1. Introduction

Cavity-enhanced absorption spectroscopy (CEAS) is an effective scheme to improve optical absorption measurements due to its enhanced detection sensitivity for systems confined to a relatively short optical path [1–5]. CEAS exploits an optical cavity to increase the effective optical path-length, and the higher the cavity finesse, the larger the sensitivity gain that can be achieved. However, the long residence time of light in a high-finesse cavity may preclude the time resolution needed for fast measurements in transient environments. To address this issue, recent studies from our research group have demonstrated the use of CEAS with a relatively low-finesse cavity for species-selective time-resolved (microsecond) measurements to study chemistry behind shock waves using the mid-IR [6,7], near-IR [8], and visible [9,10] spectral regions. Here we extend this work to the ultraviolet (UV) and demonstrate for the first time CEAS using a ps-pulsed laser with quasi-cw detection, with improved spatial-resolution and noise performance compared to our earlier work with cw lasers.

Sensitive absorption measurements using CEAS must account for variation in the laser intensity transmitted by the cavity due to laser-cavity coupling noise [11]. Jitter in the laser wavelength and/or mechanical or thermal changes to the cavity appear as noise on the laser intensity transmitted through the cavity, which obscures the absorption signals. There are two approaches to suppress this interference: (1) actively lock the cavity length and the laser frequency to couple to a single longitudinal mode of the cavity, e.g. via electrical [12] or optical [13] feedback; or (2) couple with many cavity modes by using off-axis alignment [14], rapid scanning of the laser wavelength [15], rf-modulation of the laser wavelength [16], or using a light source with a broad spectral bandwidth. For example, reduction of the laser-cavity coupling noise has been demonstrated using broadband light sources such as incoherent broadband cavity-enhanced absorption spectroscopy (IBCEAS) [17], as represented by several recent studies that utilized arc lamps [18] and light emitting diodes [19,20] together with dispersive or interferometric schemes to detect gas phase species such as iodine oxide [18] and NO_x [19,20]. However, despite its success in suppressing the coupling noise in a simple and economic manner, IBCEAS suffers from high baseline drifts resulting from the lack of spatial and spectral coherence in the light source, which effectively limits its applications to static/long-time-averaged measurements in relatively homogenous environments, and its useful cavity finesses to less than 100 [21].

Recent advances in pulsed lasers have enabled a new category of CEAS methods utilizing coherent broadband light sources, namely mode-locked CEAS (MLCEAS) [21] or cavity-enhanced direct frequency-comb spectroscopy (CE-DFCS) [22]. It has been demonstrated that these methods are capable of reaching a spectral bandwidth of 100 nm [23]. However, most of them either essentially employ the mode-matched coupling scheme [21,22], which is sensitive to acoustic and vibration-induced frequency noise, or use wavelength-sweeping coupling schemes [22,23] that require long integration times (typically ranging from a few milliseconds to a few seconds). As a result, their applications are mostly limited to low-speed measurements.

A combination of off-axis alignment and modulation of the laser wavelength was used in our previous studies [6–10] with narrow-bandwidth continuous (cw) laser sources due to the simplicity of its experimental setup that is robust to the mechanical vibrations of a gasdynamic shock tube. Earlier studies from other research groups have also successfully increased the sensitivity of absorption-based detection in shock tube experiments. For example, Kappel et al. [24] measured H₂O₂ and HO₂ at 215 nm using a 11-pass arrangement with a frequency-quadrupled fs-pulsed Ti-sapphire laser (80 fs pulses at 82 MHz); Krasnoperov and Michael [25] measured OH near 308 nm with an OH resonance lamp using an on-axis CEAS setup (gain = 52 +/− 2) described in the work of Grebenkin and Krasnoperov [26]. In the current work, we combine the merits of both approaches, and employ an on-axis CEAS strategy with similar gain (~50) and use a frequency-quadrupled wavelength-tunable ps-pulsed Ti-sapphire laser (2 ps pulses at 78 MHz). The longer pulse duration in the current study leads to narrower bandwith (~0.15 nm), which is essential to resolve fine spectral structures of molecules such as methyl radical (CH₃), while maintaining the suppression of laser-cavity coupling noise. The ps-laser pulse couples into roughly 1000 longitudinal modes of the cavity and the transmitted light is detected quasi-cw using a detector with a 150 kHz analog bandwidth, effectively averaging the transmitted light over many cavity modes and more than 500 laser pulses. These advantages provide excellent immunity to laser-cavity coupling noise. As this method requires no external wavelength stabilization or modulation, it is ideal for high-speed (μs) measurements in transient environments.

