ICL-Based OF-CEAS: A Sensitive Tool for Analytical Chemistry

Nov 28, 2016 - Optical-feedback cavity-enhanced absorption spectroscopy (OF-CEAS) using mid-infrared interband cascade lasers (ICLs) is a sensitive te...
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ICL-Based OF-CEAS: A Sensitive Tool for Analytical Chemistry Katherine M. Manfred,† Katharine M. Hunter, Luca Ciaffoni, and Grant A. D. Ritchie* Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford, United Kingdom ABSTRACT: Optical-feedback cavity-enhanced absorption spectroscopy (OF-CEAS) using mid-infrared interband cascade lasers (ICLs) is a sensitive technique for trace gas sensing. The setup of a V-shaped optical cavity operating with a 3.29 μm cw ICL is detailed, and a quantitative characterization of the injection efficiency, locking stability, mode matching, and detection sensitivity is presented. The experimental data are supported by a model to show how optical feedback affects the laser frequency as it is scanned across several longitudinal modes of the optical cavity. The model predicts that feedback enhancement effects under strongly absorbing conditions can cause underestimations in the measured absorption, and these predictions are verified experimentally. The technique is then used in application to the detection of nitrous oxide as an exemplar of the utility of this technique for analytical gas phase spectroscopy. The analytical performance of the spectrometer, expressed as noise equivalent absorption coefficient, was estimated as 4.9 × 10−9 cm −1 Hz−1/2, which compares well with recently reported values. race gas detection is of interest in many fields, with interest growing particularly in medical and atmospheric applications.1−4 Absorption spectroscopy is a popular method for identification and quantification of trace gases as it yields absolute number densities via application of the Beer−Lambert law. Selective and sensitive detection is ensured by employing high fidelity light sources, utilizing spectroscopic transitions with the largest absorption cross sections, and employing path length enhancing and/or phase-sensitive detection techniques. Detection strategies based on optical cavities, such as cavity ring-down spectroscopy (CRDS) and cavity-enhanced absorption spectroscopy (CEAS), involve trapping light between highly reflective mirrors to give optical path lengths of the order of a few kilometres within a small physical path length, thus allowing detection limits of the order of parts-per-billion-byvolume (ppbv) or lower to be achieved.5 One particularly attractive optical cavity method is optical-feedback cavityenhanced absorption spectroscopy (OF-CEAS), first developed by Morville et al. in 2005,6 which uses light leaking from a high finesse optical cavity and returning to the laser to “lock” the laser frequency to resonant frequencies of the cavity. Over the past decade, several research groups have demonstrated absorption spectrometers based on this optical locking mechanism to achieve high levels of detection sensitivity, particularly when used with mid-infrared laser sources capable of probing fundamental ro-vibrational transitions that offer large absorption cross sections and high spectral selectivity.7 The pursuit of this mid-IR “fingerprint” region is clearly demonstrated by the large amount of research into the development of semiconductor lasers operating above 3 μm, with quantum cascade lasers (QCLs) representing the most popular class.8 These devices have been combined with several techniques for sensitive spectroscopy, including CRDS, CEAS, and OF-CEAS, with numerous examples of trace gas detection applications in the literature.9−12 We note, however, that few

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© XXXX American Chemical Society

QCLs have been designed for operation at the shortest wavelengths, about 3 μm, as the smaller energy gap between the injector states and the continuum above the quantum wells leads to a higher probability of charge carriers leaking into the continuum, which has a detrimental effect on laser performance. This spectral region is, however, an important analytical region as it encompasses C−H, N−H, and O−H stretching vibrations. A more recently developed class of mid-IR laser source is that of interband cascade lasers (ICLs), which covers the 2−4 μm spectral region, filling the gap between QCLs3,4,13,14 and nearIR diode lasers.6,15−20 This new technology has advanced rapidly since its invention, with single-mode, cw ICLs operating at room temperature recently becoming available commercially,20−26 and being used in conjunction with several spectroscopic techniques with applications in breath analysis and environmental trace gas monitoring.27−30 Coupling ICLs with OF-CEAS is, however, a very new area of study, with the first ICL based OF-CEAS study reported by Manfred et al. in 2015,31 and a more recent work published by Richard et al.32 In this paper we improve upon that initial work31 and present a new V-cavity OF-CEAS experiment, alongside a model that shows how optical feedback affects the laser frequency as it is tuned across several longitudinal modes and simulates the cavity transmission to determine the feedback rate. The model also predicts how feedback enhancement effects under strongly absorbing conditions may cause underestimations in the measured absorption, and these predictions are tested experimentally. Finally, we demonstrate that ICL-based OFCEAS is a robust and practical tool for analytical chemistry/ spectroscopy by presenting a short case study on nitrous oxide Received: October 13, 2016 Accepted: November 28, 2016 Published: November 28, 2016 A

