High-sensitivity spectroscopy of methane around 3 μm was carried out by means of a 5.5-mW cw difference-frequency generator in conjunction with a high finesse cavity in off-axis alignment. By cavity-output integration a minimum detectable absorption coefficient of 5.7∙10-9 cm-1Hz-1/2 was achieved, which compares well with results already reported in the literature. Detection of methane in natural abundance was also performed in ambient air, for different values of total pressure, allowing direct concentration measurements via evaluation of the integrated absorbance of the spectra. In particular, at atmospheric pressure, a minimum detectable concentration of 850 parts per trillion by volume (pptv)∙Hz-1/2 was demonstrated.
©2006 Optical Society of America
Detection and quantification of trace gases are relevant in several areas of research, such as atmospheric chemistry and environmental monitoring, as well as biomedical diagnostics and molecular astrophysics [1–8]. In the last decades, great advances occurred in the field of spectroscopic techniques based on high-finesse optical cavities, where effective absorption path lengths of several kilometers can be realized. One of the most popular is cavity ring-down spectroscopy (CRDS), which relies on a cavity-field decay-time measurement and allows to observe absorption spectra intrinsically free from laser source amplitude noise, providing minimum detectable absorption coefficients ranging from 10-8 cm-1Hz-1/2 to 10-11 cm-1Hz-1/2 [9–14]. Comparable sensitivities have been also obtained with another valuable method, known as cavity-enhanced absorption spectroscopy (CEAS), which consists in detecting the cavity transmission while keeping the laser locked on a cavity mode that is rapidly scanned around the molecular resonance [15–18]. As opposed to CRDS, the latter scheme gives the advantage of a higher spectral resolution on the cavity transmission. However, for both methods the detection sensitivity enhancement is associated to a significant technical demand, due to complicated electronics for fast time-resolved measurements, as far as CRDS is concerned, and a fast, tight and low-noise frequency-locking loop for CEAS. All that, together with the high mechanical stability required by both techniques, poses severe limitations on their use for in-situ trace gas monitoring applications.
A scheme for high-sensitivity gas detection that overcomes most of these drawbacks is off-axis integrated-cavity-output spectroscopy (OA-ICOS). It combines the detection principle of CEAS with a very simple set-up, using a multipass-like geometry for the high finesse optical cavity. This so called “off-axis” alignment results in the excitation of an extremely dense mode spectrum and may ideally lead to a continuous transmission. With this in mind, the interaction between the laser and the cavity can be considered “always-resonant”, thus eliminating the need for frequency locking. Furthermore, as the excitation of any transverse TEMmn mode contributes to the detection of the intracavity absorber, the off-axis set-up is almost insensitive to vibrations and small misalignments. The OA-ICOS scheme was first proposed and demonstrated in the near IR spectral region, providing very low minimum detectable absorption coefficients thanks to the pathlength increase, though only few works performed a quantitative concentration analysis on gas samples [19–23]. The mid-IR is particularly attractive for trace gas detection as the strongest ro-vibrational transitions of several molecular species occur in this spectral region, and some examples of highly-sensitive spectroscopic detection based on OA-ICOS have been already reported [24, 25]. However, the spectral coverage of available laser sources in the mid IR is still discontinuous. In particular, the window between 2.5 and 3.5 μm, where the C-H, N-H and O-H bonds exhibit their characteristic vibrations, is not accessible to single laser devices (except for HeNe and CO overtone lasers, which have discrete line-tunability though). Thanks to wide tunability, low-noise and narrow linewidth, optical parametric oscillators (OPOs) and difference-frequency generators (DFGs), proved to be the most effective tools for high resolution and high sensitivity spectroscopy in this wavelength interval [26, 27]. However, OPO-based spectrometers need special devices in order to be used in cw, mode-hop-free operation, thus making the set-up cumbersome and sophisticated [12, 28]. On the other hand, the output power of DFG sources, typically limited to a few hundreds μW, has so far prevented their use in conjunction with off-axis high-finesse cavities, since the most relevant drawback of OA-ICOS technique is the significantly reduced transmission through the cavity. Recent improvements in non-linear optical crystals as well as in rare-earth-doped fiber amplifiers have allowed the development of more powerful DFG sources, now competitive with OPOs and commercially available semiconductor lasers for spectroscopic use [29–31].
