1 Introduction

Applications for trace gas detection are numerous and diverse, ranging from the environmental and atmospheric to the industrial and medical [1–5]. In many cases, absolute number densities are required and absorption spectroscopy is one technique that can provide such quantitative analysis. For many applications, high sensitivity and selectivity are also needed in order to monitor weakly absorbing species or those at low concentrations. These requirements can be achieved using techniques such as phase-sensitive detection [6] and path length enhancement [7], the latter comprising the use of either multipass cells (such as Herriott or White cells) or optical cavities [8, 9]. A range of cavity-enhanced methods exist, including cavity-enhanced absorption spectroscopy (CEAS) [10, 11], optical feedback cavity-enhanced absorption spectroscopy (OF-CEAS) [12], cavity ring-down spectroscopy (CRDS) [13, 14], phase-shift cavity ring-down spectroscopy (PS-CRDS) [15], and saturated-absorption cavity ring-down spectroscopy (SCAR) [16]. In all instances, path lengths of the order of 1–10 km are readily achievable. In CRDS, the technique employed in this work, the absolute concentration of species present in a sample, can be calculated from the changes in the time constant of the exponentially decaying light intensity leaking from the cavity [8, 9].

In order to perform sensitive and selective spectroscopy, coherent light sources with narrow spectral linewidths and continuous, rapid tunability are essential, and compactness, reliability, room-temperature operation, fiber-coupling, single-mode behavior, and moderate output powers (10–50 mW) are also highly desirable. Conventional distributed feedback (DFB) devices have these favourable properties [17], and there are many examples of their use in commercially available gas analyzers (e.g. the Tiger-i series from Tiger Optics [18]). Such diode lasers, however, only possess a modest tuning range (typically ∼1 nm), whereas a wider tunability across a large wavelength range would be highly beneficial as it would enable multi-species detection or the study of broadband absorbers. Recently, driven by demand from the telecommunications industry, a range of solutions to this problem has been developed [19]. These include using arrays of individual lasers, adopting external cavity configurations [20, 21] and the development of monolithic tunable lasers [22, 23]. This latter class of devices comprises modulated grating Y-branch (MG-Y) [24, 25], sampled grating distributed Bragg reflector (SG-DBR) [26, 27], and digital supermode distributed Bragg reflector (DS-DBR) [28–31] lasers. The spectroscopic potential of the DS-DBR laser has already been the subject of investigation by this group using direct and wavelength modulation spectroscopy in the near- and mid-IR [32, 33].

In this paper, we use a novel, widely tunable DS-DBR laser to perform CRDS in the near-IR over the 1,563–1,613 nm wavelength range. To demonstrate the use of this CRD spectrometer for sensitive trace gas sensing, studies of the narrow-band absorber CO2 at various wavelengths across the DS-DBR tuning range were performed, using air, calibrated CO2 mixtures and breath samples.

2 Experimental

2.1 Operation of the DS-DBR

The DS-DBR laser has been characterized in a previous paper [32] and its operation is summarized briefly here. The laser, based on indium phosphide (InP) gain material and produced by Bookham Technologies (now Oclaro Inc.) [28–31], consists of four major parts: a rear phase-grating section, a phase control section, a multi-quantum well gain section, and a front chirped-grating section. The multi-contact front grating provides coarse wavelength (supermode) tuning by choice of front pair contacts, whereas the rear and phase control sections allow small frequency adjustments through selection and tuning of the longitudinal modes. This DS-DBR platform has been monolithically integrated with a semiconductor optical amplifier (SOA) to boost the output power. By selection of the front pair contacts and the injection currents of the different sections, the 1,563–1,613 nm wavelength range of the laser can be accessed.

In our previous work [32, 33], the injection currents of the different sections of the DS-DBR were modulated with an internal voltage ramp to scan the laser quasi-continuously over the 1,563–1,613 nm range. In the present work, modifications of the custom-built laser driver unit were undertaken to allow the application of external voltage ramps as well. This means that voltage ramps of varying shapes, amplitudes and frequencies can be used to scan the injection currents for the different sections, and thus the wavelength, or alternatively fixed injection currents, can be applied giving fixed output wavelengths. Through the use of a 16-bit digital-to-analog converter (DAC), current step sizes of 0.125 μA in the front and phase sections, and 1.25 μA in the rear section, are achievable, corresponding to step sizes in wavelength as small as 1.5 × 10−5 nm (6 × 10−5 cm−1, 2 MHz).

