mm and split into two parts by a 50:50 beam splitter (BS 1 ). The reflected beam-portion is collinearly superimposed onto BS 2 with the mid-IR comb, filtered by FIG. 1. Experimental setup. RF: radio-frequency signal synthesiser, ISO: optical isolator, PD: photodiode, A: attenuator, M: mirror, BS: beam splitter, L: lens, G: grating. Red arrows represent the spectroscopic signals, for each of the three adopted measurement approaches: comb-referenced direct-absorption long-scan (CR-DLS), comb-referenced wavelength-modulation scans (CR-WMS), and comb-referenced direct-absorption fast-scan (CR-DFS). QCL and COMB spectra are schematised as vertical narrow lines (green and red, respectively) along the optical path of the corresponding laser-beams, before and after recombination and after spectral filtering. a 0.01 µm resolution monochromator and focused for beat-note detection onto a liquid-nitrogen cooled 200 MHz bandwidth mercury-cadmium-telluride (MCT) detector (PD 1 , responsivity of 5.7 × 10 4 V/W, 50 nV/

√
Hz noise floor, and 60 µW saturation power-level). The beat-note signal detected by PD 1 and its instantaneous frequency f b (t) are monitored by a 12-bit digital oscilloscope (D-scope) with real-time FFT capabilities. The beat-note signal contains information on the QCL instantaneous optical frequency ν QCL which is given by ν QCL (t) = nf r ± f b (t), where n is the combmode order closest to the QCL emission line (the sign of f b depends on whether ν QCL is higher or lower than nf r ). It is worth pointing out that no contribution from the comb offset-frequency (CEO) is present since the DFG process produces a harmonic comb with a CEO constantly equal to zero. The nearest comb order n is univocally determined by measuring ν QCL with an accuracy better than half mode-spacing, by means of a ±1 ppm accuracy wavemeter with an operating wavelength-range between 4 µm and 11 µm (Bristol 621B-MIR). The wavemeter is aligned onto the QCL beam portion transmitted by BS 2 (in order to avoid misreading, a grating is used to spatially filter the comb spectrum before entering the wavemeter).
Two separate phase-locked servo-loops (PLLs) are implemented to stabilise, respectively, the comb spacing f r and the beat-note signal frequency f b (t) with respect to two distinct radiofrequency (RF) reference signals provided by a couple of low-noise RF synthesisers (respectively, RF 1 and RF 2 of Fig. 1) both synchronized to a global positioning system disciplined Rb oscillator (8 × 10 12 stability at 1 s) which distributes a 10-MHz standard clock signal over the whole setup.
In particular, f b (t) is used for locking, narrowing, and calibration of the QCL emission line.
The QCL-beam portion transmitted through BS 1 is sent to a 25 cm long stainless steel cell equipped with AR-coated Zn-Se windows and filled with the gas sample to be analyzed. Beyond the cell output-window, the beam travels, respectively, through a second lens, a 50% attenuator, and a back-reflecting mirror, providing a counter-propagating weak probe beam with roughly 25% of the pump-beam power. 16 After being collinearly superimposed with the pump inside the cell, with matching phase-fronts in the middle of the cell (probe waist diameter d PR = 1.8 mm), the probe beam is sent to a thermoelectrically cooled, 50-MHz MCT detector (PD 2 ) for detection. A 30 dB optical isolator placed at the output of the QCL prevents the onset of optical feedback, minimizing the portion of the beam back-reflected toward the QCL, due to the double pass arrangement. A personal computer (PC) running Matlab controls the whole instrumentation allowing to perform the spectroscopic scans. As a final remark, we would like to point out that, at the cost of a little complication to the setup, an extended-cavity QCL could be used instead, 18 extending the working range of the spectrometer to the 7-11 µm wavelength interval, limited on the lower side by the mid-IR comb tunability and on the upper side by the operative wavelength range of the wavemeter used for extrapolating the comb-mode order n.

III. MEASUREMENT APPROACHES
By recording the transmission signal detected by PD 2 as a function of the QCL absolute frequency, several kinds of Doppler-free measurements can be performed adopting three different and complementary scan approaches, as sketched in Fig. 2. A detailed description of these methods is presented in the following, pointing out advantages and drawbacks of each approach.