2. Measurement concept of the ps-pulsed direct-absorption CEAS

The idea of ps-pulsed direct-absorption CEAS is straightforward: a ps pulse from a wavelength-tunable, Ti-sapphire mode-locked laser is frequency quadrupled and coupled into a CEAS cavity of modest finesse, and the total cavity output is collected with a single detector. No laser-cavity mode matching is enforced, nor is the laser wavelength swept with any external modulation; the laser-cavity coupling noise is sufficiently suppressed that an on-axis alignment can be used in the relatively short (15.24 cm) cavity. This on-axis configuration constrains our measurement volume to a single line-of-sight perpendicular to the shock wave propagation with a beam diameter <1 mm, and is thus an improvement in spatial resolution compared to our earlier work using off-axis alignment. Such spatial resolution enables capture of fine-scale phenomena in non-homogeneous reacting systems, and provides fast temporal resolution in measurements behind shock waves.

The success of the ps-pulsed direct-absorption CEAS method depends largely on its immunity to laser-cavity coupling noise, which can be visualized either in the time domain or in the frequency domain. In the time domain, the pulsed laser emits short (~2 ps) packets of light separated by the pulse repetition interval (~12.8 ns) that have little chance to interact with each other even after hundreds of reflections in the cavity. On the output side of the cavity, the photo-detector looking at these non-overlapping pulses has a finite bandwidth (f_-3dB = 150 kHz) that is much less than the laser repetition rate (78 MHz); it thus time-averages more than 500 pulses.

In the frequency domain, both the pulsed laser output spectrum and the cavity transmission spectrum are represented by dense teeth structures with sharp peaks at frequencies of f_n = nf_r + f_ceo and f_m = mFSR, respectively, where FSR is the free spectral range of the cavity, f_r is the repetition rate of the laser, m and n are the mode numbers of the cavity and of the laser, and f_ceo is the carrier envelop offset frequency, which takes on values between –f_r/2 and + f_r/2. In reality, these teeth structures are usually not static, since f_r, f_ceo and FSR are susceptible to independent jittering from the acoustic or vibration-induced noise of the laser and the measurement cavities [22]. As a result, the cavity is effectively looking at a continuous light source spectrum – the envelope of the laser mode structure. The width of this envelope, as described by its Fourier transform, is proportional to the reciprocal of the pulse duration; for a ps pulse, this is in the THz range, three orders of magnitude larger than the nominal FSR of a 15-cm cavity (1 GHz). Thus the laser output is effectively coupled into about a thousand cavity modes, and any small deviation induced by the jittering of individual cavity modes is effectively averaged, resulting in a constant coupling efficiency. This frequency-domain picture of CEAS is analogous to pulsed cavity ring-down spectroscopy (CRDS). For a rigorous noise analysis of pulsed CRDS, please refer to the work of O’Keefe and Deacon [27].

Like all direct-absorption CEAS methods the spectral resolution of the work here is limited by the bandwidth of the laser, and the pulsed laser used has a relatively broad bandwidth (0.15nm). Thus, the current scheme is quite useful for species with relatively broad absorption features at the elevated temperatures and pressures for many shock tube chemistry studies. The current scheme is less well-suited to structured narrow-bandwidth absorbers such as OH. However, the large absorption strength of OH allows a shock tube detection limit of 0.3ppm with conventional single-pass absorption with a narrow-bandwidth laser [28].

3. Experimental setup

Shown in Fig. 1 is the experimental setup of the current study. A Ti:sapphire laser (Coherrent Mira-HP ps-model), pumped by a 18W cw laser at 532 nm (Coherrent Verdi-V18), was passively mode-locked with the Kerr-lensing effect. Stable mode-locked operation was maintained by constant water-cooling and N₂-purging around the Ti:sapphire resonator. The center wavelength of the pulsed laser output was manually tunable with a typical tuning range of 700 – 980 nm. In the current study, the center wavelength was set near 862 nm. Since no dispersion compensation component was installed in the Ti:sapphire resonator, the FWHM bandwidth of the laser output was constrained to 200 - 300 GHz, or equivalently about 0.6 nm at a center wavelength near 862 nm. And because no external frequency standard was used to pin the laser repetition rate f_r, nor was the carrier-envelope offset frequency f_ceo stabilized by any feedback servo, the spectral components of the pulsed laser output were jittering throughout the experiment, resulting in an effectively continuous laser output spectrum as shown in Fig. 2. The output of the pulsed laser was then frequency-quadrupled with two angle-tuned LBO crystals to generate UV light at center wavelength of 206 nm – 245 nm, with a FWHM of about 0.15 nm, or in frequency units, ~1 THz. The fundamental and the 2nd harmonic were rejected by the angular dispersion of a Pellin-Broca prism, and the 4th harmonic was selected. The average power of the 4th harmonic was measured to be about 5 mW using a Melles Griot model 13PEM001 power meter.