In this paper we present a novel DFG-based spectrometer, emitting between 2.9 and 3.5 μm with a power of several milliwatts, in which the radiation is coupled for the first time to an off-axis high-finesse optical resonator for high-sensitivity and quantitative spectroscopy of methane. An analytical model, based on the off-axis cavity response function, enabled us to exploit the relationship existing between the integrated absorbance and the gas concentration to extract its value directly from the area under the recorded absorption profile. Using this approach, CH4 abundance in ambient air was directly measured at different total pressures, and a minimum detectable concentration level below 1 ppbv∙Hz-1/2 was extrapolated.
2. Experimental setup
The setup for the generation of the 3-μm radiation was already described into details in a previous paper . As shown in Fig. 1, the pump beam comes from a diode laser mounted in Littrow external-cavity configuration, which provides a tuning range between 1030 and 1070 nm. The beam is then amplified by an external Yb-doped fiber amplifier which delivers up to 700 mW preserving the linewidth of the injecting source (< 1 MHz). The signal beam comes from a semiconductor diode laser emitting in the interval 1545–1605 nm and is amplified by a double-stage Er-doped fiber amplifier with a maximum output power of 8 W. Then, the two laser beams are combined onto a dichroic mirror and focused by an achromatic lens into a 5-cm-long, temperature-controlled, antireflection-coated, periodically-poled lithium-niobate crystal. The latter consists of an array of 9 different channels, the poling period ranging from 29.6 to 30.6 μm. When the wavelength of each pumping source is fixed, the quasi-phase-matching condition for the DFG process is satisfied both by selecting the proper channel and adjusting the crystal temperature between 50 and 70 °C. In this way, coherent tunable radiation is produced in the 2.9–3.5 μm range, with a maximum power of 5.5 mW and a linewidth of about 1.5 MHz, basically determined by the pumping sources. The emerging idler beam, filtered from the unconverted near-IR radiation by a Ge window, is then re-collimated by a CaF2 lens.
In our experiment, the DFG beam was coupled to a 90-cm long high-finesse optical cavity. The resonator was made by a vacuum-tight stainless-steel tube, with identical mirrors, each equipped with three independent tilting screws and a piezoelectric actuator for fine adjustment and length modulation. The tube was connected through proper vacuum fittings to a diaphragm-molecular drag pump that ensured high purity conditions inside. Gas samples at controlled pressures could be injected into the cavity either from a 99.99-% CH4 gas cylinder or from laboratory air thanks to precision valves. The pressure was monitored by a pair of capacitive manometers with 1 and 1000-Torr full-scale pressure ranges. Cavity mirrors were spherical with radius of curvature r=6 m, diameter d=½” and nominal reflectivity R=99.97%. The off-axis alignment was achieved starting from on-axis position (TEM00 alignment), then horizontally shifting the beam out of the cavity axis, and slightly tilting it in the vertical direction. The light emerging from the output cavity mirror was finally focused onto a 3-stage thermoelectrically-cooled InAs detector (Judson, mod. J12TE3-66D-R01M).
As demonstrated by Herriott et al. , the off-axis geometry leads to a multiple-reflection radiation path in the cavity, resulting in a series of m spots in elliptical pattern. In this way, the beam does not overlap itself until m round-trips, corresponding to the so-called “re-entrant condition”. In the ideal case, with the spots lying on a circumference concentric to the cavity mirror, the angle θ between two successive spots is cos(θ/2)=1-L/r, where L is the cavity length, so that the beam fulfills the re-entrant condition after having traced n circles, namely p spots on each mirror (pθ=2nπ). The number of round trips p only depends on L and r, and so the cavity effective free-spectral-range (FSR) equals c/2pL. In practice, the density of the excited modes indicates how close the alignment is to the optimal one. In our setup, starting from an on-axis FSR of 166 MHz, a 15-MHz mode spacing was measured, yielding a number of round trips p=11 with n=1 (see Fig. 2). The upper limit to the p value is actually set by the finite beam spot size and mirror diameter, both affecting the maximum number of separated spots that can be accommodated on the mirror surface, superposition resulting in hard-removable fringes. The actual sensitivity enhancement of the OA-ICOS method basically relies on the ability to smooth out the cavity mode structure. This can be virtually accomplished in the case of an off-axis FSR well below the laser linewidth. However, because of the limitations discussed above, this is not our case: large peak-to-peak intensity fluctuations were observed, as can be seen from the transmission spectrum shown in Fig. 2. As we will discuss later on, in order to flatten the cavity frequency response more effectively, both laser-frequency and cavity-length modulations were introduced and combined to time integration. The residual frequency dependence was further reduced by narrowing the scan interval (down to 4 ms), so that the crossing through resonance of each mode was not long enough to complete cavity energy build-up [33, 34].