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Analytical Chemistry

for a time period longer than the cavity ring-down time. The laser is treated as being quasi-static for the duration of locking.36 Light builds up inside the cavity and so the intensity transmitted through the mirrors is far greater than without resonance. This causes a large detected signal intensity for the duration of locking and an increase in the feedback rate (defined as the ratio of power fed back to the laser to its power output). The latter leads to further narrowing of the laser line width, augmenting the coupling efficiency as a higher proportion of laser power now falls within the cavity line width. More light at the resonant frequency is fed into the cavity, and the locking range (the time for which the laser remains locked to a cavity mode) and mode amplitude are increased. This cycle continues until an equilibrium is reached.36 When the laser frequency (ν) is scanned over successive longitudinal modes of the cavity with arms of equal length (L1 = L2 = L/2) and mean mirror reflectivity R, a comb of cavity modes is generated as shown in Figure 1. When an absorbing species is introduced into the cavity, the measured cavity mode intensity is attenuated at the transition frequencies of the molecule. The peak intensities of the cavity modes, with (Iα) and without (I0) the absorbing species present, can be used to reconstruct the molecule- and frequency-dependent absorption coefficient, α(ν), spectrum according to6,37

and characterization of its absorption spectrum around 3043 cm−1, which are not reported in the HITRAN database.33

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OF-CEAS: BACKGROUND The term optical feedback describes the phenomenon whereby light entering a semiconductor laser facet perturbs the freerunning condition of the laser.34,35 The effect has been studied extensively in diode lasers, with a theoretical description of feedback-coupled laser behavior developed by Lang and Kobayashi in 1980.34 It was later exploited by Morville et al. in their development of OF-CEAS for gas sensing,6 in which the source of feedback is light returning from a (V-shaped) high finesse optical cavity. Figure 1a shows a schematic of a V-shaped optical cavity where light from a laser source is injected through mirror M0

I0(ν) α (ν )L −1= 2(1 − R ) Iα(ν)

(1)

from which the molecular concentration can be calculated. As depicted in Figure 1b, the spectrum is made of discrete points that are equally separated in the optical frequency domain by an amount equal to the free spectral range (FSR = c/2L) of the cavity.

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MODELING THE EFFECT OF FEEDBACK ON THE LASER FREQUENCY Understanding the effect of optical feedback on the emission frequency of the laser source is paramount in order to optimize its performance. In this section, this effect is modeled for a Vcavity geometry, allowing features of the cavity transmission to be predicted as a function of various experimental parameters. In general, a V-shaped cavity is commonly used because light enters the cavity at an angle to the central mirror, and so unwanted feedback from direct reflections cannot return to the laser. Furthermore, the laser-to-cavity distance must be an integer multiple of the arm length for successful phase matching of light returning to the laser to take place.6 The free running laser frequency (ν0) is affected by optical feedback, as described in the previous section, and is related to the locked laser frequency (νfb) as follows:34,36

Figure 1. (a) Diagram showing the layout of a typical V-shaped optical cavity with arms of equal length (L1 = L2 = L/2). (b) (Top) Cavity transmission signal at around 3040.2 cm−1 with the cavity filled to 50 Torr with a 0.3% mixture of methane. Consecutive modes are equally separated in the optical frequency domain by the free-spectral range (FSR = c/2L) of the cavity. (Bottom) The corresponding absorption coefficient spectrum constructed from eq 1 using the peak values of the cavity modes in the presence and absence of the absorbing gas. A HITRAN simulation33 (red) is superimposed upon the experimental discrete data points (blue).

