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Difference frequency generation using one 1.58-μm and two 1.06-μm distributed feedback Bragg-grating laser diodes and a ridge-type PPLN alternately provide two 3.2-μm coaxial waves resonant with individual isotopic transitions separated by 13 cm–1. The ν3 band R(6) A2 allowed transition of 13CH4 and the ν3 band R(6) A2 weakly allowed transition of 12CH4 are an ideal pair for isotope ratio measurements. The 13CH4/12CH4 isotope ratio is determined for three sample gases with a relative uncertainty of 0.7 ‰, and it is confirmed that the temperature dependence is smaller than the uncertainty.
© 2015 Optical Society of America
1. Introduction
Mid-infrared spectroscopy has been an attractive tool for investigations in fundamental science, applied physics, and biomedical science because most molecules have intense and characteristic absorption lines induced by the fundamental vibration in the mid-infrared region. Although there were few coherent mid-infrared sources before the year 2000, quantum cascade lasers (QCLs), optical parametric oscillators (OPOs), and difference-frequency-generation (DFG) sources have rapidly developed in the last decade, and have opened a new era of mid-infrared spectroscopy.
The 3-μm region, where H-X stretching vibrations are located, is particularly important for spectroscopic applications. However, QCLs are not available in the 3-μm region. OPOs provide intense and widely tunable 3-μm radiation, but are bulky and quite expensive. In contrast, DFG using periodically poled lithium niobate (PPLN) is a useful 3-μm source. High performance continuous wave (CW) laser diodes in the 1.0- and 1.5-μm regions have been developed for telecom applications and are applicable to DFG as pump and signal sources, respectively. These laser diodes ensure that the 3-μm idler wave has a narrow linewidth and wide tuning range. We have developed a PPLN ridge waveguide with a wavelength conversion efficiency two orders of magnitude larger than that of bulk PPLN [1]. The DFG source has been applied to sub-Doppler resolution spectroscopy [2, 3].
The isotope abundance ratio in environmental gas depends on the area where the sample was collected, reflecting the production processes and the transportation history in the atmosphere and the ocean. For instance, the 13C/12C ratio (~1/100) in CH4 varies up to a few percent for various production processes [4]. Therefore, precise isotope ratio measurements are important for evaluating the biochemical cycles of substances including greenhouse gases. Traditionally, mass spectrometry has been exclusively used for isotope ratio measurements. However, a high resolution is needed to distinguish species with a small mass difference, and mass spectrometers are so large that in situ observations are impossible. In contrast, absorption spectroscopy can easily distinguish isotopic species in terms of both mass and the configuration of the atoms in a molecule.
There have already been many demonstrations and proposals regarding absorption spectroscopy for 13C/12C isotope ratio measurements of methane using a Pb-salt semiconductor laser in the mid-infrared region [5–7], a distributed-feedback (DFB) single-mode semiconductor laser in the near infrared region [8, 9], a 3.33-μm He-Ne laser [10], a QCL in the 8-μm region [11, 12], a 3-μm CO overtone laser [13], a combination of gas-chromatography and near-infrared cavity ring down spectroscopy [14], and a 3.3-μm DFG source [15]. In almost these studies, two lines from different isotopic species are within the tuning range of a single source. Therefore, the selected pair is not the best for isotope ratio measurements. Uehara et al. demonstrated a dual wavelength laser system for 13CH4/12CH4 measurements in the 1.66-μm region [16]. The absorption length for the 12CH4 source was set considerably shorter than that for the 13CH4 source so that both absorbance had similar magnitudes. Hence, the two beams travelled along different paths, making it difficult to eliminate the difference between the paths.
In the present study, we have developed a new dual wavelength DFG source in the 3.2-μm region and applied it to isotope ratio measurements of 13CH4/12CH4. The source consists of two pump laser diodes, one signal laser diode, and one PPLN ridge waveguide. The wide matching wavelength range of the PPLN enables us to select two absorption lines separated by 13 cm−1, which is too large for a single wavelength source. The 13CH4 line is one of the strongest lines, and the selected two lines have similar absorbance. They also have the lower level associated with a common quantum state, which reduces the effects of temperature variation on the isotope ratio measurements. Because the two idler waves are generated in a single PPLN, they travel along the same optical path. This fact eliminates certain issues caused by the two-beam scheme such as differences in the optical path length, the interference, and the polarization.