3. Experimental results and discussion
In order to express in analytical form the behaviour of an off-axis cavity injected by a cw laser, a constant source term is added to the standard differential equation used to describe the change of the intracavity power , which yields
where I0 is the incident intensity, M is a factor between 0 and 1 describing the amount of incident radiation coupled to the resonator and T the mirror transmittivity. Therefore, the steady-state transmitted intensity is given by It=I0MT2/[2(1-R)], and, even for M=1, is reduced by a factor T/2 compared with the expected transmission of an on-axis resonantly-coupled cavity. Consequently, relatively powerful sources and sensitive detectors are desirable to achieve a high sensitivity with an off-axis geometry. As an example, in our case, for a 1 mW incident power and a detector-preamplifier gain of 1 V/μW, a maximum transmitted signal of about 50 mV was measured.
The presence of weakly absorbing species in the cavity can be taken into account by replacing the reflectivity with R’=Re -α(ω)PL≅R(1-α(ω)PL) and the output signal can be rewritten as
with α(ω) the absorption coefficient of the selected transition and P the absorber pressure. When the per-pass fractional absorption (αPL) is small compared to the intrinsic cavity losses, the fractional change in the transmitted intensity can be simply expressed in terms of a cavity equivalent absorption pathlength L eq=LR/(1-R). In the following, we will deal with strong ro-vibrational transitions which do not satisfy the latter approximation and, therefore, Eq (2) will be used.
To record an ICOS spectrum the following procedure was adopted. The DFG source was scanned over the molecular transition of interest at a repetition rate of 125 Hz (scan interval=4 ms), by sweeping one of the pumping lasers. By current sine modulation, the same laser was used to introduce a fast frequency dithering of the DFG beam (depth Am=25 MHz, frequency fm=10 kHz). In addition, a slow cavity-length modulation (Am=4.5 GHz, fm=410 Hz) was introduced by a piezo element on the cavity input mirror. The signal coming from the detector was low-pass filtered (f 6dB/oct low =3 kHz) and then averaged for 4 s (500 samples), resulting in an effective detection bandwidth of 6 Hz. These values were accurately chosen during a preliminary experiment and corresponded to the highest signal-to-noise ratio, preserving the absorption lineshape without any distorsion as well. In these experimental conditions a number of spectra were acquired. An example is given in Fig. 3, showing simultaneously two lines around 2961 cm-1, belonging respectively to CH4 and CH3D in a 100-mTorr sample of pure methane in natural isotopic abundance. The inset also shows the background baseline for the empty cavity, used to extract the noise level. The pressure-dependent absorption coefficients of both lines were previously measured in a 50-cm-long reference cell, in a higher pressure range, obtaining α=(3.45±0.03)∙10-5 cm-1torr-1 for the less abundant isotopologue and α=(8.51±0.02)∙10-5 cm-1torr-1 for the dominant one. Therefore, from the CH3D line (S/N=600 Hz1/2), we calculated a noise-equivalent absorption coefficient given by
The measured absorption coefficient and Eq (2) also provided a realistic estimate of the equivalent pathlength and thus of the mirror reflectivity. Since a relative absorption of 45.0±0.2 % was measured from the spectrum of Fig. 3, we obtained Leq=1.80±0.02 km corresponding to R≅99.95 %.
In the following, we demonstrate that these features can be successfully exploited to provide direct gas concentration from the absorption spectra in the cavity. From Eq. (2), it is straightforward to calculate the integrated absorbance, that is
where P = c∙Ptot is now the partial pressure, proportional to the CH4 concentration c, and I t,α=0 is the empty-cavity transmitted intensity. The left-hand term of Eq. (4) could be retrieved from the experimental spectra according to the following procedure. For each sample pressure the baseline level I t,α=0 and the line profile It(ω) were acquired. The normalized signals were then analyzed by a nonlinear least-squares routine based on Levenberg-Marquardt algorithm using different line models for low and high pressure regimes. In particular, for Ptot=120, 190 and 250 Torr a Voigt function was assumed for the absorption coefficient, while at higher pressures a Lorentzian profile was adopted. Also, the amplitude modulation due to the DFG source scan was taken into account by a quadratic baseline in the fit procedure. Finally, the area under the fit curves was numerically measured for each pressure. The full-width half-maximum (FWHM) derived from these fits exhibited a very good linear dependence on gas pressure with intercept consistent with the expected Doppler width. That enabled us to measure the pressure broadening coefficient Cp, which was found to be 0.144±0.002 cm-1 atm-1.