ν0 = νfb +

and is reflected in a V pattern with a small angle between the two cavity arms. As the laser frequency is scanned over that of a cavity resonance, phase-matched light can return to the laser, and a resonant feedback field is generated. The line width of the returning field from a high finesse optical cavity is narrow (on the order of 10 to 100 kHz) in comparison to the free running laser line width (on the order of MHz). The returning field “injection seeds” the laser and causes it to emit at the resonant frequency with a narrowed line width.6,18,36 The laser is said to be “locked” to the cavity and emits at the resonant frequency

⎛ 4πL′νfb ⎞ β (1 − R 0)c ⎡ ⎢9(hfb)sin⎜ + Φ⎟ 2n0l R 0 ⎣⎢ ⎝ c ⎠

⎛ 4πL′νfb ⎞⎤ − 0(hfb)cos⎜ + Φ⎟⎥ ⎝ c ⎠⎥⎦

(2)

where β is the feedback rate, R0 is the reflectivity of the laser facet, l is the length of the laser cavity, n0 is the refractive index of the gain medium, L′ is the laser-to-cavity distance, c is the speed of light, Φ is a phase factor, and hfb is the transfer function of light fed back to the laser. The transfer function B

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Analytical Chemistry describes changes to the field intensity and phase due to external optics, and is defined as the ratio of the field leaving the cavity (E) to the incident field (Ei). It is derived by considering light leaking through the central folding mirror and returning to the laser on each round-trip and calculated from36 hfb =

the experimental setup. An example of this comparison is shown in Figure 2, where the simulated cavity transmission, shown in panel (b), closely matches the measured data shape and locking range, shown in panel (c). The value of β found from this comparison is 1.2 × 10−4, which is in good agreement with the value of 8.2 × 10−5 previously reported for a similar spectrometer.32

(1 − R ) R exp( −(2ik + α)L/2 ) 1 − R2 exp( −(2ik + α)L)

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(3)

EXPERIMENTAL SETUP: CONSTRUCTION AND CHARACTERIZATION The experimental setup is shown in Figure 3. For all experiments, a function generator (TTI TG1304) applied a

where α is the absorption coefficient, L is the total cavity length, and k is the wave-vector. Here a program has been developed that uses eqs 2 and 3 to calculate the coupled laser frequency as a function of free running laser frequency. The ICL was modeled as an InAs gain medium with refractive index of 3.51,38 within a laser cavity 1.5 mm long and with a laser facet reflectivity of 0.3. Using the transfer function for light arriving at the detector (derived similarly to hfb), the cavity transmission was simulated, and the results are summarized in Figure 2. It is worth noting that the

Figure 3. V-cavity layout. Light leaving the ICL passes through two mode matching lenses before entering the cavity at M0. It is reflected in a V shape by the three mirrors. Light transmitted through M1 is focused with an OAPM onto the detector, and that transmitted through M0 is fed back to the ICL. The laser-to-cavity distance is adjusted with the delay line, and the mirror mounted on a PZT is used for fine phase control.

triangle function with a frequency of 10 Hz to a 3.29 μm cw single mode distributed feedback ICL (Nanoplus) emitting up to 4 mW optical power, operating between 10 and 20 °C, and with a maximum driving current of 50 mA. The low driving current indicates improved power conversion efficiency compared to the previous laser model used by Manfred et al. An antireflection coated aspheric lens with a 4 mm focal length ( f; Thorlabs C036TME-E) was mounted next to the laser to collimate the beam over about 1.5 m, with collimation verified using a microbolometer (WinCamD). A V-shaped cavity was constructed in a 22.5 L aluminum and plexiglass box with three spherical, plano-convex ZnSe mirrors with 1 m radius of curvature (CRD Optics). The cavity arm length was 43.6 cm, giving a FSR of 172 MHz, and the laser-to-cavity distance, L′, was 87.2 cm. Manual adjustment of L′ was possible by moving the two mirrors forming the delay line, which were mounted on a translation stage. Light leaving the cavity after M1 was focused using an off-axis parabolic mirror (OAPM) with f = 2.54 cm onto a photovoltaic detector (VIGO PVI-4TE-3.4), the output of which was sent to a data acquisition (DAQ) card for recording and analysis using a custom LabVIEW program. Phase matching was maintained using a steering mirror mounted on a piezoelectric transducer (PZT), controlled by the same LabVIEW program which also assesses the symmetry of the cavity modes and generates an error signal for the PZT to maintain optimal phase matching. The program is adopted from work of Ohshima and Schnatz,39 and similar principles have been used for other OF-CEAS studies.6,31,37 Determination of the path enhancement introduced by the cavity, which is paramount for accurately determining absolute concentrations, was carried out by a series of measurements at different pressures. Transmission spectra of the isolated R(1)

