Introduction

Addressing critical challenges such as global climate changes, industrial emissions, or the presence of hazardous substances often requires quantitative measurements of small amounts of molecular gases. Among the various techniques that have been developed for these types of applications, due to their unique properties, predominantly a combination of high detection sensitivity, high species selectivity, and rapid response time, the laser based spectroscopic techniques stand out as particularly useful [1, 2]. Moreover, since a large number of molecules have their strongest absorption lines in the mid-IR (MIR) region [3], and thanks to the growing number of powerful, stable, and tunable coherent sources in this wavelength region [4–8], this spectral region has started to be the preferred one for these types of technique. A number of laser based spectroscopic techniques for detection of molecular species in gas phase in the MIR have therefore been developed over the last years [9–13]. With access to such techniques, many types of molecular species can be detected down to low abundances.

Among all laser-based spectroscopic detection techniques that have been developed for the MIR region, those based on an optical cavity for prolongation of the interaction length have demonstrated the highest detection sensitivities [14]. A few examples of such are cavity ring-down spectroscopy (CRDS) [15, 16] and its related saturated-absorption cavity ringdown (SCAR) [17, 18], off-axis integrated cavity output spectroscopy (OA-ICOS) [19, 20], and optical feedback cavity enhanced absorption spectroscopy (OF-CEAS) [21, 22]. However, despite their advantages, these techniques cannot always provide the exceptional high detection sensitivities that some applications demand. Techniques with yet higher detection sensitivities are therefore needed.

It can be concluded though that even though all the aforementioned techniques incorporate optical cavities, they do not require a tight lock of the frequency of the laser to that of a transmission mode of the cavity. However, it has repeatedly been demonstrated that the techniques that make use of a tight lock of the laser to the cavity in combination with frequency modulation (FM) for reduction of noise, in particular heterodyne-detected cavity ring-down spectroscopy (HD-CRDS) [23] and noise-immune cavity-enhanced optical heterodyne molecular spectrometry (NICE-OHMS) [24, 25], can provide the best detection sensitivities. For example, the latter one has demonstrated astonishing detection sensitivities in the 10⁻¹⁴ cm⁻¹ range [24, 26]. These types of technique have therefore been considered as extraordinary powerful for ultra-sensitive detection of molecules in gas-phase. However, a drawback with them is that they so far have predominantly been realized in the near-IR (NIR) region, in which most molecules have weak overtone transitions. This implies that their full power for trace gas detection has not yet been assessed. It is therefore of importance to develop them further so as to incorporate also the important MIR region.

In NICE-OHMS the carrier is locked to one of the modes of the cavity while the modulation frequency is chosen equal to the free-spectral range (FSR) of the cavity (or an integer thereof). By this, each spectral components of the frequency modulated light interacts with its own cavity mode. The NICE-OHMS signal constitutes the transmitted light demodulated at the FM frequency.

One important property of NICE-OHMS is that it is inherently background free; since FM spectroscopy is a background free technique, there is similarly no NICE-OHMS signal from an empty cavity. Another is that, for a properly optimized system, all components of the light are affected in an identical manner by the frequency-to-amplitude noise conversion that plagues cavity enhanced direct absorption spectroscopy. This implies that although any such noise conversion will affect the transmitted power, it does not contribute to the NICE-OHMS signal from an empty cavity. This is commonly referred to as “noise immunity” [24]. Moreover, due to counter propagating wave fronts, the technique is also capable of detecting both Doppler-broadened (Db) and sub-Doppler (sD) signals [27]. All this implies that NICE-OHMS has a huge potential for a number of applications, not least sensitive trace gas detection, in particular that based on isotopologue studies.

Since its first realization using a narrow linewidth fixed-frequency Nd:YAG laser [24], the technique has mostly been developed around tunable lasers, for other types of applications, predominantly spectroscopy of weak transitions [28, 29] and for trace gas detection [27, 30].

Moreover, due to the broad availability of optical and electro optic components in the near-infrared (NIR) telecom region a significant part of the development of the technique has so far taken place in this wavelength region [31–33]. Most notably, a Db NICE-OHMS system based on an Er-doped fiber laser emitting at ~1.5 µm has demonstrated a white noise equivalent absorption per unit length (WNEAL) of 2.6 × 10⁻¹³ cm⁻¹ Hz^−1/2 and an absorption per unit length for the optimum integration time, the latter henceforth referred to as the detection sensitivity per unit length (DSL), of 9 × 10⁻¹⁴ cm⁻¹ over 30 s [26]. Since C₂H₂ has transitions with large line strengths in this wavelength region [~10⁻²⁰ cm⁻¹/ (molecule cm⁻²)], this DSL corresponds to a concentration detection limit (CDL) of C₂H₂, defined as the concentration that gives a certain S/N ratio (in this field commonly taken as unity), in the sub-ppt (parts-per-trillion) range.