 

Fig. 1 Schematic of the experimental setup.

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Fig. 2 Snapshot of the pulsed laser output spectrum measured with a Bristol 721 spectrometer.

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It is worthy to note here, that although the lack of frequency stabilization is generally not welcomed in conventional mode-locked laser or frequency comb systems, it has brought unique advantages to the direct-absorption CEAS method in the current study. The frequency jittering acted as rapid wavelength modulation that aids suppression of laser-cavity coupling noise, and as such, was an ideal feature for the current experiment.

The pulsed UV light was then injected into a 6-inch cavity (L = 15.24 cm, FSR = 0.984 GHz) made from a stainless-steel static gas cell with two weakly focusing mirrors (radius of curvature = −100 cm, diameter = 2.00 cm, manufactured by Rocky Mountain Inc, USA), both coated in the wavelength region of 210-230 nm to achieve a nominal reflectivity of R = 0.98, which translated to a cavity finesse of ~155.

Two aluminum-coated mirrors, which controlled both the position and the angle of the incoming beam, were used to align the beam to the optical axis of the cavity. The beam path inside the cavity was fine-tuned by six adjustment screws on the mirror mounts of the cavity. Alternatively, the laser beam can be redirected via a flip mirror to an identical optical cavity inside a shock tube as described in earlier work [6–10].

The cavity output was collected with a CaF₂ focusing lens (f = 15 cm) onto a UV detector. To accommodate different levels of light intensity, we used two types of UV detectors in the study: a New Focus 2032 UV-enhanced large area silicon detector (f_-3dB = 150 kHz) was suitable for relatively high intensity measurement; and for quantifying very low light intensities, a photo-multiplier tube (PMT) (Hamamatsu R1104, with a transimpedance amplifier of DC gain = 100 V/mA and f_-3dB = 150 kHz) was employed. Low-frequency (10-100 Hz) variations of the laser intensity were observed, and to eliminate their influence on our measurement results, a common-mode rejection scheme was implemented: part of the UV light was sampled by a reference detector (New Focus 2032) using a beam splitter; its intensity was then used to normalize the raw CEAS signal. No laser-cavity coupling noise was observed above the detector noise level.

4. Gain characterization

Absorption measurements are performed by recording the laser intensities transmitted by the cavity in the presence (I) and absence (I₀) of an absorbing sample. In the conventional CEAS method, the single-pass absorbance (α_SP) is calculated, assuming standard Beer-Lambert behavior, via the following equation obtained from Fiedler et al. [17]:

For an accurate CEAS measurement, it is pertinent to determine the gain factor G precisely. Calculation using the manufacturer specified mirror reflectivity, R = 0.980 +/− 0.005, would result in a large uncertainty of ~25% in G. The most direct method to determine G would be a direct measurement of the cavity ring-down time, but this requires very fast and sensitive optical detectors, especially for this low-finesse cavity. Here we chose to determine G through via calibration, which enables the use of inexpensive detectors and electronics. The known absorption of methyl formate (HCOOCH₃) was used to determine the CEAS gain factor. It is a strong UV absorber at room temperature with an unresolved absorption spectrum containing a peak near 215 nm.

We first measured the absorption cross-section of methyl formate (MF) in a single-pass cavity configuration, achieved simply by replacing the high reflectivity mirrors with two anti-reflection coated transparent windows. We filled the cavity with a 1% MF/argon mixture and recorded the absorbance as a function of total pressure (Fig. 3a), and the simple proportional relation between the two confirmed that we were in the linear response region of the detectors. The single-pass experiment recovered a MF cross-section (σ = 1.96 x 10⁻¹⁹ cm²/molecule) that was in close agreement (within +/−5%) with literature values [29,30]. We then switched back to the CEAS configuration, and performed a similar absorption measurement with a more diluted mixture of 250ppm MF in argon. The absorption gain factor, G, was then determined by comparing the total CEAS absorbance to the single-pass absorbance calculated with the MF cross-section measured before (see Fig. 3b), using the relation of Gα_SP = I₀/I-1 = exp(α_CEAS)-1. The value of G was determined to be 49 +/− 2 from repeated measurements. Previous studies in our laboratory [6–10] find that the gain factor is stable before, during and after the passage of the shock wave in experiments with dilute mixtures. However, care is advised for experiments involving soot-forming reactions or species susceptible to surface adsorption, as contamination of the mirror surface could reduce the CEAS gain.