(1) Comb-Referenced, Direct-absorption, Long frequency-Scans (CR-DLSs) where calibrated scans of several cm 1 frequency span with a maximum SNR ∼ 10 2 (with respect to the saturated Lamb-dip contrast) can be performed. In this configuration, the beat-note frequency, f b (t), is tightly locked to a RF signal of constant frequency f RF provided by RF 2 , while f r is varied by discrete steps. 17 For each value of f r , the spectroscopic signal from PD 2 is recorded by a 16 bit, 400 kS/s data-acquisition board (DAQ) as a function of the corresponding QCL absolute optical frequency ν QCL ( f r ). This simple approach requires long acquisition times (several minutes to tens of minutes per scan) and allows moderate frequency sampling intervals (δν QCL ∼ 1 MHz), with an SNR mainly limited by the low-frequency intensity noise of the QCL. transmittance signal from PD 2 is de-modulated in a lock-in amplifier. Again f r is scanned step-by-step while the de-modulated signal is recorded as a function of ν QCL ( f r ). Compared to the CR-DLS, this approach grants a higher SNR (∼10 3 ) and background rejection while maintaining the same acquisition times. By contrast, it requires additional data-analysis efforts in order to assess spectroscopic information from the retrieved data and to take into account modulation-induced line-profile distortions. 19 In order to achieve the above specified SNR values for CR-DLS and CR-WMS, a ∼1 s waittime per sample point is required. The typical measurement settings are therefore a compromise between the number of spectral elements acquired, frequency span, and measurement time. Considering a reasonable measurement time of about ∼20 min per scan, the maximum number of resolved spectral elements is limited to ∼1200. The sampling interval strictly depends on the width of the spectral features to be measured and is usually set between ∼100 kHz and ∼1 MHz, leading to frequency spans per single-scan from ∼120 MHz to ∼1.2 GHz wide.
(3) Comb-Referenced, Direct-absorption, Fast frequency-Scans (CR-DFSs) where the repetitionfrequency f r is kept fixed, while a frequency modulation in the kHz range is applied to the QCL (as in the CR-WMS method but with a larger modulation-depth, up to f r /4), allowing for optical frequency scans up to ∆ν QCL ∼ 100 MHz. In this novel approach, the periodic transmission signal from PD 2 is sent to D-scope together with the frequency-modulation waveform, which acts as a trigger for the acquisition. Thanks to a very short single-scan acquisition-time, corresponding to the inverse of the modulation-frequency (few tens of µs), a great number of scans can be acquired and real-time averaged into a single CR-DFS measurement lasting only few seconds. This approach grants for very narrow sampling intervals as small δν QCL ∼ 1 kHz (limited by the sampling speed of the D-scope), a large number of spectral points (∼10 000), and a very high SNR (∼10 4 in 10 s). Thanks to the high SNR achieved and the large number of spectral points acquired, combined to a direct measurement of the sub-Doppler profile, precise determination of spectroscopic parameters can be obtained, without any modulation-induced line-shape distortion.

IV. LOCKING SCHEME
Measurement precision, resolution, and SNR critically depend on the performance of the PLL which has to be carefully designed, independently on the chosen approach. For this purpose, we chose low-noise wide-bandwidth electronic components and we introduced a divide-by-16 digital frequency-prescaler in the control loop. We also adopted a low-noise QCL current driver (noise spectral-density as low as 3 nA/ √ Hz) provided with an electrical modulation input-connector with an RF bandwidth of 2 MHz. As shown in Fig. 3(a), due to the overlapping QCL and comb electric fields, a ∼40 dB, ∼1 MHz full-width half-maximum (FWHM) beat-note signal is detected by PD 1 in open-loop conditions. By adjusting the input bias current of the QCL driver, we coarsely set f b (t) to ∼70 MHz. The ∼70 MHz low-pass filtered and amplified beat-note f b (t) is mixed with a 890 MHz harmonic-signal provided by a low-noise RF synthesiser and upscaled to ∼960 MHz; then it is frequency-divided by 16 in a digital prescaler and compared in a fast phase-frequency detector (1 MHz output bandwidth) to a f RF = 60 MHz low-noise reference-signal. After being processed by a field programmable gate array based digital proportional-derivative-integrative (PID) servo, the error signal from the phase-detector is fed back to the QCL current driver. In closed loop operation, the RF spectrum of f b (t) shrinks down to below the measurement resolution and exactly at a central frequency of 70 MHz, showing the good performances of the locking-servo [gray narrow peak of Fig. 3(b)].