However, since most other types of molecules have primarily only weak overtone transitions in this wavelength range [often with line strengths around or below 10⁻²³ cm⁻¹/(molecule cm⁻²)] [3], the use of fiber lasers for NICE-OHMS does not provide similarly low CDLs for them. They can then solely be detected typically down to hundreds of ppt or at ppb (parts-per-billion) levels. This has so far restricted the use of NICE-OHMS for trace gas detection. A way around this is to apply NICE-OHMS to the mid-infrared (MIR) region, in which the species can be addressed on fundamental vibrational transitions that have larger line strengths [often ~10⁻¹⁸ cm⁻¹/(molecule cm⁻²)] [3]. If NICE-OHMS could be realized down to similar WNEALs or DSLs in this region, CDLs in the low ppq (parts-per-quadrillion) range are expected for a multitude of molecular species. However, the NICE-OHMS technique has not yet been developed to the same performance in the MIR range. On the other hand, since there are no (or very few) fundamental reasons why the NICE-OHMS technique should not be able to reach similarly impressive WNEAL or DSLs in the MIR region as in the NIR, it is of importance to develop the technique further into the MIR region. However, it is far from trivial to realize this in reality, mainly due to technical reasons, predominantly a lack of suitable electro optic components working in this wavelength region.

The first realization of MIR NICE-OHMS was performed by Taubman et al. in 2004, using a quantum cascade (QC) laser [34]. However, because of significant amounts of residual amplitude modulation (RAM) the instrumentation was used in the sD mode of detection, since this requires small scanning ranges (which keeps the amount of RAM down). By targeting an sD feature in NO at 8.51 µm they could achieve a WNEAL of 9.7 × 10⁻¹¹ cm⁻¹ Hz^−1/2 [34].

However, sD detection is limited to low pressures, often in the mTorr or low Torr regime [35]. When applied to trace gas detection, the use of such low pressures reduces the CDL as well as the dynamic range of the technique. In contrast, for the Db mode of detection, the optimum pressure (the one that provides the best DSL) is often significantly higher, typically ~0.1 atm (depending on the transition targeted and the experimental conditions [36]), which implies that lower (better) CDLs result for a given WNEAL. In addition, the dynamic range can be larger, typically several orders of magnitude [37]. For ultra-sensitive trace gas detection, Db detection is therefore often seen as more advantageous than sD detection.

A way around the problem with excessive amounts of RAM in MIR NICE-OHMS systems is to base the system on a singly resonant optical parametric oscillator (OPO). In such an OPO, one of the outputs is locked to a mode of the cavity. A consequence of this is that a modulation of the pump light will be directly transferred to the other (non-resonant) field [38]. Since OPOs can be pumped by light in the NIR region, frequency modulated light in the MIR region can therefore be produced by such an OPO-based system without access to EOMs working in the MIR region. The use of an OPO with a resonant cavity for realization of frequency modulated light in the MIR region was first demonstrated by Crabtree et al. who used such an OPO for noise-immune cavity-enhanced optical heterodyne velocity modulation spectroscopy of ions and could demonstrate a WNEAL of 3.4 × 10⁻⁹ cm⁻¹ Hz^−1∕2 [39].

The first NICE-OHMS system based on an OPO was realized by Silander et al., who recently, by the use of a cavity with a finesse of 500 and by addressing a transition in methane at around 3.4 µm, demonstrated a WNEAL of 3 × 10⁻⁹ cm⁻¹ Hz^−1∕2 and a DSL of 1.5 × 10⁻⁹ cm⁻¹ measured over 20 s [40]. It was found, among other things, that the WNEAL of this system was sufficient to address the ¹³CH₄ isotopologue in the atmosphere, although it was still not possible to detect the less abundant CH₃D isotopologue, which only exists at concentrations ~1 ppb, with sufficient accuracy. Since these two isotopologues are the most important ones for assessment of sources and sinks of methane in our environment [41], and a simultaneous assessment of the two might require the use of transitions with line strengths below the maximum ones, the detection sensitivity (i.e. the signal to noise ratio) of this OPO-based NICE-OHMS system needed to be improved. This can be done by implementing a cavity with a higher finesse and by reducing the frequency noise of the light transmitted through the cavity, both which can be achieved by improving the lock of the laser to the cavity [32].

Since the locking of the laser to the cavity in the first realization of an OPO-based NICE-OHMS system was limited by the restricted bandwidth of the piezo of the seed laser to the OPO system [40], this system was improved by implementation of an acousto optic modulator (AOM) directly after the seed laser. By this, it was possible to lock the OPO to a cavity with a higher finesse, in this case 4000. In fact, the AOM provides sufficient bandwidth for the locking servo to not only lock the laser but also to narrow the OPO idler linewidth so it becomes narrower than the cavity linewidth, similar to the system realized in the NIR region [32]. To the authors’ knowledge, this is the first time a cw OPO has been locked to a cavity with medium-high finesse. This has also implied that it was possible to realize an OPO-based NICE-OHMS system around a medium-high-finesse cavity (in this case with a finesse of 4000) that is aimed for detection of trace gases in the MIR C-H stretch region.