 

Fig. 3 Gain characterization. Left panel (a): Single-pass absorption of 1% methyl formate. Right panel (b): CEAS absorption of 250ppm methyl formate.

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Though it is possible to achieve larger value of G by using mirrors of higher reflectivity, the absorption in the UV mirror material (from 0.5 to 1% per reflection) ultimately limited the useful gain to be less than 200. Note, however, that this mirror absorption did not affect our measurement results, as this contributed equally to I and I₀.

5. Performance analysis

To evaluate the performance of the current CEAS setup, we compared its minimum detectable (i.e. noise-equivalent) single-pass absorbance in quiescent conditions (in a static gas cell) to that of the direct single-pass (i.e. non-cavity-enhanced) setup, and the results are shown in Fig. 4. Both the single-pass and the CEAS measurements were recorded with a 150 kHz detector (New Focus 2032 silicon detector for the former and Hamamatsu R1104 PMT for the latter), and sampled by a 14-bit National Instrument PXI-5122 digitizer at a rate of 100 MS/s. In the CEAS case, the 1-σ minimum detectable absorbance (MDA) was measured to be 8.7x10⁻⁵, which corresponded to a noise-equivalent absorption sensitivity (NEAS) of 1.5x10⁻⁸ cm⁻¹Hz^-1/2 when normalized by the optical pathlength and the measurement bandwidth. Compared to the single-pass case, the NEAS or MDA in the CEAS case was improved by about a factor of 20. This number was slightly smaller than the absorption gain factor G, probably due to the reduced transmitted intensity in the CEAS measurement and hence increased influence from the detector noise.

 

Fig. 4 Performance of the current CEAS method.

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The performance of the above measurements can be better viewed through a standard Allan deviation analysis, which evaluates the MDA (σ) as a function of the integration time (τ) [31,32]. As shown in the bottom panel of Fig. 4, the MDA in both the CEAS and the single-pass cases decreases with the integration time, in the region of 3 μs < τ < 200 μs. The roll-off of σ at the high frequency side (close to an integration time of 1 μs) was due to the low-pass filtering effect of the detectors. Note that the detectors had a finite bandwidth of f_-3dB = 150 kHz, so that both measurements had an effective (1/e) time-resolution of 1/2πf_-3dB ≈1 μs. At τ = 1 μs, σ < 5 x 10⁻⁵ was achieved under the current CEAS setup; and a minimum MDA of σ ~8 x 10⁻⁶ was achieved at an optimal integration time of τ_opt ~300 μs. Although this number of τ_opt was small compared to other CEAS studies [16,20,23,32], it fit our purpose well, since the current setup was primarily targeted for time-resolved measurements (e.g., ~1 μs for events occurring in ~1 ms). Extension to longer test time is possible through future optimizations, for example, by employing better laser stabilization and a more advanced common-mode rejection scheme.

6. Proof-of-concept measurement in a shock tube

The final goal of this study is to apply our new CEAS method to time-resolved measurements of chemistry behind shock waves. Of particular interest to us are the shock tube studies of non-equilibrium processes in combustion of gases [7,33,34]. Shock tubes are effective experimental systems with capability of almost instantaneously creating a uniform, well-controlled test environment of known high-temperature at a user-specified pressure [33]. Detailed descriptions of the Stanford shock tube facilities have been documented elsewhere [34], and here only their fundamental operation principles are presented. Briefly, a shock tube is a long, cylindrical tube consisting of two sections separated by a diaphragm: a low-pressure driven section is initially filled with gas mixture of precursors to the chemistry being studied, and a high-pressure driver section is subsequently filled with an inert gas. The high-pressure driver gas bursts the diaphragm and an incident shock wave propagates down the tube, heating, compressing and accelerating the gas behind it. The shock wave then reflects off the endwall of the tube, stagnates the gas and further increases its temperature and pressure. The resulting temperature and pressure, uniform in both space and time, are precisely known from measured shock velocity. Measurements are usually performed behind the reflected shock waves, and the post-reflected-shock test-times, limited by arrival of other reflected waves, are typically in the range of a few milliseconds.