This ability to set fixed wavelengths of the DS-DBR (by fixing the injection currents of the different sections) means that the laser can be discretely stepped, rather than continuously scanned, across a wavelength range that is ideal for CRDS. Furthermore, when the laser is operated in a scanning mode, the presence of mode hops results in jumps in the laser output frequency, thereby preventing access to certain spectral regions [32]; however, by selecting appropriate fixed injection current settings, the entire wavelength range can be accessed without any mode hops.

This contiguous tuning is demonstrated in Fig. 1. In (a), the output wavelengths when changing the rear current (i r) with a fixed front pair (FP) of 2 and phase current (i p) of 0 mA are reported and (b) is similar but for various fixed values for i p. The mode hops observed can be explained by considering (c), which illustrates the longitudinal modes in each supermode or front pair as a function of i r and i p (adapted from Ward et al. [29]). On varying i r at a fixed i p (as shown by the vertical dashed lines), these longitudinal modes are crossed and at every crossing, a mode hop is observed. To avoid these, both i p and i r must be carefully selected (as exemplified by the curved dotted lines) and the results of such a methodology for one FP are given in (d).

Fig. 1
figure 1

Selecting the DS-DBR settings, as explained in the text. This method was used to select the settings for each front pair, finding approximately 70 settings per front pair covering ∼7 nm in ∼0.1 nm steps, which overall spanned the entire 1,563–1,613 nm DS-DBR wavelength range. Settings giving a higher wavelength resolution for particular regions of interest were also obtained. Fig. 1(c) is adapted from Ward et al. [29]

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The wavelengths corresponding to different combinations of fixed injection currents applied to the various sections ("settings") were found. A database of these settings with their correlative wavelengths has thus been created. In order to record spectra, the user simply has to select the DS-DBR settings that produce the wavelengths of interest; the range and step size can also be controlled by the choice of the appropriate settings. In addition to the small short-term frequency drifts (∼20 MHz ≈ 2 × 10−4 nm) seen on switching the device immediately off and on, or to different settings and back again, the DS-DBR was also observed to offer long-term wavelength stability (as spectra recorded two weeks apart using the same settings demonstrated a similar frequency shift as those seen in the short-term studies [34]). This high degree of frequency reproducibility means that the previously calibrated DS-DBR settings can be used confidently in future experiments.

2.2 CRDS setup

The experimental setup used for CRDS using the DS-DBR as the laser source is illustrated in Fig. 2. The DS-DBR laser light, with an output power of 23 mW, was passed through a fiber-optic in-line isolator (Newport), which had a peak isolation of 52 dB at 1,550 nm, to avoid back reflection into the laser, and then through an acousto-optic modulator (AOM, Gooch & Housego), controlled by an 80 MHz radio frequency generator, which resulted in a power of 6.5 mW in the first-order diffracted beam. The light exited the fiber via a fiber coupler (F240APC-1550, Thorlabs) and was then collimated to a spot size (radius) of 0.54 mm by a 60 cm focal length, plano-convex lens (Newport) placed 3.4 cm after the fiber coupler. Another plano-convex lens (Thorlabs), with a 50 cm focal length placed 1.8 cm before the cavity, was used for mode-matching for optimal coupling of light into the cavity.

Fig. 2
figure 2

Experimental setup for CRDS. DS-DBR digital supermode distributed Bragg reflector laser; IL-OI in-line optical isolator AOM acousto-optic modulator; FM flip mirror; L1, L2 collimating and mode-matching lenses, respectively; M1, M2 turning mirrors; PZT piezoelectric transducer; Ld focusing lens onto detector; Amp variable gain; low noise current amplifier; RF gen radio frequency generator to switch AOM. Mode-matching was achieved by placing a 60 cm focal length lens at L1 at a distance d 1 = 3.4 cm after the fiber coupler to collimate the beam, and a 50 cm focal length lens at L2 at d 2 = 1.8 cm before the cavity for focusing

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Wavelength calibrations were performed as required by using a flip mirror placed before the cavity to send the laser light into a wavemeter (WA-1000, Burleigh), with an absolute accuracy of ±1.0 ppm, to correlate the DS-DBR settings and wavelength.

The cavity was composed of a pair of 25.4 mm diameter plano-concave mirrors with 1.5 m radii of curvature (REO). These mirrors had a quoted reflectivity of R∼ 0.9999 and were designed for broadband reflectance over the range 1,550–1,650 nm. The length of the cavity was 36.6 cm, corresponding to a free spectral range of 410 MHz and the beam waist at the cavity center was 0.49 mm at 1,565 nm. The first mirror was mounted on a piezoceramic transducer (PZT) so that cavity modes could be excited by applying a voltage ramp to the PZT to scan the cavity length. The cavity also had several inputs for connections to a dry pump, gas samples, and either a calibrated 10 or 100 Torr capacitance manometer (Oerlikon Leybold Vacuum).