The implementation of an AOM in an OPO system does thus not only provide a possibility to lock the laser to a higher finesse cavity, it also reduces the frequency noise of the light transmitted through the cavity. It was thereby found that the performance of MIR NICE-OHMS could be significantly improved by the simultaneous incorporation of an AOM and a cavity with a higher finesse. To our knowledge, this work thereby constitutes the first demonstrations of both the narrowing of the linewidth of an OPO with respect to an external cavity by the use of an AOM and the realization of a Db NICE-OHMS system in the MIR range with a WNEAL in the 10⁻¹⁰ cm⁻¹ Hz^−1/2 range. Since a multitude of species have vibrational transitions that have line strengths in the 10⁻²⁰ - 10⁻¹⁸ cm⁻¹/(molecule cm⁻²) range in this region, this implies that the system is capable of providing CDLs well into the ppt region.

Experimental Setup

The experimental setup is shown in Fig. 1. It is based upon the system described in detail in [40], although realized around a 4000 finesse cavity and with an AOM implemented in the OPO-system. In short, light from a seed laser, lasing at 1.064 µm, (NKT Photonics, Koheras Adjustik Y-10) is sent through a fiber-coupled AOM (AA SA, MT110-IR20-FIO) for an increased frequency control bandwidth, a fiber-coupled electro optic modulator (EOM, Photline, NIR-MPX-LN-05) for creation of sidebands of the seed laser light, and a fiber amplifier (IPG Photonics, YAR-10 K-1064-LP-SF) for amplification of the modulated laser light above the threshold of the singly resonant OPO (Aculight, Argos 2400 SF, module C). The frequency of the OPO idler is given by the difference between the frequencies of the seed laser and the OPO signal output, which both were picked off after the OPO by a wedged window and monitored with a fiber-coupled wave meter (Burleigh, WA-1500-NIR-89).

 

Fig. 1 Schematic illustration OPO-based NICE-OHMS system realized in this work. It is based on the system described in detail in [40], realized around a plano-concave cavity with a finesse of 4000, to which an AOM has been implemented. The PDH servo for locking the 3.2 - 3.9 µm OPO idler output (red in color) to the cavity gives feedback to the seed fiber-laser PZT at frequencies < 40 Hz while the fast components go to the AOM.

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The idler output (3.2 - 3.9 µm) was attenuated to ca. 50 mW by the use of a prism (Thorlabs, PS862). The light reflected from its first surface was sent into a closed plano-concave cavity (whose curved mirror had a radius of 1 m) with a length of 39.5 cm and a FSR of 380 MHz. The unused parts of the signal and the idler outputs, as well as the transmitted part of the pump beam, were dumped into beam dumps. The cavity spacer is made from low-thermal expansion Zerodur and two cylindrical piezoelectric transducers (PZT) for FSR tuning. The mirrors were made on zinc selenide substrates with a reflectivity of 99.92% (LohnStar), providing a finesse of 4000. Both the back reflected and the transmitted beams were sampled using a beam sampler with 1% reflectance (Meller Optics, SCD1553-01B) and monitored by fast detectors with a bandwidth close to that of the modulation frequency (~370 MHz, Vigo, PVI-4TE-8-1x1). To control the sample pressure and evacuate the system, the cavity was connected to a vacuum system. The pressure in the cavity was measured using two pressure gauges (Leybold CTR 101) that together cover a pressure range of 10⁻⁴ to 1000 Torr.

The carrier of the modulated light was locked to a longitudinal mode of the cavity by the use of the Pound-Drever-Hall (PDH) technique [42], while the FM frequency was locked to the FSR of the cavity by the DeVoe-Brewer (DVB) method [43]. To generate sidebands for the PDH locking and the FM detection, the EOM was simultaneously modulated at 20 and 380 MHz using a fixed frequency and a voltage controlled oscillator (VCO), respectively. The PDH and the DVB error signals were generated by demodulating the back reflected light at 20 and 360 MHz respectively. The PDH error signal was sent through servo electronics, which control the idler frequency by use of the fiber laser PZT and the AOM. The DVB error signal was sent through servo electronics to the 380 MHz VCO.

The modulation index of the 380 MHz modulation, β, was set to 0.46. Since the nonlinear frequency conversion in an OPO is instantaneous, and the signal wave is resonant with a mode of the OPO-cavity, the mode structure of the pump beam is directly transferred to the idler [38]. Since this mode structure matches that of the cavity, most of the idler is transmitted through the cavity, imprinted with information about the gas in the cavity. By demodulating the transmitted signal with the VCO frequency in an IQ mixer (Sigatek QD54A10) two NICE-OHMS signals, detected at in-quadrature phases, are simultaneously produced. The detection phases were set to pure in-phase and out-of-phase detection, respectively.