We first discuss the phase matching of the PPLN and then how to select two absorption lines appropriate for isotope ratio measurements. Secondly, we describe the experimental setup and techniques for precise measurements. Subsequently, we determine the 13CH4/12CH4 ratios of three samples and compare them with values determined from mass spectrometry. Finally, we evaluate the uncertainty and consider additional experiments related to pressure and temperature dependences.
2. Tuning bandwidth of PPLN
A 3-μm idler wave is generated in a PPLN waveguide using 1.5-μm signal and 1.0-μm pump waves, which are provided by high performance laser diodes developed for telecommunications. The tuning range of the idler wave is determined by that of the signal and pump sources and the phase matching bandwidth of the PPLN waveguide.
The quasi phase matching condition is fulfilled when the phase mismatching wavenumber
vanishes, where λp, λs, and λi are the pump, signal, and idler wavelengths, and Λ is the poling period. ne is the refractive index and defined as [17]from Sellmeier equation, whereT is the PPLN temperature, and T0 is the reference temperature given in kelvin. The parameters, ai (i = 1 ~6), bj (j = 1 ~5), and T0, are given in the previous work [17]. The converted idler wave power, Pi, is given in terms of the propagation length L of the PPLN asSellmeier equation is valid for a bulk PPLN, and there is, in addition, waveguide dispersion for a waveguide PPLN. The conversion curve is, however, similar for both PPLN’s.Figure 1 shows conversion efficiencies calculated for a 50-mm long bulk PPLN crystal with a poling period of 30.3 μm and a temperature of 60°C. The blue curve is drawn for a case when the pump wavelength is fixed at 1.062 μm and the signal wavelength is tuned. In contrast, the red curve indicates the opposite case where the signal wavelength is fixed at 1.585 μm and the pump wavelength is tuned. It is evident that the red curve has a wider tuning bandwidth than the blue curve, and the FWHM of the normalized conversion efficiency is about 30 cm−1.
Fig. 1 Calculated conversion efficiency spectrum. The blue curve is for a fixed pump frequency and the varied signal frequency. The red curve is for the fixed signal frequency and the varied pump frequency. The PPLN waveguide is 50 mm long with a poling period of 30.3 μm.
3. Choice of methane transitions
The intense ν3 fundamental band of methane is located in the wavelength range of 3.2 to 3.4 μm. The dual wavelength 3-μm source allows us to choose a pair of the isotope transitions with little bothering by the tuning range of the source.
Table 1 lists the selected transitions, A and B, of 12CH4 and 13CH4, together with the spectroscopic data from the HITRAN 2012 database [18]. The numbers in Transition column are the total angular momentum quantum numbers, and the subscripts are the rotational angular momentum quantum numbers. Figure 2 shows a spectrum calculated in the vicinity of these transitions, assuming an absorption length of 40 cm, a methane gas pressure of 133 Pa, and a temperature is 300 K. Then the absorption lines have Gaussian profiles caused by Doppler broadening, and the widths are about 140 MHz (half width at half maximum, HWHM). This pair is selected by the following reasons.
Table 1. Spectroscopic data of selected 12CH4 and 13CH4 transitions
Fig. 2 Calculated spectra around the selected transitions. (a) Selected 12CH4 transition (A). (b) Selected 13CH4 transition (B). C is the hot band transition of 12CH4.
- 1) The B transition is the fifth strongest of the 13CH4 transitions in the ν3 band at room temperature (296 K). The four most intense lines overlap with adjacent lines. The lower rotational state J = 6 is abundantly populated at room temperature, and the A1 and A2 species have fivefold degeneracy, whereas E, F1, and F2 species are doubly, triply, and triply degenerated, respectively [15].