The light exiting the cell was focused with a lens onto a fast InGaAs detector (DET10C/M, Thorlabs) with a 10 ns rise time. The signal was amplified with a variable gain, low noise current amplifier (DLPCA-200, FEMTO) set at a gain of 105 VA−1 with a bandwidth of 400 kHz.

2.3 The electronics and analysis routine

When a cavity mode was excited and the transmitted signal exceeded a set level, a custom discriminator box with an input impedance of \(5\,\hbox{M}\Upomega\) triggered the AOM to switch off and so allow the light in the cavity to ring-down. This decay was recorded using a 16-bit data acquisition card (PCI-9846D/512, Adlink) at a 10 MHz sampling rate, ±0.2 V input voltage range and \(50\,\Upomega\) impedance, and analyzed using a LabVIEW program, in a similar method as utilized in the previous studies [35]. Rapid determination of the exponential decay constants was achieved using an extension of the corrective successive integration method [36] known as linear regression of the sum (LRS) [37]. The first 2.5 μs of data was discarded and an exponential fitted to the next 140 μs of data to find the ring-down time (RDT). This value was actually a combination of the true RDT and a contribution from the detector bandwidth [38]:

$$\tau_{\rm meas}^{2} = \tau_{\rm det}^{2} + \tau_{\rm act}^{2}$$
(1)

where τmeas is the RDT recorded, τdet is the contribution from the electronics (calculated as 0.8 μs using τdet = 1/ π BW and the known 400 kHz bandwidth of the amplifier), and τact is the true RDT.

Another PC data acquisition card (DAQ-2501, Adlink) was used to create waveforms to scan the cavity length. This card had four analog output (AO) channels with 12-bit resolution and an update rate of 1 MHz. One of these AO channels was used to generate a triangular waveform with an amplitude of 4 V and a frequency of 10 Hz, which was applied to the PZT via a high-power piezo driver. The modulation amplitude was chosen in order to scan over one cavity free spectral range to ensure at least one cavity mode was excited each time, and the scan rate selected to allow enough time for sufficient light to couple into the cavity between ring-down events.

2.4 LabVIEW control of the DS-DBR

LabVIEW control of the DS-DBR was developed so that the laser could be switched on and off remotely. The capability to set and change the fixed injection currents of the different sections, thereby allowing the user to set the laser wavelength, was also established. This control of the DS-DBR, combined with the methodology outlined in Sect. 2.3, was used to write LabVIEW programs to perform two different experiments:

  1. 1.

    Recording ring-downs at a single wavelength (Sects. 3.1, 3.2). One combination of settings was sent to the DS-DBR and successive ring-downs recorded and fitted at a fixed laser wavelength.

  2. 2.

    Recording CRD spectra across a wavelength range (Sects. 3.3, 4). The DS-DBR was sent a series of settings and at each one, a desired number of ring-down events, n avg, were recorded. As each of these settings corresponded to a known fixed wavelength, a plot of RDT against wavelength was created.

This RDT against wavelength plot was then converted into an absorption spectrum as follows. In CRDS, the RDT in the absence of an absorbing or scattering medium is given by \(\tau_{0} = \frac{L}{c(1-R)}\), where L is the mirror separation and R is the average mirror reflectivity, \(R=\sqrt{R_1 R_2},\) with R 1 and R 2 being the reflectivities of the individual mirrors. If an absorbing medium is present, occupying a region of length d, then a reduced RDT, τ, is observed. This change in RDT can be used to calculate the absorption coefficient, α (cm−1), according to:

$$\alpha = \sigma N = \frac{L}{cd} \left( \frac{1}{\tau}- \frac{1}{\tau_{0}}\right)$$
(2)

where σ is the absorption cross section, N is the concentration of species in question, and c is the speed of light. The sensitivity of a CRD spectrometer is described by the minimum detectable absorption coefficient, α min, and is given by:

$$\alpha_{\rm min}=\frac{L}{c d \tau_0} \frac{\Updelta\tau_{\rm min}^0}{\tau_0}$$
(3)

where \(\Updelta \tau_{\rm min}^0\) is the minimum change in RDT that can be measured [9].