The design of the PDH servo

The aim of the implementation of the AOM is to narrow the linewidth of the 100 kHz wide idler output to below that of the cavity (which is 80 kHz). This requires a minimum locking bandwidth of 100 kHz [44]. While feedback to the PZT of the fiber laser can provide high gain at low frequencies, which is needed to reduce the influence of drifts and making scanning possible, its bandwidth had to be limited to around 1 kHz due to two resonances in the fiber laser PZT; a strong at 23.4 kHz and a weak around 35 kHz, which together add a 360° phase shift and a gain roll-off with a slope of −80 dB/decade. Since the AOM is not limited by such resonances and since it can provide gain up to 100 kHz, it could be used to provide locking also at higher frequencies.

To implement the AOM in the system in the best possible way, the PDH error signal was split into three branches, termed the PZT-servo, the PZT-resonance-servo, and the AOM-servo. The first two were added to control the PZT of the fiber laser, while the last one was fed to the AOM. The Figs. 2(a) and 2(b) show the gain and phase of the open loop transfer functions of these servos, respectively (which include the responses of the actuators and the cavity). To allow the fiber laser to follow slow drifts and the scan of the cavity, the PZT-servo (dash-dotted green curves) includes a double-integrator stage that adds high gain at low frequencies. At around 40 Hz the AOM-servo takes over (dashed orange curves) and compensates for high frequency jitter of the idler (up to 100 kHz). Although the PZT-servo is designed to filter out high frequencies it was found that the PZT resonances are still excited by the PZT driver and acoustic noise. Since the resulting oscillation at 23.4 kHz puts high load on the AOM-servo a PZT-resonance-servo (dotted blue curves) that gives feedback around this PZT resonance frequency was implemented.

 

Fig. 2 Panel (a) and (b) illustrate the gain and the phase, respectively, of the open loop transfer functions of various parts of the PDH servo (i.e. Bode plots). The four curves in these panels represent the responses of the PZT-servo (dash-dotted, green), the PZT-resonance-servo (dotted, blue), the AOM-servo (dashed, orange), and their combination (solid, black). Panel (c) shows the power spectrum from the PDH error signal when the laser is locked with the PZT servo only (green), after implementation of the AOM servo (orange), and when all three servos, including the PZT-resonance-servo, are active (black). Panel (d) illustrates, as area-normalized histograms, the amplitude distribution of the PDH-error signal in terms of laser-cavity frequency jitter for the three sets of data presented in panel (c).

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The electronics of the PZT-resonance-servo consist of a gain stage with a high pass filter that compensates for the low-pass roll off of the PZT-response, so as to lift the response around the resonance above the gain of the AOM-servo. To provide stable handover, both the gain and the corner frequency of this filter can be tuned so that the phase differences between the responses of the PZT-resonance-servo and the AOM-servo loops at the two handover points (which are just below and above the center frequency of the strongest PZT resonance) are below 90°. When correctly optimized, the AOM servo takes care of any remaining oscillations originating from the steep zero gain crossings of the PZT-resonance-servo.

The performance of the three servo branches is illustrated in Figs. 2(c) and 2(d). The three sets of data in the two panels show the PDH error signal for three different locking schemes: PZT servo only (green curve and histogram), after implementation of the AOM servo (orange curve and histogram), and when also the PZT-resonance-servo is active (black curve and histogram). The two panels show the power spectrum and the corresponding amplitude distributions of the PDH error signal for the three locking schemes where the frequency scale of the latter was constructed by assuming that the peak-to-peak value of the PDH error signal (2.2 V) corresponds linearly to twice the half width half maximum (HWHM) of the cavity linewidth (2 × 47 kHz).

In addition to a broad response the power spectra in Fig. 2(c) indicate the existence of resonances at various discrete frequencies. These can be attributed to either electronic oscillations, e.g. higher harmonics of the frequency of the power lines (50 Hz), or acoustic resonances in the system.

The linear conversion of the amplitude voltage to frequency implies that parts of the peaks of the green histogram in Fig. 2(d) in reality should be attributed to frequency jitter whose amplitude is larger than the HWHM of the cavity linewidth. This implies that the laser frequency in fact might have a somewhat broader distribution of amplitudes than shown in the figure. Despite this, this histogram shows that when the laser is locked solely with the PZT servo, the servo manages only to hold the laser center frequency at the cavity resonance; it is not able to significantly reduce the laser-cavity jitter that appears at higher frequencies and thereby narrow the laser.

Figure 2(c) shows that after adding the AOM servo (orange curve and histogram) the laser noise is reduced between 15 and 25 dB for the frequency range between 10 Hz and 30 kHz. Figure 2(d) indicates that this implies a narrowing of the laser linewidth relative to the cavity. The small bump in Fig. 2(c) at 100 kHz corresponds to the AOM servo bandwidth.

Finally, as can be seen from Fig. 2(c), when also the PZT-resonance-servo is implemented (black curve) the oscillations from the strongest resonance in the fiber laser PZT at 23 kHz are suppressed. However, Fig. 2(d) (black contour histogram) shows that this does not significantly affect the amplitude distribution of the PDH error signal.