In order to perform CR-DFS and CR-WMS measurements, we apply a frequency modulation ∆ f (t) to the reference signal f RF , respectively, with triangular and sinusoidal temporal shapes, with modulation frequencies f mod from 1 kHz to 100 kHz and modulation depths ∆ f in the 100 kHz-5 MHz range. In order to check whether ∆ f (t) coherently transfers to ν QCL (t), we used D-scope [triggered by f RF (t) = f RF + ∆ f (t)] to perform a sliding-window FFT analysis of the beat-note f b (t). In particular, two different snapshots of f b (t) [red peaks of Fig. 3(b)] are measured in correspondence with the minimum and the maximum of ∆ f (t). The maximum measured frequency deviation ∆ f b of 4.8 MHz from the 70 MHz non-modulated value is consistent with the pre-scaled maximum modulation depth of ∆ f = 300 kHz applied to f RF (t), confirming that the modulation signal is completely transferred to the QCL optical frequency (note that the ∼150 kHz FWHM of the modulated beat-note is consistent with the 76 kHz resolution-bandwidth adopted for the FFT). As a result, a very accurate calibration of the instantaneous optical frequency can be achieved both in direct-and modulation-spectroscopy scans, even when modulation frequencies of few tens of kHz are applied to the QCL optical frequency.

V. SPECTROSCOPIC MEASUREMENTS
The molecular species investigated for testing the system performances is a sample of pure CHF 3 at room temperature. A pump beam intensity of 190 mW/cm 2 and a CHF 3 pressure ranging between ∼1 and ∼20 Pa are typically used to acquire the Lamb-dip signals.
An initial alignment optimisation and a coarse frequency calibration are done to monitor the gas absorption signal from PD 2 while sweeping the QCL current in an unlocked condition.
The free-running scan allows us to monitor the sample absorption spectra in order to maximise the saturated-absorption signal (Lamb dip), minimize alignment-related etalon effects, and choose the desired frequency window for the precision spectroscopy measurements: in particular, we focus onto the r R 40 (64) line which is, among those with higher line-strength factor within the QCL tuning region, one of the most isolated lines. By activating the PLL, we tight-lock the QCL emission frequency to the value ν QCL = nf r + f b , with f r = 250 MHz and f b = 70 MHz while the exact value of the comb mode order n = 138 968 is determined by the initial value of ν QCL measured by the wavemeter.
We evaluated the frequency resolution in tight-locking conditions by measuring the frequencyto-intensity noise conversion on the shoulder of a saturated absorption-dip of CF 3 H (Fig. 4). Such a narrow feature of ∼2 MHz FWHM with a slope of ∼0.15 mV/kHz allowed us to verify narrowing of the ∼1 MHz free-running QCL linewidth (light-blue dotted line of Fig. 4) to ∼160 kHz when the QCL is tight-locked to the comb, for 1-s integration time. We attribute this value to the frequency jitter of the mid-IR comb tooth, which in turn is ascribable to a coherent noise transfer from the RF 2 synthesizer adopted to stabilize f r . A further improvement by a factor of ∼8 of the resolution is feasible by replacing RF 2 with a synthesiser with improved noise characteristics. 21 The precise identification of the frequency-position of the saturated-absorption dip profiles is first performed by ∼1 GHz wide CR-DLS recordings at ∼5 Pa pressure [ Fig. 5(a)]: starting from a desired value of ν QCL , at each step, f r is incremented by a fixed amount δf r = 1 Hz (corresponding to an optical frequency step of δν QCL = n·f r = 138.968 kHz) in order to create a linear array of absolute optical frequencies. At the same time, the signal from PD 2 is acquired by the DAQ board while f r is recorded using a 12 digit frequency counter. Each point of the scan is acquired in 1-s integration time, essentially limited by the f r scanning speed and frequency counter measurement time, for a total acquisition time of ∼1000 s per scan and a maximum SNR of ∼10 2 with respect to the Lamb-dip amplitude.