3 Initial measurements

3.1 Cavity modes

Cavity mode transmission of the system was investigated using both the DS-DBR and a DFB diode laser (NTT Electronics), with a reported output power of 20 mW and a quoted laser linewidth of 2 MHz, both emitting at 1,577.5 nm. The upper trace in Fig. 3 shows the sharp cavity modes (Lorentzian FWHM of 0.5 MHz, limited by the DFB linewidth) observed when using the DFB laser. The regular spacing between the fundamental TEM00 modes and the presence of only small neighbouring transmissions implied that the cavity was well aligned, thus guaranteeing that the discrimination level could be set such that the system was only triggered by the TEM00 modes. A good signal was obtained using a lower amplifier gain (104 VA−1) than that required for the DS-DBR.

Fig. 3
figure 3

Cavity transmission of near-IR light at 1577.5 nm using a DFB diode laser (upper trace) and the DS-DBR (lower trace). The gain of the amplifier was set 10 times larger for the recording of the DS-DBR data. The upper trace shows that a well-aligned CRDS cavity supporting predominantly TEM00 was achieved, though the use of the DS-DBR as a laser source resulted in much noisier cavity modes

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The lower trace in Fig. 3 shows the transmissions observed when using the DS-DBR. Although cavity modes with regular spacings were readily identifiable and the integrated areas under the modes were the same as those found in the DFB case (when accounting for the different signal amplifications used), they were much noisier and broader (Lorentzian FWHM of 24 MHz) than those seen with the DFB. Similar quality cavity modes were also observed at other wavelengths using different front pair contacts. The fact that the cavity is well aligned, as illustrated by the DFB studies, indicates that the more chaotic structure of the cavity modes was not caused by the excitation of additional higher-order modes, but instead was due to intrinsic noise of the DS-DBR laser light itself or its coupling into the cavity.

RDTs at 1,577.5 nm were recorded using both the DFB and DS-DBR. In both cases, the trigger level of the discriminator box was set such that it was high enough so that only the most intense cavity modes would trigger an event to be recorded giving consistent RDTs, but low enough to allow frequent triggering. In spite of the difference in the observed quality of the cavity modes, both laser sources gave similar RDTs for an evacuated cavity: 23.72 ± 0.10 μs for the DFB and 23.45 ± 0.12 μs for the DS-DBR. This verification of the RDTs measured using the DS-DBR, despite its noisy cavity modes, meant that it could be used to record CRD spectra.

The exact source of the noise of the cavity modes observed with the DS-DBR is still unclear. On first sight, it might be thought that behavior may be due to a difference in linewidths of the lasers, with the DS-DBR linewidth being significantly greater than that of the DFB, so resulting in worse coupling of the DS-DBR output into the cavity; however, the literature values estimate the linewidth of the DS-DBR to be 0.4–1.8 MHz [31], i.e. smaller than the reported linewidth of the DFB. Camera images and knife-edge measurements (recorded to enable beam collimation and mode-matching) ruled out the possibility of poor beam shape or an excess of high-order modes being a factor. The in-house built DS-DBR laser driver had comparable noise levels in its output currents as the commercial laser current driver (Thorlabs) used to power the DFB, implying that the effect is not due to the power supply. In addition, feedback from the rest of the system is improbable due to the presence of the optical isolator located directly before the laser. Nevertheless, it may be possible that there is some feedback at the laser facet (where the laser light is first coupled into the fiber) as an artifact of the manufacture process. Alternatively, and most probably, it is the laser-field phase noise intrinsic to the laser that results in rapid frequency fluctuations inside the laser linewidth, which in turn produce constructive or destructive interference when scanning the cavity as the instantaneous frequency falls inside or outside the mode, thereby converting the laser-field phase fluctuations into amplitude fluctuations giving noisy cavity modes [39]. Unfortunately, it is difficult to test either of these for final confirmation of the root cause. It is worthy of note that similar noisy cavity mode behavior was also observed in other CRDS experiments with a different DFB diode laser (Fitel) at 1,556 nm using the same laser drivers and mounts as used for the 1,577 nm DFB above, which implies yet again that the cause is intrinsic to the laser itself or its fiber-coupling.

3.2 Ring-downs at a single wavelength

The DS-DBR wavelength was set at 1,605.476 nm and 2,200 ring-downs recorded of an evacuated cavity over a period of 7 min. These were then fitted with the LRS fitting routine described in Sect. 2.3 and τ0 found using Eq. (1). Conditioning criteria, as used in previous work [35], were applied to ensure the removal of results from fitting exponential decays to non-ring-down events and to discard poor RDTs calculated from weak cavity modes. These criteria, which were also used in later experiments (Sect. 3.3 and 4), were:

  1. 1.

    The R 2 value of the exponential fit must be greater than 0.9999.

  2. 2.

    The calculated RDT must lie within ±3 standard deviations of the average of all the results.