Figure 2. Comparison of simulated and measured cavity transmission. (a) Plot of coupled laser frequency as a function of free running laser frequency (top panel), with a close-up of a region where the laser is locked to the cavity. (b) Simulated mode amplitude as a function of free running laser frequency (bottom panel). (c) Measured cavity transmission. The parameters used in the simulation were L′ = L = 0.872 m, R = 0.9989, and Φ = 0.3. The value of β found from this comparison is 1.2 × 10−4. The spike between cavity modes in (b) is due to higher order TEM mode excitation, which is not observed experimentally as the rate at which the laser frequency is scanned does not allow locking to these modes.

phase of the returning light affects the coupled laser frequency and the appearance of cavity modes; the closer the returning light is to being in phase with the outgoing laser light, the more symmetric the cavity modes are. Calculations have shown that optimal phase matching is achieved for a phase value of Φ = 0.3, which is in agreement with work by Morville et al.36 The laser’s frequency tuning close to a cavity resonance with the phase optimized is shown in detail in Figure 2(a). We also note that Φ is not the only parameter which affects the simulated cavity transmission. For example, increasing the feedback rate, β, causes the duration of locking to increase. An experimental value of β is obtainable by varying its input value in the simulation until the simulated cavity transmission best matches that measured, with all other parameters set to match C

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Analytical Chemistry transition of CH4 at 3041.427 cm−1 were recorded at varying partial pressures of a calibrated mixture of 0.3% CH4, 0.3% CO, and 0.3% C2H2 in N2 (buffered to the same total pressure with N2); the path enhancement term was then extrapolated from the gradient of the linear fit to the areas of the absorption spectra plotted against the partial pressures of methane. Mode Matching. The coupling efficiency of light into an optical cavity is improved by increasing the spatial overlap between the field incident on the cavity and that within it. The overlap is maximized by matching the phase fronts of the incident and intracavity fields, which ensures that only one resonant transverse cavity mode (TEM mode) is excited, usually the TEM00. This was achieved by making use of an appropriate set of lenses which modifies the laser beam such that the beam spot size and wavefront radius of curvature for the light entering the cavity are the same as those calculated for the intracavity field. Under these conditions, the optical cavity is said to be mode matched.40,41 This generally results in a higher feedback rate, giving greater cavity mode locking range, stability, and transmitted intensity and ultimately promotes higher levels of detection sensitivity.42,43 Injection Efficiency. In order to achieve stable locking of the laser to the cavity, the intracavity field must be large enough to give a sufficient feedback rate to initiate the feedback cycle described previously. The rate at which the laser frequency is scanned must therefore allow enough time for the intracavity field to be built up. At rates above a critical value, it is not possible to build up a sufficient field feeding back to the laser to affect the laser emission frequency, and so the laser does not lock to the cavity effectively.6,36 The critical scanning speed for the experimental setup was determined by recording the cavity transmission while increasing the rate at which the function generator applied a triangle function to the laser; a limiting value of approximately 1000 GHz/s was observed, which is similar to previous observations for QCLs and diode lasers.6,36 When a scanning speed of approximately 160 GHz/s was used, the laser appeared to remain locked to each cavity mode for 260 μs, significantly longer than the cavity ring-down time of 5.3 μs, allowing a large intracavity field to reproducibly build up. Detection Sensitivity. The level of sensitivity offered by the V-cavity setup was inferred from fitting a line shape model to an experimental absorption spectrum and using the rootmean-square value of the residuals from the non−linear regression analysis. For the setup previously introduced, the laser frequency was tuned at 10 Hz across the P(8) transition of the ν1 + 3ν2 band of N2O at 3039.4 cm−1 with the cavity filled to 45 Torr with 5% N2O in N2 (BOC). The resulting absorption spectrum and fitted Galatry profile are shown in Figure 4, together with the residuals of the fit. Expressing the sensitivity of the spectrometer in terms of the noise equivalent absorption sensitivity (NEAS) scaled to path length and given as a per acquisition bandwidth,44 this leads to an estimated value of 4.9 × 10−9 cm−1 Hz−1/2. Despite the moderate cavity finesse (∼1500) and relatively small number of data points across the spectral profile, this result corresponds to almost a 20-fold improvement in the sensitivity reported in the previous ICL study by Manfred et al.,31 and it is approximately a factor of 2 away from the NEAS level recently achieved by Richard et al., with a similar spectrometer operating at 4.015 μm.32

Figure 4. Spectrum of N2O absorption coefficient for the P(8) ν1 + 3ν2 combination band transition at 3039.4 cm−1 obtained from a 45 Torr sample of 5% N2O in N2. Data measured using the moderate finesse (∼1500) OF-CEAS cavity (black circles) is compared to a Galatry fit (red) with the residual (magenta) shown below.