Evaluation and calibration procedures

Measurements were performed by repeatedly scanning the cavity modes to which the laser carrier and sidebands were locked over the transition targeted. To evaluate the measured signals a model function for Db NICE-OHMS was fitted to each scan. Two different functions were used. The first was the commonly used expression for Db NICE-OHMS, here referred to as the conventional (CONV) expression, which is valid when the single pass absorption is significantly smaller than the empty cavity losses, i.e. α₀L << π/F, where ${\alpha }_o$, $L$, and $F$ are the absorption coefficient, the cavity length, and the finesse, respectively, given for example by [40] or Eq. (1) in [45]. This condition was not fulfilled when the upper part of the dynamic range of the system was assessed. Therefore, a recently derived description of Db NICE-OHMS that is valid also when the α₀L << π/F condition does not hold, given by the Eqs. (35), (36) and (38) in [45], referred to as the FULL description, was also used.

Both these descriptions assume that the light can be modelled as a triplet. However, it has also been shown that for large modulation indices, primarily for $\beta$ > 0.5, it is more appropriate to model the light as consisting of several pairs of sidebands [36, 46]. On the other hand, in this case, it was found that, for the CONV description, there was no appreciable difference whether the laser was modeled as a triplet, using the description given in [40] and Eq. (1) in [45], or whether it was considered to consist of multiple sidebands, as described in [33, 36, 46]. The same was found for the FULL description, which for this purpose was extended to be valid also for multiple sidebands (to be described in an upcoming publication). For simplicity, in the analysis, it was therefore assumed that the laser was modulated in such a way that it can properly be described as a triplet.

As was alluded to above, since the detection phases were set to pure in-phase and out-of-phase detection, for the cases when the CONV description is applicable, the outputs of the IQ-mixer represent pure dispersion and absorption NICE-OHMS signals, respectively [45].

The transition addressed was the F2-F1 transition in the R(6) manifold of the ν₂ + ν₄ band in ¹²CH₄ at 3.393 µm, which has a line strength of 1.51 × 10⁻²¹ cm⁻¹/(molecule cm⁻²) [3] and previously has been suggested as one of the optimum transitions for detecting the ratio of ¹³CH₄ to ¹²CH₄ [47]. This transition was found to be suitable for assessment of the performance of the system by use of a commercially available reference gas containing 45 ppm of methane for a multitude of reasons. Firstly, the dynamic range could be assessed within pressure ranges for which the pressure gauges used have a linear response and sufficient precision (0.1 mTorr for pressures up to 1 Torr and 100 mTorr above this). Secondly, over the whole dynamic range non-linear pressure dependent effects, e.g. Dicke narrowing and speed dependent effects [48, 49], could be neglected. By this, the entire pressure dependence could be described by a single line shape parameter, viz. the ordinary pressure broadening coefficient, which for this transition previously has been assessed to 2.45 MHz/mTorr [3]. Thirdly, measurements could be performed under a minimum of optical saturation. To avoid any remaining influence of optical saturation, the signal was detected in pure in-phase (dispersion) phase, since it has been shown that in the Doppler limit this signal is independent of optical saturation [50]. All this vouches for a sturdy, reliable, and accurate assessment of absorption coefficients and concentrations from fits.

For evaluation of the system, measurements were performed at different pressures using the reference gas or, alternatively, on an empty cavity. The system was calibrated using 1 Torr of the reference gas. At this pressure, and with this particular transition addressed, the concentration of the gas can be considered stable over time while the α₀L << π/F condition necessary for the CONV description is still fulfilled. Once the system had been calibrated, fits of the model functions to individual scans provide the absorption coefficient and thereby the concentration of the analyte (as assessed by the particular model used).

Results

Although the system provides Db NICE-OHMS signals that are well described by the two model descriptions used, it also gives rise to background signals (i.e. a signal that is present also in the absence of analyte) whose noise and drifts limit the detection sensitivity of the instrumentation. As is described in the discussion section below, this originates predominantly from multiple reflections between optical surfaces, so called etalons. Typical Db NICE-OHMS signals from 106 Torr and 911 mTorr of the reference gas (together with corresponding fits of the model functions) are displayed by the black curves in the two panels [(a) and (b), respectively] in Fig. 3. The signal in Fig. 3(a) originates from raw-data while that in Fig. 3(b) represents a background-subtracted signal, i.e. the net signal obtained by subtracting the signal from an empty cavity from that measured for the amount of analyte stated. The signal in Fig. 3(a) has not been subjected to any such background subtraction for two reasons. Firstly, since it is significantly larger than that shown in Fig. 3(b), the influence of any background signal on the fit of the model function is virtually insignificant. Secondly, due to the shifts of the cavity modes with pressure, unless the scans are subjected to an absolute frequency reference, as suggested in [51], a background signal measured under low pressure would not be a proper representation of the background signal that exist under the high pressure at which the data in Fig. 3(a) are taken.

 

Fig. 3 Upper windows: single scan NICE-OHMS signals of the F2-F1 transition in the R(6) manifold of the ν₂ + ν₄ band of methane at 3.393 µm (black) at 106 Torr (panel a) and 911 mTorr (panel b) together with their fitted line-shapes (red). Lower windows: the residuals of the fits (lower parts).