However, the high quality of the ring-downs recorded meant that most RDTs were retained. Averaging all the filtered results gave τ0 = 24.54 ± 0.04 μs, corresponding to an effective path length of 7.4 km and a geometric mean mirror reflectivity of 0.99995 at this wavelength.

The conditioned results of this data set were also used to construct an Allan variance plot [40], shown in Fig. 4. The gradient of the Allan variance plot up to 20 s is equal to −1, indicating that the system is initially limited only by white shot noise. From this plot, it was also seen that the maximum sensitivity corresponds to an average of 100 RDTs, yielding an α min = 2.8 × 10−10 cm−1 over 20 s. It was judged, however, that an average of 35 RDTs, giving an α min = 4.1 × 10−10 cm−1 over 7 s, would be appropriate for the recording of spectra to reduce the overall acquisition time, as the averaging procedure must be repeated at many points across a given wavelength range to build the spectrum.

Fig. 4
figure 4

An Allan variance plot of the α min values calculated from the sequential ring-downs recorded the evacuated cavity at 1,605.476 nm, each RDT taking ∼0.2 s to acquire. Inspection of this plot indicated that an optimum number of ring-downs to record and average per point would be 100, giving an α min = 2.8 × 10−10 cm−1. Also, in the figure is given an indication of a higher detection limit (α min = 4.1 × 10−10 cm−1) obtainable in a faster acquisition time (35 samples, ∼7 s)

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3.3 Ring-downs across the DS-DBR wavelength range

The ability to record CRD spectra across the whole 1,563–1,613 nm DS-DBR wavelength range using this setup was then investigated. The cavity was filled with 80 Torr of N2 and 35 RDTs were measured and averaged at 450 points across the wavelength range over a period of 45 min. Figure 5 clearly demonstrates that the system is capable of acquiring such broadband spectra. No adjustment to the cavity alignment was made during the data acquisition, indicating that the cavity alignment and mode-matching was good enough to sustain cavity mode transmission across the whole 50 nm range.

Fig. 5
figure 5

RDTs across the whole wavelength range of the DS-DBR. About 450 points across 48 nm were recorded with the cavity filled with 80 Torr of N2. Each point is the average of 35 recorded RDTs, and the wavelength range is divided into segments according to the different front pairs (FP) used (dashed lines). RDTs at smaller wavelength intervals were also measured, as shown in the insets, showing the large periodic variation in mirror reflectivity, R, with wavelength, with a frequency of ∼16 GHz. At point P, λ = 1,581.596 nm, τ = 26.2 μs, and R = 0.999953; at Q, λ = 1,581.657 nm, τ = 20.7 μs, and R = 0.999942: this indicates a 20 % reduction in RDT over 0.06 nm in the wavelength domain

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Fluctuations in the RDT across the wavelength range are clearly observed and these are caused by a periodic variation in the mirror reflectivity, R, with wavelength; this is most obvious in the RDTs measured over smaller wavelength intervals as shown by the insets. About 20 % reductions in RDT over 0.06 nm in the wavelength domain are seen, which corresponded to a decrease in the effective path length of 1.6 km. This "large" variation in R over a small wavelength means that a change in wavelength of less than just 0.01 nm (900 MHz) can result in a change in the RDT of 1 μs. Identical spectra recorded one hour apart displayed residuals of less than 1 μs at equivalent points, averaging to zero across the operating range. These residuals can thus be attributed to the highly varying R, the mechanical stability of the cavity, and the wavelength reproducibility of the DS-DBR over time and on adjusting the settings.

As well as the ∼16 GHz (0.12 nm) periodic variation in R, a beating in R is also discernible with a frequency of ∼1100 GHz (9.5 nm). As R is the geometric mean of the reflectivities of the two individual mirrors, this beating can be explained by assuming that the reflectivity of each mirror, R n (λ), varies in wavelength with a slightly different periodicity; indeed, simulations indicate that a change in the period of R n (λ) as small as 1.5 % would be enough to account for the beating observed. Such minute changes in reflectivity between different mirrors is understandable given the unavoidable variations during the manufacturing process in each coating run due to subtle differences in surface roughness, interfacial imperfections (e.g. interface roughness and diffuse intermixing) between layers and thickness irregularities within the multilayer stack [41].