- 2) The A and B transitions are, as shown in Fig. 2, isolated from the neighboring transitions of 12CH4, 13CH4, and 12CH3D. The B transition is by 1.2 GHz from the adjacent line, which has a similar absorption intensity to A. The separation is so large compared with the Doppler width that the overlapping has no effects on the isotope ratio measurements.
- 3) The A and B transitions have a lower level with a common rotational quantum number J = 6 and an irreducible representation with A2 symmetry. Moreover, 12CH4 and 13CH4 have very similar rotational constant because the carbon atom is located at the center of mass [18]. Therefore, the absorption coefficients of the A and B transitions have similar temperature dependences, and the isotope ratio measurement is thereby insensitive to the temperature variations.
- 4) The A and B transitions have comparable absorption coefficients, which maintain the wide dynamic range of the measurement system. The absorption coefficient of 12CH4 is two orders of magnitude larger than that for the identical rotation-vibration transition of 13CH4 because of its natural abundance. Accordingly, we selected the weakly allowed transition A. The rotational quantum number does not change for allowed transitions, as shown in Table 1.
Even though the A and B transitions are 13 cm−1 apart, we can access them using a dual wavelength source.
4. Experimental apparatus
Figure 3 is schematic of the spectrometer. Two DFG waves with wavenumbers of 3077 and 3090 cm−1 are generated using two 1.06-μm DFB laser diodes and a 1.58-μm DFB laser diode. The pump and signal wavelengths are monitored with a wavelength meter through a part of these waves extracted by two 99:1 tap couplers and adjusted by changing the laser temperature. The pump waves are combined at a 3 dB fiber coupler, further overlapped with the signal wave at a wavelength division multiplexing (WDM) dichromatic filter, and launched into the PPLN waveguide module. The fabrication and structural detail of the PPLN waveguide module have already been described [1]. The pump and signal waves with a power level of 3 and 10 mW are launched into the waveguide PPLN and converted into the 10-μW idler wave. The DFG source is 20 cm × 20 cm × 5 cm and all the optical components are connected with optical fibers. Therefore, it is compact, transportable, and suitable for fieldwork.
The output beam from the PPLN module is collimated by a convex CaF2 lens with a focal length of 15 mm. The beam passes a 40-cm-long absorption cell filled with pure methane gas in a temperature of 20 to 25°C and an optical band pass filter for removing the pump and signal waves, and the transmitted idler wave is detected with a liquid-nitrogen-cooled InSb photovoltaic detector. The photocurrent is converted to a voltage signal and recorded using a digital oscilloscope with a resolution of 11 bits. Sample pressure is measured with a Baratron.
The idler frequency is swept to record the absorption spectrum by applying a ramp voltage to the injection current supply of the pump DFB laser diodes, while the signal DFB laser diode operates at a fixed injection current. Figure 4 is schematic of the timing chart of the injection currents of the two pump laser diodes. For a period of t1 to t2, pump laser diode 1 emits a pump wave that generates an idler wave resonant with the transition A and the idler frequency decreases as the injection current increases while pump laser diode 2 is turned off for a period of t0 to t2. For a period of t3 to t4, pump laser diode 2 operates to record the absorption spectrum of the transition B whereas pump laser diode 1 is turned off. This time sequence is programmed using a two-channel function generator. The two idler frequencies are swept around transitions A and B with a span of about 0.3 cm–1 in 0.1 s. The spectrum is repeatedly recorded and averaged over typically 64 frequency sweeps for a high signal-to-noise ratio.
Fig. 4 Timing chart of the injection current of two pump laser diodes (LDs). Low level represents LD off. t4 corresponds to t0 of the subsequent period, and the same action is repeated.