The right-hand term of Eq. (4) was evaluated assuming a Lorentzian shape for the absorption coefficient, leading to
where NL is the Loschmidt number, and S is the transition linestrength. The Lorentzian profile assumed to calculate the integral in the right-hand term of Eq. (4) has been chosen essentially to provide an analytical relationship between the experimental area and the gas concentration. In principle, a full numerical calculation could be implemented for any pressure assuming a Voigt profile for α(ω) in Eq. (4). However, the Lorentzian approximation is well satisfied above 500 Torr, and therefore does not affect the procedure at pressures close to the atmospheric one. From Eq. (5) the IA values directly yield the c parameter, provided the product SLeq is known. In our experiment, S was taken from HITRAN04 database  and for Leq the value previously measured was used.
To demonstrate gas concentration measurements from the acquired spectra, the CH4 abundance in ambient air was estimated. For this purpose we moved to a stronger transition belonging to the ν3 band (ν=2948.107924 cm-1, S=8.4×10-20 cm/molec) and recorded the absorption line profile on the cavity output, using ambient air samples at different total pressures. The resulting spectra are shown in Fig. 4(a), while the corresponding fit lineshapes are plotted in Fig. 4(b).
The main frame of Fig. 4 shows the experimental IA values obtained varying the total pressure, with the error bars given by the root-mean-square fit residuals. Hence, by fitting Eq. (5) to the IA values, a concentration c=1.06±0.01 ppm was extracted. A fully consistent value was obtained from the IA at 760 Torr. Although not far from the expected ambient level (about 1.8 ppm), the obtained value is not strictly consistent with it. This discrepancy can be likely attributed to the value adopted for the SLeq product, which was not derived by a rigorous calibration procedure in a certified gas mixture. However, the method accuracy will probably be the issue of a future work. It is worth noting the very good agreement of the experimental points with the predicted linear trend, even for pressures below 500 Torr. As a proof of the model appropiateness, we remark that the line intercept is consistent with zero within 3σ. Finally, inserting the value obtained for c into Eq. (3) and scaling by the measured signal-to-noise ratio (S/N=1150 Hz1/2), a minimum detectable concentration of 850 ppt/Hz1/2 was found at atmospheric pressure.
We have reported on an off-axis cavity-enhanced DFG-based spectrometer working between 2.9 and 3.5 μm. Using ICOS a minimum detectable absorption coefficient of 5.7∙10-9 cm-1Hz-1/2 was obtained, which is comparable with other cavity enhanced spectroscopic techniques. Moreover, the possibility of direct concentration measurements up to atmospheric pressure was demostrated. The developed procedure enabled us to retrieve the gas concentration directly from the spectrum area, accounting for the nonlinearity in the absorption introduced by the cavity. For methane this resulted in a minumum detectable concentration of several hundreds ppt∙Hz-1/2 at atmospheric pressure. One can expect similar sensitivity levels for a number of gas species such as C2H4, NH3 and N2O, absorbing in the operation range of our DFG source. The demonstrated performances can be further improved using higher-reflectivity and/or larger-diameter mirrors. On the other hand, the proposed method may be similarly applied to retrieve the linestrength of very weak ro-vibrational transitions using accurate standard gases. This is particularly relevant in molecular spectroscopy studies, most databases still lacking experimental data in this spectral region.
Finally, the wide source tunability combined to the insensitivity to misalignment and the simplicity of the apparatus, makes our DFG OA-ICOS set-up well suited for in-situ operation. Indeed, work is currently in progress to make the spectrometer set-up more compact and robust using all-fiber optical components. This will lead to the development of a portable analyzer for field, real-time gas-concentration measurements, analogous to a recently-reported near-IR spectrometer, devoted to monitoring of gas effluxes in volcanic areas .
This work has profited significantly from discussions with D. Romanini and F. K. Tittel. The experimental activity was funded by the Italian Ministry for Education, University and Research in the framework of “Progetto P.O.N.-S.I.MON.A.”
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