4 Spectroscopic applications

4.1 CO2 in air

CRD spectra of the narrow-band absorber CO2 were recorded, sourcing the CO2 from a variety of samples. Firstly, studies were made of the \(\nu(301\leftarrow 000)\,R(14)\) transition at 6,238.77 cm−1 in 10 Torr of laboratory air. Using settings found in Sect. 2.1, spectra of τ against λ over the wavelength range 6,238.699–6,238.825 cm−1 in 0.0013 cm−1 steps were recorded over a period of 6 min per spectrum. The periodic variations in R seen in Sect. 3.3 were observed in the baseline of the CRD spectra, with the same frequency and magnitude. Thus, a sixth-order polynomial was used to fit a τ0 baseline to the data before calculating α using Eq. (2). A Voigt profile was then fitted to the absorption feature, fixing the Gaussian width as the Doppler width at 348 MHz (FWHM). The data acquisition was repeated three times; an example is shown in Fig. 6.

Fig. 6
figure 6

CRD spectrum of the \(\nu(301\leftarrow000)\,R(14)\) transition of 12CO2 at 1,602.9 nm (6,238.77 cm−1) in 10 Torr of laboratory air. The raw data (open circles) and Voigt fit (solid line) are shown in the upper trace and the residuals between the two in the lower trace. In fitting the Voigt profile, the Gaussian width was fixed at the expected Doppler width of 348 MHz. For this case, the returned Lorentzian width was 62 ± 3 MHz (expected 57 MHz), and using the root mean square error value of the τ0 baseline fit as \(\Updelta \tau^0_{\rm min}, \alpha_{\rm min}\) was estimated as 1.1 × 10−9cm−1

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The fitted Voigt profile, together with the data values reported in the HITRAN database [42], was used to estimate the concentration of CO2 present in the laboratory air. Utilizing both the area of the Voigt fit with the integrated cross-sectional absorption value and the peak α data value with an estimate of the peak σ value returns CO2 concentrations of 622 ± 13 ppm and 604 ± 14 ppm from repeated and averaged measurements, respectively, which are typical values for indoor environments [43]. This implies that the quicker method of measuring only the α value at the line center is a viable alternative to recording the whole spectrum; however, in employing this procedure, care is required to ensure that the highly varying τ0 baseline is fully accounted for.

4.2 CO2 in breath

One potential medical application of CO2 detection in breath analysis is monitoring the deviations in the exhaled 13CO2/12CO2 isotopic ratio, δ13C, from its natural baseline. Such changes can infer metabolic activity associated with Helicobacter pylori infections such as gastritis, peptic ulcers and stomach cancer [44], and already breath tests, such as the 13C-urea breath test [45], are proving favourable diagnostic tools in this area. By choosing 12CO2 and 13CO2 transitions that originate from rotational levels that are as close as possible in energy (ideally the same J), the susceptibility of δ13C measurements to temperature variations is minimized. Often, such transitions do not both occur within the operating range of a single DFB laser, but the broad tuning range of the DS-DBR would allow such transitions to be monitored by one laser and with fast switching between the two absorption features. 12CO2 and 13CO2 transitions with similar J, free from water lines and of similar intensity were therefore selected for investigation to demonstrate the use of the DS-DBR CRDS system in a medical situation (Table 1).

Table 1 Line positions, integrated absorption cross sections, and transitions of the CO2 features under investigation \((\ast)\) and their neighbouring weaker lines in the breath studies [42]
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Initially, studies were performed using a 5.05 ± 0.25 % calibrated mixture of CO2 (BOC) and then with breath samples. Breath samples were collected in breath bags (Fischer Analysen Instrumente GmbH, 1.5 l) and transferred to the cell without water removal or filtration of aerosol particles. The cavity was filled with approximately 10 Torr of the sample under investigation, and CRD spectra were recorded for the 13CO2 transition and then the 12CO2 transition without changing the sample. Each spectrum took between 4–10 min to be recorded. A high-order polynomial was used to fit a τ0 baseline to the data and α calculated using Eq. (2). For the 13CO2 transition, a single Voigt profile was fitted to the absorption feature; for the 12CO2 transition, three Voigt profiles were fitted to account for the main transition and two neighbouring features. In fitting the Voigt profiles, the Gaussian widths were fixed at the Doppler widths of 348 and 345 MHz for the 12CO2 and 13CO2 lines, respectively, and the baseline offset fixed at zero. Two sets of spectra were recorded using the calibrated mixture, and three with the breath samples. Examples of the CRD spectra obtained for the different cases are given in Fig. 7, with small absorption features due to the weaker neighbouring transitions in the 12CO2 spectra clearly visible.