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FEEDBACK ENHANCEMENT UNDER STRONG ABSORPTION The equations for calculating α given in section “OF-CEAS: Background” are derived under the assumption of weak absorption. In this section we consider the effects of strong absorption on OF-CEAS spectra and the potential error introduced in the retrieval of the molecular concentration. Theory. The extent of the laser line width narrowing induced by the optical feedback (in the case where 1/f noise dominates) is given by36,45 Δνlocked =

⎛ τlas ⎞ ⎟ ⎜ [β ϵ2hfb(1 + αH2 )]1/2 ⎝ τRD ⎠ Δν0

(4)

where Δνlocked and Δν0 are the locked and free-running laser line widths, respectively, β is the feedback rate, hfb is the feedback transfer function, and τlas and τRD are the laser photon lifetime and cavity ring-down time, respectively. The ϵ2 term is the overlap integral between intracavity (Ecav) and incident laser (Elas) fields,46 ϵ2 =

| ∫ E las(ν)Ecav (ν)dν|2

∫ |E las(ν)|2 dν ∫ |Ecav (ν)|2 dν

(5)

The overlap increases as the laser emission narrows, which enhances the coupling into the resonant cavity field and, hence, promotes a larger feedback rate. As stated in eq 4, this increased feedback rate will further narrow the laser line width, generating a quasi-positive feedback cycle until the laser line width is well below the cavity bandwidth and the feedback rate reaches an equilibrium. In addition, absorption alters these fields in several ways. When an absorbing species is present in the cavity, the intracavity photon lifetime is decreased and the cavity bandwidth is broadened. At the same time, the feedback rate is decreased, which leads to less signifcant narrowing of the laser line width compared to the absorption-free condition. All these effects are therefore heavily coupled to each other; an iterative algorithm was therefore written to quantitatively determine the equilibrium values of these parameters, and investigate the dependence of ϵ2 on α. In this model the intracavity field (Ecav) was described as an amplitudenormalized Airy function47 (with an α-dependent cavity mirror reflectivity) and the laser emission function (Elas) modeled as D

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Analytical Chemistry an area-normalized Lorentzian function.36 Several factors influence the α value required for ϵ2 to become dependent on α, including the cavity mirror reflectivity and feedback rate. The effects of varying these parameters are displayed in Figure 5a and b, respectively. It is worth noting that, for the same value

that under regimes of strong absorption eq 1 might not correctly describe this relationship. In order to quantitatively describe this phenomenon, we consider the absorption coefficient expected for a given rovibrational spectral line (with absorption cross-section σ(ν)) of a molecule present in a gas sample at a known concentration (C), calculated as αcalc(ν) = C × σ(ν). Additionally, we modify eq 1 and introduce a coupling efficiency parameter, γfb, that encapsulates the effects of the absorption-dependent lasercavity overlap integral term (ϵ2) on Iα(ν) αmeas =

⎞ I 2(1 − R ) ⎛ ⎜⎜ γfb 0 − 1⎟⎟ L Iα ⎝ ⎠

(6)

In the regime of small values of the absorption coefficient, the overlap term is unperturbed by the presence of the absorber and γfb = 1, leading to αEq1 meas = αcalc, that is, for an OF-CEAS experiment conducted under these experimental conditions, eq 1 provides a correct relationship between the cavity transmitted signals and the molecular concentration. Conversely, in the regime of strong absorption we have that γfb > 1, and therefore, the use of eq 1 would lead to αEq1 meas < αcalc, which would result in an underestimation of the molecular concentration. Equation 6, on the other hand, accounts for the effects of the absorptiondependent coupling efficiency on the cavity transmitted signals, allowing the correct concentration value to be retrieved. Experimental Results. In order to verify the predictions of the model, we recorded absorption spectra of N2O in various gas mixtures whose absorption profiles exhibited maximum values close to, and well above, the cutoff value of 1 × 10−6 cm−1. N2O was chosen as a suitable test gas as it has several strong, isolated transitions in the frequency range of the ICL which could be expected to clearly show the feedback enhancement effect. The laser was scanned over the P(7)e transition of the ν1 + 3ν2 band of N2O at 3040.294 cm−1 (σint = 6.277 × 10−25 cm2 cm−1).33 Spectra were recorded with volume fractions of nitrous oxide ranging from 10% to 100% at 100 Torr total pressure, buffered with N2. Two experimental spectra and fitted profiles obtained for 100 Torr of pure N2O (α = 4.3 × 10−5 cm−1 at the maximum of the absorption profile) and 20 Torr of pure N2O buffered to 100 Torr with N2 (α = 1.0 × 10−5 cm−1) are displayed in Figure 6a in purple and red, respectively. To emphasize the underestimation in measured values of the absorption coefficient at the maximum of the absorption, the values of αEq1 meas were