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Since the high pressure data in Fig. 3 are taken under conditions for which the CONV description is not appropriate (see discussion below) both fits were simulated by the FULL description. The lower window in each panel displays the residuals, i.e. the difference between the measured data and the fits. The figure shows, by Fig. 3(a), that for high pressures, for which the number density of absorbers is significantly above the detection limit of the system, the residual shows some broad noisy structure. This is assumed to originate from compromised lockings of the laser carrier to the cavity mode addressed as well as the modulation frequency to the FSR of the cavity, both caused by the high absorbance in the cavity. It is also possible that the symmetric parts of the residual can originate from Dicke narrowing or speed dependent effects, which were not included in the line-shape models used in this work. If so, these parts of the residuals could then potentially be improved by the use of more extensive line shape functions [48, 49], which, however, is outside the scope of this work. Figure 3(b) shows that under low pressures the residual does not show any such broad structure; it is dominated by an etalon in the system (further discussed below).

The sensitivity and the stability of the instrumentation presented in this work were compared to those of the previous system [40]. Db NICE-OHMS signals were measured from an empty cavity with a scanning rate of 1 Hz over a time span of 7 hours. As was alluded to above, the absorption coefficient of each scan was estimated by the use of fits of the aforementioned model functions. The results of such measurements, for both the present and the previous systems, are presented in Fig. 4 in form of Allan-Werle plots in terms of absorption per unit length.

 

Fig. 4 Allan-Werle deviation of the absorption coefficient from an empty cavity as a function of integration time, evaluated by fitting the CONV model function to the NICE-OHMS signal in pure dispersion phase. The upper and lower curves (black and blue) represent the results of measurements with the 500 finesse cavity system (previous system) and the 4000 finesse system including the AOM (present instrumentation), respectively.

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Figure 4 shows that while the low finesse system (upper curve, black in color) has a WNEAL of 3 × 10⁻⁹ cm⁻¹ Hz^−1∕2, the system described in this work (lower curve, blue in color) displays a WNEAL that is more than one order of magnitude lower (better), viz. 2.4 × 10⁻¹⁰ cm⁻¹ Hz^−1∕2. It can also be seen that the high finesse system shows the same improvement up to integration times of 100 s. For yet longer integration times, for which drifts often start to affect the detection sensitivity, there is still an improvement although not as large. The best DSL, which was found to appear for an integration time of 20 s, was assessed to 1.3 × 10⁻¹⁰ cm⁻¹.

The dynamic range of the system was assessed by evaluating the NICE-OHMS signals for a large variety of pressures of the reference gas. Figure 5 shows curves of growth where the assessed (estimated) on-resonance absorption per unit length, ${\alpha }_0^{est}$, is plotted as a function of the nominal on-resonance absorption per unit length, ${\alpha }_0^{nom}$. The former entity is obtained from the NICE-OHMS data using the fitting procedure described above, where the red crosses and the blue circles correspond to fits using the CONV and the FULL description, respectively, while the latter, for each pressure, was calculated by the use of tabulated transition data (the line strength and the pressure broadening coefficient) using a Voigt line shape function.

 

Fig. 5 Individual markers: the estimated (assessed) on-resonance absorption per unit length, ${\alpha }_0^{est}$, versus the nominal on-resonance absorption per unit length, ${\alpha }_0^{nom}$, for the particular transition addressed. Each marker represents an individual scan (measured at 1 Hz) and all data were taken with a non-diluted reference gas containing 45 ppm of methane at different pressures (between 40 mTorr and 120 Torr). The ${\alpha }_0^{est}$-values were extracted from NICE-OHMS measurements by the use of the FULL or the CONV description, blue circles and red crosses, respectively. Solid line: the ideal case.

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The red crosses show that when the CONV description is used for evaluation of the data ${\alpha }_0^{est}$ is an appropriate assessment of ${\alpha }_0^{nom}$ up to an absorption per unit length of around 3 × 10⁻⁶ cm⁻¹. For larger absorptions the response becomes less accurate as the α₀L << π/F condition is no longer fulfilled. The blue circles, on the other hand, show that assessments based on the FULL description are more appropriate for the highest absorption per unit length, and that this description can be used for absorption coefficients at least up to 3 × 10⁻⁵ cm⁻¹.

To ascertain that the measurements are not affected by an incorrect pressure broadening coefficient, the linearity of the curve-of-growth was confirmed by measurements with a diluted reference gas (for which pressure dependent effects should be more significant than any possible inherent non-linarites in the NICE-OHMS signal, data not shown).

It should be noticed that the rightmost/uppermost data point in Fig. 5 represents a situation for which the single pass absorbance, ${\alpha }_{0}L$, is equal to the empty cavity losses, $\pi /F$, i.e. when $F{\alpha }_{0}L/\pi$ $\approx$ 1. Beyond this, the system gets instable because of disturbances of the FSR-lock caused by the strong absorption and dispersion.