Fig. 7
figure 7

Examples of CRD spectra of the \(\nu(301\leftarrow000)\,R(0)\,^{12}\hbox{CO}_{2}\) and \(\nu(301\leftarrow000)\,R(4)\,^{13}\hbox{CO}_{2}\) transitions under investigation in both a 5.05 ± 0.25 % CO2 calibrated mixture (a, b) and breath samples (c, d) at ∼10 Torr. The raw data are shown by the open circles and the total fit by the solid line. In fitting the Voigt profiles, the Gaussian widths were fixed at the expected Doppler widths and the baseline offset fixed at zero, but other parameters were allowed to float with the Lorentzian widths expected to be in the range 60–70 MHz. For the 12C transition of interest in (a) and (c), two neighbouring features were also fitted, as shown in the plot insets

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The amount of the CO2 present in the samples was estimated using the peak α data value. This approach, which was shown to be a viable technique in Sect. 4.1, was employed rather than using the area of the Voigt fit as it avoided any potential issues arising from the interference of the small, neighbouring transitions in the 12CO2 case and also any possible inaccuracies in the wavelength calibration; previous studies have indicated that the laser exhibits a nonlinear wavelength–current dependency, which is not observable with the spectral resolution of the wavemeter [32, 33]. In the calibrated mixture studies, average CO2 concentrations were found to be 4.96 ± 0.07 % and 4.85 ± 0.05 % from the 12CO2 and 13CO2 transitions, respectively (errors reported based on the standard deviation of repeated measurements). These values are close to, and within the reported error of, the quoted 5.05 ± 0.25 % of the calibrated mixture. For comparison, the breath studies reported average CO2 concentrations of 3.81 ± 0.02 and 3.87 ± 0.06 % using the 12CO2 and 13CO2 transitions, respectively (again, errors based on the variability of repeated measurements). The α min values were estimated using the root mean square error (RMSE) of the fitted τ0 baseline as the \(\Updelta \tau_{\rm min}^0\) value in Eq. (3) and found to be ∼1 − 2 × 10−9 cm−1. This is approximately 2–3 times greater than the α min estimated with the Allan variance study for n avg = 35 in Sect. 3.2 Given that the mirror reflectivity, and thus RDT, changes significantly with wavelength, and that these α min values correspond to different wavelengths, this variation is unsurprising.

As well as studying these transitions using CRDS, spectra were also recorded using CEAS. The setup in Fig. 2 was modified and the DS-DBR scanned over the transitions of interest via an external voltage ramp supplied by the computer. The appropriate DS-DBR settings and voltage ramps were carefully selected to avoid mode hops and were calibrated using a 2.32 MHz spectrum analyzer (Melles Griot) and the known transition frequencies. Many cavity modes were excited simultaneously by the removal of the collimating and mode-matching lenses, off-axis injection of light into the cavity and applying a high frequency (106 Hz), asymmetric triangular ramp to the PZT to jitter the cavity length. The laser was scanned across the transitions at 11 Hz and averaged 300 times to give smooth transmission spectra, each of which took approximately 30 s to acquire.

Converting the CEAS measurements into absorption spectra was complicated by the need to account for both the amplified spontaneous emission (ASE) transmitted by the cavity and the highly variable R across the regions of study (as illustrated in Sect. 3.3). Also, a non-zero offset in the 13CO2 case was required to account for the absorption wings of strong, neighbouring 12CO2 transitions, which had become significant at the higher pressures used in the CEAS experiments.

An example of a CEA spectrum compared to a CRD spectrum for the \(\nu(301\leftarrow 000)\,R(4)\,^{13}\hbox{CO}_{2}\) transition at 6,245.74 cm−1 is shown in Fig. 8. Both were recorded using the 5.05 ± 0.25 % CO2 calibrated mixture, but at different pressures: 53 and 9 Torr for the CEA and CRD spectra, respectively. In fitting the Voigt profiles, the Gaussian widths were fixed at the expected Doppler widths of 345 MHz. The CEAS study reported a CO2 concentration (calculated from the Voigt fit area), Lorentzian width, and α min value of 4.88 ± 0.11 %, 379 ± 2 MHz (expected value 360 MHz), and 6.8 × 10−9 cm−1, and equivalently 4.79 ± 0.07 %, 58 ± 6 MHz (expected value 60 MHz), and 2.0 × 10−9 cm−1 for the CRDS study. The α min value in the CRDS case is smaller than that found using CEAS, as anticipated for a time-domain (CRDS) measurement compared to an amplitude-domain (CEAS) one as the former is less susceptible to intensity noise.