Figure 5. Effect of R, β, and L on calculated overlap. (a) Plot of ϵ2 vs α for L = 87.2 cm and β = 1 × 10−4, with R = 0.997 (black), 0.998 (red), and 0.999 (blue). (b) Corresponding plot for L = 100 cm and R = 0.999, with β = 10−2 (black), 10−3 (red), 10−4 (green), and 10−5 (blue).

of α (e.g., 2 × 10−5 cm−1), an increase in R (and, therefore, in the cavity finesse) leads to a greater absolute change in the coupling efficiency term ϵ2 compared to the low absorption regime. Conversely, a smaller change in ϵ2 is expected as the feedback rate β increases. Performing the calculation for cavity parameters matching the experimental setup (R = 0.9989, L = 87.2 cm, and β = 1.2 × 10−4) informs us that the change in ϵ2 becomes significant only when α ≥ 1 × 10−6 cm−1. In summary, changes in both the cavity bandwidth and laser line width due to the presence of a strong absorber will alter the coupling efficiency of light into the cavity, which in turn will affect the transmitted intensity Iα(ν). This suggests that the relationship between the OF-CEAS transmission signals and the absorption coefficient is dependent upon the ϵ2 term, and

Figure 6. Feedback enhancement results. (a) OF-CEAS spectra of the P(7)e transition at 3040.294 cm−1 for 100 Torr of pure N2O (αmax = 4.3 × 10−5 cm−1, purple) and 20 Torr of pure N2O buffered to 100 Torr with N2 (α = 1.0 × 10−5 cm−1, red); experimental points are shown alongside the fitted profiles. (b) Calculated overlap between cavity and laser broadening functions (black, left-hand y-axis), and αcalc − αEq1 meas for the P(7)e transition (green, right-hand axis). The vertical lines indicates the maximum α values of the absorption profiles for the two samples. (c) Calculated γfb values, with color coding the same as in (b). E

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Figure 7. N2O spectrum and PGOPHER simulation. (a) HITRAN data for 100 Torr of N2O (orange), compared to spectra of 20 Torr of pure N2O (green) and 20 Torr N2O buffered to 150 Torr with N2 (blue). Data are offset by 3 × 10−5 cm−1 for clarity. (b) PGOPHER stick spectrum simulation of the N2O absorption spectrum with gray lines representing P and R branches and red lines representing the Q branch. (c) Broadened Q-branch simulation (gray) compared to data taken at 150 Torr (blue).

similar to that seen experimentally, and the best fit of the simulation to the experimental spectrum yielded B and D values of 0.41904935 cm−1 and 6.2347 × 10−8 cm−1, respectively, for the 1420 state. These values are very close to those reported by Toth (B = 0.419031158 cm−1, D = 3.41776 × 10−8 cm−1),51 and give the simulation displayed in Figure 7b,c. The discovery of the 1420 ← 0110 hot band exemplifies the utility of laser sources in this frequency range. With continuing development of ICLs, the mid-IR can be further explored to allow a more complete understanding of the detailed spectroscopy of similar small molecules.

subtracted from the corresponding calculated value αcalc. The results plotted in Figure 6b, alongside the calculated ϵ2 values, show that at the point where the laser−cavity fields overlap becomes dependent on α there is a correspondingly larger underestimation in αmeas. For the 100 Torr of N2O sample (dotted purple line in Figure 6b), the resulting error in the concentration is as high as 10%. A similar trend can be observed in Figure 6c for the values of the coupling efficiency parameter (γfb) plotted as a function of αcalc; these values were calculated by subtracting eq 1 from eq 6 and rearranging the result. This study demonstrates how, when conducting OF-CEAS measurements of strongly absorbing species, these effects may cause underestimation in concentration measurements which needs to be corrected. Strong intracavity absorption also modifies the feedback rate, an effect that can be accounted for by the use of a second detector placed so as to monitor the feedback field.