CR-WMS scans are showed in Fig. 5(b). The optical modulation signal is directly applied to f b (t) = f b (0) + ∆ f b sin(2πf mod t) while the absolute optical frequency axis is again scanned by changing f r of fixed amounts δf r = 1 Hz. We adopted a modulation depth ∆ f mod of 10 kHz and a modulation frequency f mod = 100 kHz, well within the locking bandwidth of the f b servo. After being de-modulated in a lock-in amplifier with a 300 ms integration time, the spectroscopic signal from PD 2 is acquired by the DAQ board and recorded as a function of ν QCL (∼160 spectral points for a total acquisition time of ∼5 min per measurement).
For the CR-DFS measurements, we used a triangular modulation of frequency f mod = 1 kHz and a depth ∆ f RF = 300 kHz, which translates into ∆ f b = ±4.8 MHz due to the prescaling factor of 16 [∆ f b (t) = 16∆ f RF ]. The direct absorption signal from PD 2 is sent to the D-scope and recorded as a function of time after averaging. The oscilloscope time scale can be accurately and univocally remapped onto the absolute optical frequency scale using the usual formula ν QCL = nf r ± f b (t), where the temporal behavior of f b (t) is precisely determined by the settings of the synthesiser generator RF 2 (∆ f RF , f mod , function shape, and timing trigger function). Figure 5(c) reports a set of 8 measurements acquired at different pressures ranging from 1 Pa to 16 Pa. Each measurement, consisting in ∼2500 spectral points, is a real-time average of 10 000 consecutive single-scans for a total acquisition time of 10 s per measurement.
CR-DFS were analyzed by fitting the saturated-absorption dip with a Voigt function. For the CR-WMS measurements, a linear combination of the zero, first, second, and third order Fourier coefficients of a Voigt function has been adopted for the Lamb-dip profile, in order to properly take into account any residual-modulation-amplitude (RAM) effect. 19 The Doppler-broadened absorption background underlying the Lamb-dip has been included in the fitting routine by adding a Gaussian contribution and its first derivative, respectively, for the direct-absorption and the modulation-spectroscopy case.
From the fit-residuals plotted in Figs. 6(a) and 6(b), a 6.8 × 10 3 maximum SNR and a 9.6 × 10 2 maximum SNR, calculated over the Lamb-dip signal amplitude, can be, respectively, estimated for the CR-DFS and CR-WMS approaches. In both cases, the maximum SNR is achieved at a pressure of 10 Pa. The residuals reveal some structures, especially in the CR-WMS measurements and more evident at low pressures, which cannot be accounted for using a simple Voigt fit of the absorption dip. The nature of such fine-structure, still under investigation, may be ascribed to a hyperfine line splitting of the CHF 3 molecule. 22 We believe that the presence of such spectral features in the residuals, in particular, for the CR-WMS method, prevents for a precise evaluation of the pressure shift and the pressure broadening coefficients of the investigated line. The retrieved values of the r R 40 (64) line center frequency are, respectively, 34 742 646 956(8) kHz and 34 742 646 943(10) kHz for the CR-WMS and CR-DFS methods, consistent within the statistical uncertainties of the interpolations. In the case of the less ambiguous CR-DFS measurement, by interpolating the observed Lamb-dip linewidth, Γ FWHM , with the following relation: Γ FWHM = (Γ 0 + Γ 1 · p) 1 + 1 + Ω 2 0 /(Γ 0 + Γ 1 · p) 2 (where Γ 0 is the transit time linewidth, Γ 1 is the pressure broadening, p is the gas pressure, and Ω 0 is the Rabi frequency), 23 we were able to evaluate the pressure-broadening coefficient of the r R 40 (64) line in 35 (3) kHz/Pa, with a fractional precision better than 10%.
In conclusion, we presented a versatile mid-infrared sub-Doppler comb-referenced spectrometer, capable of performing absolute frequency calibrated GHz-wide scans with a frequency resolution of ∼160 kHz using three different measurement approaches in both direct spectroscopy and modulation spectroscopy configurations. Experimental validation of the spectrometer was conducted by the sub-Doppler spectroscopy of the room-temperature CHF 3 molecule. In particular, using the novel fast frequency scan direct-absorption approach, a maximum signal to noise ratio in the observation of sub-Doppler CHF 3 features of ∼ 7 × 10 3 for 10-s integration time was achieved underlying the spectroscopic potential of the proposed instrument.