Fig. 8
figure 8

Example spectra of the \(\nu(301\leftarrow000)\,R(4)\,^{13}\hbox{CO}_{2}\) transition at 1,601.1 nm (6,245.74 cm−1) recorded using (a) CEAS at 53 Torr and (b) CRDS at 9 Torr of a 5.05 ± 0.25 % CO2 calibrated mixture. The raw data are shown by the open circles and the total fit by the solid line; in (a), a reduced number of data points are shown for clarity. The data are shown on the same scale for the ease of comparison of the noise in the baseline. In fitting the Voigt profiles, the Gaussian widths were fixed at the expected Doppler widths of 345 MHz

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5 Conclusions and further work

The DS-DBR laser has once again been demonstrated as an attractive laser source for high-resolution, multi-species gas sensing. By applying fixed injection currents to the different sections of the DS-DBR ("settings"), the laser can emit fixed wavelengths over the telecom L-band, 1,563–1,613 nm; by choosing a series of such settings, the wavelength of the DS-DBR can be stepped over a region of interest with high resolution without mode hops.

The potential of using the DS-DBR laser in this way for CRDS has been demonstrated. Ring-downs were measured for an evacuated cavity across the whole wavelength range without the need for adjustments to the cavity alignment or mode-matching. Measurements at the single wavelength of 1,605.476 nm reported a τ0 of 24.54 ± 0.04 μs, and an Allan variance study of these data implied an optimal minimum detectable absorption coefficient of 2.8 × 10−10 cm−1 over 20 s for this system when filtering and averaging 100 ring-downs per point.

The use of such a DS-DBR CRDS system for spectroscopic applications was illustrated by performing experiments on CO2 at low pressures for a variety of samples and at a selection of wavelengths. Studies of the \(\nu(301\leftarrow 000)\,R(14)\) transition were used to determine the concentration of CO2 present in laboratory air. Two other lines, the \(\nu(301\leftarrow000)\,R(0)\, ^{12}\hbox{CO}_{2}\) transition and the \(\nu(301\leftarrow000)\,R(4)\, ^{13}\hbox{CO}_{2}\) transition, were also studied at high resolution in both calibrated CO2 mixtures and breath samples, with the calculated concentrations from the calibrated mixture experiments in agreement with the reported values. These transitions were further investigated using CEAS. These two transitions were studied owing to their potential use in the 13CO2/12CO2 isotopic ratio analysis of breath samples to infer diseases associated with Helicobacter pylori bacteria. If it were desired to use this experimental system and these transitions to perform such measurements, this could be done quickly and simply by the determination of the peak α data values of the absorption features, a method whose viability was ascertained in Sect. 4.1 This would involve recording τ and τ0 values at just two frequencies corresponding to the top and bottom of the absorption feature by rapid switching of the DS-DBR between these well-defined frequency points, a feat made possible by the high sensitivity and wavelength reproducibility of the DS-DBR. The Allan variance measurements of Sect. 3.2 indicate that α min values of ∼10−10 cm−1 could be achieved with a sub-minute acquisition time by sampling 100 RDTs at both of these points. It has been shown previously that such sensitivities are adequate for such an isotope ratio measurement [46] and the possibilities of easily accessing a temperature-independent transition couple (i.e. originating from the same ro-vibrational level in the two CO2 isotopologues) provide further benefits.

In summary, the DS-DBR can be combined favourably with CRDS for gas monitoring applications. High-resolution spectra with high sensitivities are achievable, and the wide tunability of the DS-DBR across 50 nm renders the possibility of multi-species detection or the investigation of broadband absorbers. Additionally, the high reliability and reproducibility of the output wavelength selection allows sequential jumping between discrete spectral regions, which is valuable for probing many, spectrally widely separated, absorption features, and also the repetition of measurements over extended periods of time.

Another approach to improving detection limits, in addition to using cavity-enhanced spectroscopic techniques, is to exploit the strong fundamental vibrational molecular transitions in the mid-IR, 2.5–10 μm. This region of the spectrum also offers the possibility for selective detection, with the 3 μm region being of particular importance as fundamental C–H, N–H, and O–H stretches absorb strongly here [4, 47]. Previous work has already demonstrated that the DS-DBR can be combined with 1,064 nm radiation in a periodically poled lithium niobate (PPLN) crystal to generate mid-IR light by quasi-phase-matched difference frequency generation (QPM-DFG) covering the range 3,000–3,200 cm−1 [33]. Higher powers may be required in order to use this mid-IR radiation for CRDS, which can be attained by replacing the 1,064 nm diode laser formerly used with a YAG laser capable of providing 100 s of mW of pump radiation, or by the use of a more powerful EDFA to increase the signal power. It is noted that others have achieved relatively high powers of mid-IR power using fiber laser and diode sources [48, 49]. If this mid-IR light can be combined with CRDS, a broadly tunable DFG-based mid-IR CRD spectrometer would be created, capable of detecting sensitive and selective trace gas of multiple species or broadband absorbers for both medical and environmental applications.