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CONCLUSIONS

In this work, we have considered the theory and construction of a mid-IR laser spectrometer combining a 3.29 μm interband cascade laser source with optical-feedback cavity enhanced absorption, and its application to trace gas detection. After a discussion of optical feedback theory, the behavior of a laser under various conditions of optical feedback from a V-shaped optical cavity was modeled and used to simulate the cavity transmission. Characterization of an experimental setup was focused on the optimization of various experimental parameters, namely beam mode matching, frequency tuning speed and feedback rate. This led to an instrumental performance, reported as noise equivalent absorption sensitivity (NEAS), of 4.9 × 10−9 cm−1 Hz−1/2 estimated from probing the P(8) transition of the ν1 + 3ν2 combination band of N2O at 3039.4 cm−1. Investigating a strongly absorbing molecule such as N2O showed that, for relatively high values of absorption coefficients (α), the efficiency of the laser-cavity coupling becomes dependent on α, causing an underestimation in the molecular concentration determined from an absorption spectrum. A model was therefore constructed to describe how feedback enhancement is affected under conditions of strong absorption, and experimental results using nitrous oxide were shown to corroborate these predications. Finally, an absorption spectrum of nitrous oxide over the operating range of the ICL allowed identification of the 1420 ← 0110 hot band, itself unlisted on the HITRAN database, exemplifying the novelty and utility of 3 μm semiconductor laser sources.

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APPLICATIONS: A CASE STUDY We conclude this paper by presenting a short case study on N2O that highlights the utility of OF-CEAS for trace gas monitoring and molecular spectroscopy in general. N2O is a long-lived greenhouse gas with a high global warming potential which, on reaching the stratosphere, enhances ozone depletion as a source of NOx.48,49 In the operating region of the ICL (3039−3045 cm−1), the HITRAN33 database shows six isolated transitions corresponding to the P(8)e − P(3)e transitions of the 1310 ← 0000 (ν1 + 3ν2) band.50 Absorption spectra over the entire aforementioned frequency range were initially recorded with a 20 Torr sample of pure N2O (BOC); the experiment was then repeated with the gas sample buffered to 150 Torr with N2, and the resulting spectra were compared to a HITRAN simulation for this region. Several lines were present in the spectrum at just below 3043 cm−1, which had no equivalent in the database, as shown in Figure 7a. These lines resemble a red-shaded Q-branch with the band center falling at 3042.8 cm−1, and comparison of relative energies of vibrational states of N2O indicates that the hot band 1420 ← 0110 is responsible for these unlisted transitions.51 In order to make this assignment more conclusive, a PGOPHER52 simulation of N2O was made using reported rotational constants,51 and making sure that the simulation of the ν1 + 3ν2 combination band matched the HITRAN database. The Q-branch of the hot band simulated by PGOPHER was F

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +44 (0)1865 285723. Fax: +44 (0)1865 275410. ORCID

Luca Ciaffoni: 0000-0003-1545-8498 Present Address †

NOAA Earth System Research Laboratory (ESRL), Chemical Sciences Division, Boulder, CO, U.S.A., and Cooperative Institutes for Research in Environmental Sciences (CIRES), University of Colorado Boulder, Boulder, CO, U.S.A. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We would like to thank N. Lang, J. Röpcke, and J. H. van Helden from the Leibniz Institute for Plasma Science and Technology (INP Greifswald) for the use of the CRD Optics ZnSe mirrors. This work has been conducted through an Organisation Research Excellence Grant (IND63-REG2) from the European Metrology Research Programme (EMRP). The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union.

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DOI: 10.1021/acs.analchem.6b04030 Anal. Chem. XXXX, XXX, XXX−XXX

Article

Analytical Chemistry (52) Western, C. M. PGOPHER, a Program for Simulating Rotational, Vibrational and Electronic Structure, 2016; http:// pgopher.chm.bris.ac.uk.

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DOI: 10.1021/acs.analchem.6b04030 Anal. Chem. XXXX, XXX, XXX−XXX