In this study, we demonstrated the first application of the UV ps-pulsed CEAS method by measuring the vibrational relaxation of O₂ in a shock tube. A total of 5 shock experiments were performed in the temperature range of 1227 – 1503 K and at pressures near 1 and 2 atm, using a mixture of 1% O₂ in argon. The relaxation of O₂ in argon (i.e., vibrational-translational or VT relaxation) was observed via absorption near 215.55 nm, targeting at the v” = 4 and v” = 5 bands of the Schumann–Runge ($B^3{\Sigma }_u^{-}\leftarrow X^3{\Sigma }_g^{-}$) transitions [35]. Usually such experiment could be performed only at much higher temperatures where the absorptions are stronger; but with the sensitivity improvement of of CEAS, the lower temperature region could be studied, as shown by the representative examples in Fig. 5a. The current measurement exhibited microsecond temporal resolution, as evident by the narrow width of the Schlieren spikes (~2 μs FWHM) captured at the arrival of the reflected shock waves. Under the current experimental conditions, the average speed of the reflected shock wave was about 550 m/s, and the diameter of the UV beam was about 1 mm; this resulted in a physical time resolution of less than 2 μs (limited by the transit time of the shock wave across the laser beam), which, when combined with the 1 μs detector resolution, yielded an overall time resolution of roughly 2 μs.

 

Fig. 5 Proof-of-concept experiment in a shock tube. Left panel (a): Example absorbance traces of O₂ vibrational relaxation in argon. Right panel (b): O₂-Ar vibrational relaxation time measured at 1273 K, 2.09 atm.

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Figure 5b illustrates our determination for the vibrational relaxation time of O₂ in argon. The vibrational relaxation times (τ_VT) were calculated by best-fitting the absorbance time-history with exponential curves in the form of α = α₀[1-exp(-t/τ_VT)]. A conservative uncertainty bound of +/−30% was assigned to τ_VT, based on the noise levels of the absorption time-history curves. The measured relaxation times were plotted on a Landau-Teller diagram (Fig. 6), in comparison with the UV light absorption study of Camac [36], the interferometry study of White and Millikan [37], the extensive review of Millikan and White [38] and the recent laser absorption study of Owen [39]. The current data agreed well in trend with the previous measurements and had less scatter.

 

Fig. 6 Landau-Teller plot of the O₂-Ar vibrational relaxation time.

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Due to beam-steering induced by the gas turbulence in the boundary layers and gain saturation at relatively high absorbances, the shock tube measurements exhibited higher noise than the the static cell measurement. Nonetheless, a single-pass MDA on the-order-of 10⁻⁴ was easily achievable in the shock tube under the current configuration. We compare this with other recent progress on absorption diagnostics for shock tube measurements, for example, MDA ~5x10⁻³ achieved by Kappel et al. [24] using a Xe lamp, MDA ~2x10⁻³ achieved by Davidson et al. [40] using a narrow-linewidth dye laser, MDA ~1x10⁻³ achieved by Lam et al. [41] with a similar dye laser with higher power, and MDA ~5x10⁻⁴ achieved by Dammeier and Friedrichs [42] using a narrow-linewidth dye laser and balanced detection. The current study using CEAS has improved the MDA by about a factor of about five over the best previous results.

7. Concluding remarks

We presented a new CEAS method suitable for microsecond-resolved measurements in transient environments. Based on a direction-absorption scheme using a ps-pulsed UV laser, this method allowed for an absorption gain of 49 to be achieved with suppression of all laser-cavity coupling noise to below the detector noise floor. The method was demonstrated in a 6-inch static gas cell and a 6-inch diameter shock tube. In the static cell experiment, the MDA of the current CEAS setup was determined to be 8.7x10⁻⁵ at a measurement bandwidth of 150 kHz, which corresponded to a NEAS of 1.5x10⁻⁸ cm⁻¹Hz^-1/2. In the shock tube experiment, a time resolution of 2 μs was achieved. As an example application of this CEAS method, we have measured the vibrational relaxation times of O₂ in argon at T < 1300 K using laser absorption spectroscopy, and obtained quite satisfying results.

As a result of its substantial improvement in detection sensitivity without compromising time resolution, the direct-absorption ps-pulsed CEAS method promises to be a powerful tool for shock tube studies of combustion kinetics. For example, it will enable experiments on highly dilute mixtures that have negligible complications of heat release and allow more direct study of specific reaction channels; in addition, concentrations of target species in quantum states with low populations that may be important for nonequilibrium situations can be monitored. Such data could provide unique targets for testing theoretical models of chemical kinetics.