Since an absorption per unit length of 10⁻⁸ cm⁻¹ corresponds, for the particular transition addressed, to a partial pressure of methane of 2 µTorr, for which the sample concentration under repeated measurements is affected by outgassing or adsorption in the cavity, we attribute the spread in the data in the lowest part of the figure to uncertainties in the sample concentration and not fluctuations in the NICE-OHMS signal.

Taking into account the fact that the DSL for an empty cavity is 1.3 × 10⁻¹⁰ cm⁻¹, it can be concluded that the NICE-OHMS system, when addressing a single line, has a dynamic range (in terms of absorption per unit length or concentration) of at least 5 orders of magnitude.

Discussion

The detection sensitivity of the system, which is assessed to correspond to a WNEAL of 2.4 × 10⁻¹⁰ cm⁻¹ Hz^−1∕2 and a DSL of 1.3 × 10⁻¹⁰ cm⁻¹ (the latter for an integration time of 20 s), is currently limited by drifting background signals and the incoupling of noise through these. The main contribution to this is assumed to originate from an etalon with an FSR of 32 MHz (corresponding to an optical path length of about 5 m). The residual in Fig. 3(b) can be related to this etalon. It can be noted that the peak-to-peak value of this residual is one order of magnitude smaller than the signal taken at 911 mTorr, which corresponds to an on-resonance absorption per unit length of 2.2 × 10⁻⁷ cm⁻¹. It was found that although this etalon is not present before the fiber amplifier it exists in the pump as well as in the signal output of the OPO. Moreover, as the etalon signal does not vary when the OPO cavity (and thereby the signal frequency) is scanned, it can be assumed that it is formed in the fiber amplifier.

It is interesting to note that the DSL predicted by the Allan plot in Fig. 4, which is 1.3 × 10⁻¹⁰ cm⁻¹, is two orders of magnitude below the peak-to-peak value of the residual displayed in Fig. 3(b). This is plausible since the fit of the Db NICE-OHMS signal used to determine the Allan variance picks up only a small fraction of an etalon with a significantly shorter FSR than the width of the line shape. Figure 4 in [26] indicates in fact that a fit of a Db NICE-OHMS signal from a scan similar to that in Fig. 3(b) will pick up at the most −60 dB (i.e. less than a factor of 10⁻³) of the signal from a drifting etalon whose FSR is less than 4% of the half width of the NICE-OHMS signal). This implies that the DSL is not primarily limited by drifts of the fiber amplifier etalon. However, the signal from such an etalon can couple in various other types of noise, e.g. frequency noise, intensity noise, or acoustic noise, into the detected NICE-OHMS signal that can restrict the DSL of the system to the assessed value.

There is also evidence of a background signal that is created by an etalon with a FSR of about 1500 MHz (thus corresponding to an etalon with a length of about 10 cm). As this depends on both the frequency of the pump and signal output of the OPO, it could be concluded that it is formed in the OPO. Although it has an amplitude that is similar to that of the 32 MHz etalon signal, it was found that it is stable over sufficiently long time-scales that it can be efficiently eliminated from the signal by background subtraction of an empty cavity measurement. However, it might still contribute to long term drifts.

The sensitivity of a trace gas detection method can be expressed in a variety of ways, making direct comparisons between various instruments strenuous. However, it can be conclude that the WNEAL and DSL for the MIR NICE-OHMS system presented in this work, 2.4 × 10⁻¹⁰ cm⁻¹ Hz^−1∕2 and 1.3 × 10⁻¹⁰ cm⁻¹ (for an integration time of 20 s), respectively, compare favorably to virtually all other WNEAL and DSL values for detection of molecules in gas phase reported for laser-based MIR cavity enhanced detection techniques.

For example, using MIR light at 3.346 µm produced by difference frequency generation Whittaker et al. have demonstrated detection of CH₄ by CRDS down to 2.8 × 10⁻⁸ cm⁻¹ over 6 s and, based on an Allan plot, predicted detection down to 2.9 × 10⁻⁹ cm⁻¹ over 44 s [16]. Similarly, Genoud et al. have reported detection of ¹⁴C¹⁶O₂ down to 2.1 × 10⁻⁹ cm⁻¹ Hz^−1∕2, corresponding to a CDL of 50 ppt [52]. Although not specifically quoting any WNEAL or DSL values, other authors have demonstrated impressive CDLs using CRDS, e.g. McCatt et al. have reported on detection of ¹⁴C¹⁶O₂ down to low (~3.5) ppt levels [53]. Albeit not directly comparable, but still a demonstration of special interest in this respect, is the work by Mizouri et al. who used CRDS in combination with laser induced fluorescence to detect SD radicals in supersonic jets. They reported on a WNEAL of 1.6 × 10⁻⁹ cm⁻¹ Hz^−1∕2 and a DSL of 7.9 × 10⁻¹¹ cm⁻¹ over 200 s [54].

Using cavity enhanced optical frequency comb spectroscopy, Foltynowicz et al. have demonstrated detection of H₂O₂ at 3.76 µm down to 5.4 × 10⁻⁹ cm⁻¹ Hz^−1∕2, which corresponded to a CDL of 8 ppb [55].

By use of cavity coupled photo acoustic spectroscopy, Borri et al. have demonstrated detection of CO₂ at 4.33 µm down to 1.4 × 10⁻⁸ cm⁻¹ over 4 s, corresponding to 300 ppt [56]. Other authors have demonstrated similar CDLs in the MIR region, e.g. Patimisco et al. have detected CO₂ down to 300 ppt over 20 s [57], while Peltola et al. have demonstrated detection of HCN down to 190 ppt (over 1s) and methane down to 65 ppt (over 30 s) [58].

Using OA-ICOS, when detection methane, Malara et al. have demonstrated a WNEAL of 5.7 × 10⁻⁹ cm⁻¹ Hz^−1∕2, corresponding to a CDL of 850 ppt [59]. By use of the cavity-leak-out spectroscopy (CALOS) technique and addressing OCS by the use of a 5 µm laser Halmer et al. have demonstrate an impressive WNEAL of 7 × 10⁻¹¹ cm⁻¹ Hz^−1∕2 for a single spectral point, corresponding to a CDL of 7 ppt [60].

In addition to all this, and seemingly the most impressive achievement so far is that by Galli et al. who, by use of the SCAR technique, have demonstrated detection of ¹⁴C¹⁶O₂ at 4.5 µm addressing a line with a line strength of 3 × 10⁻¹⁸ cm⁻¹/(molecule cm⁻²) down to 43 ppq, but unfortunately without reporting on any WNEAL or DSL value [18].

It is possible to conclude that among all these demonstrations, the WNEAL and DSL values of our system compare favorably to most of those of the other systems developed, with the exceptions being the WNEAL value for detection of OCS by CALOS reported by Halmer et al. [60] and the DSL value of the jet detection instrument developed by Mizouri et al. [54]. A comparison of the CDL between various systems is more difficult and less straightforward to perform, since such will depend largely on the line strength of the transition addressed. However, since it can be concluded that our system, whose WNEAL and DSL values correspond to CDL values in the low ppt range if transitions with line strengths in the 10⁻¹⁸ cm⁻¹/(molecule cm⁻²) range would be addressed, would compare favorably also in this respect to most of the aforementioned works.

Conclusions

In summary, by implementing an AOM after the seed laser with servo electronics that provided feedback up to 100 kHz the idler output of a singly resonant OPO could be locked to a cavity with a finesse of 4000. To reduce oscillations at the resonances of the fiber laser PZT a resonance feedback scheme was implemented in the PDH servo. When locked to a cavity, this system provided a significant narrowing of the idler output. To the authors’ knowledge, this is the first time the linewidth of an OPO has been narrowed by the use of an AOM.

By this, the detection sensitivity of a previously developed MIR OPO-based NICE-OHMS system could be improved by one order of magnitude. It has been demonstrated that the system has a white noise equivalent absorption per unit length (WNEAL) of 2.4 × 10⁻¹⁰ cm⁻¹ Hz^−1∕2 and a detection sensitivity per unit length (DSL) of 1.3 × 10⁻¹⁰ cm⁻¹, the latter obtained for an integration time of 20 s. To our knowledge, these detection sensitivities are the lowest so far reported for Db MIR NICE-OHMS and they compare favorably to most others reported for laser-based MIR cavity enhanced detection techniques.

It can additionally be concluded that for the transition addressed in this work, which has a line strength of 1.51 × 10⁻²¹ cm⁻¹/(molecule cm⁻²), a DSL of 1.3 × 10⁻¹⁰ cm⁻¹ solely corresponds to a CDL in the low ppb range when the sample is detected at 50 Torr. However, since there are transitions with significantly larger line strengths than this in the wavelength range covered by the OPO system, it can be surmised that if any such transition would be addressed, the CDL of the system would be significantly lower, presumably in the low ppt range. Moreover, the dynamic range of the system was shown to be at least 5 orders of magnitude. All this opens up for a variety of future applications for MIR OPO-based NICE-OHMS, not least for isotopologue ratio measurements for environmental applications.

When applied to detection of methane and its various isotopologues, it is possible to conclude that although the transitions in the CH₃D isotopologue have somewhat lower line strengths than those in CH₄, and since its concentration in the atmosphere is the order of 1 ppb, the presented system should allow for accurate measurements of the concentration of the CH₃D isotopologue in atmospheric samples. However, since isotopologue studies rely on detection of the ratio of two (or several) signals, and since efficient detection of an isotopologue ratio requires identification of a set of transitions with specific properties—it should consist of at least two transitions relatively close to each other (so that they can both be addressed within a single scan), although not be fully overlapping, and have line strengths that largely compensates for the concentration ratio of the two isotopologues—the study of the capability of the OPO-based NICE-OHMS system presented here for detection of various isotopologues of methane is deferred to a separate work.