5. Result
5.1 Estimation of source linewidth
We first evaluated the spectral linewidth of the pump and signal waves. To this end, the spectrum of an Er-doped-fiber-laser based optical frequency comb is expanded to the 1.0-2.0 μm wavelength range with a highly non-linear fiber. The pump/signal wave was overlapped with the output beam of the expanded comb, and the beat note was observed with an RF spectrum analyzer. Figure 5 shows the RF spectrum of the beat note between the free-running pump laser diode 1 and the nearest comb mode at a spectral resolution of 100 kHz and a sweep time of 50 ms. It is about 1 MHz wide, which corresponds to the linewidth of laser diode 1 because the comb modes are typically less than 20 kHz wide [20]. The pump wave from the laser diode 2 and the signal wave were also measured and were both approximately 1 MHz wide. Therefore, the DFG idler wave is estimated to be a few MHz wide, which is sufficiently narrow to carry out Doppler-limited resolution spectroscopy. Low-noise current sources are essential for realizing the measured linewidths of the laser diodes.
5.2 Determination of isotope ratio
Figure 6 shows a typical recorded spectrum. It was averaged over 64 scans, and it took 13 seconds. The left and right spectra as well as the inset in Fig. 3 correspond to Fig. 2(b) and 2(a), but note that the direction of the horizontal axes is reversed. In our analysis, we assume that the elapsed time is proportional to the idler frequency variation. The standard deviation of the proportional constant is verified to be less than 0.8% by observing the transmission spectrum of a Fabry-Perot etalon. The absorption coefficient ratios (ACRs) are derived according to the following procedures.
- 1) Determine the zero signal level which is given, say, for a period of −0.10 to −0.09 s when both pump laser diodes are turned off.
- 2) Extract a part of the spectrum around either the transition A or B, and fit it to the following model function,
where ν is the idler frequency, P0 is the idler power level at the starting point of the frequency sweep, β is the frequency-to-power slope, α0 is the absorption coefficient of the transition A or B at ν = ν0, Δν is Doppler width (HWHM), ν0 is the transition frequency, and l is the absorption length. Five adjustable parameters in least square fit are P0, β, α0, Δν, and ν0, whereas l is fixed at 40 cm. Most of the measurements were performed at the sample pressures less than 200 Pa, in which the pressure broadening is estimated less than 5 MHz from the self-broadening coefficient of 24 kHz/Pa [21]. Because the pressure width is only 1/30 times the Doppler width, the Gaussian profile reproduces the observed line shape very well. In contrast, it is difficult to determine the absorption coefficient with a small uncertainty by fitting the line shape to the Voigt profile.
Fig. 6 Typical recorded spectrum. The absorption length is 40 cm, and the methane gas pressure is 190 Pa at room temperature.
Figure 7 shows R13CH4 values determined for samples X, Y, and Z from several consecutive measurements. Each new measurement was carried out 1 hour after the preceding measurement. The error bars result from the fitting uncertainties of α0,A and α0,B. The ratio of 13CH4/12CH4 of these samples was determined using near-infrared laser spectroscopy by Tsuji et al. [22]. Table 2 lists the weighted averages and standard deviations of means of R13CH4 determined in the measurements. The value for sample X is 0.5489 ± 0.0004, which gives the smallest relative uncertainty of 7 × 10−4 (0.7 ‰) among the three samples. Table 2 also includes delta values, δ13CH4,ss', which represent the difference between the R13CH4 values of two samples and are given as
where subscripts “s” and “s´” denote the two samples. These values of δ13CH4,sWS were determined by Yoshida and his colleagues using mass spectrometry and a common working standard (WS) [22]. Because we do not measure the value of R13CH4WS, Table 2 indicates the values of δ13CH4,sX determined from mass spectrometry and laser spectroscopy. The values of δ13CH4,sX from mass spectroscopy are given byThe values obtained from absorption spectroscopy coincide with those obtained from mass spectrometry within the relative uncertainty of absorption spectroscopy.Fig. 7 Variations in determined absorption coefficient ratio, R13CH4. Squares (blue), diamonds (red), and triangles (green) denote sample X, Y, and Z, respectively.
Table 2. Measured R13CH4and comparison with mass spectroscopy based on sample X.
The obtained relative uncertainty is three times larger than 0.21 ‰ reported by Witinski et al. [12], which is the smallest relative uncertainty for methane, as far as we know, yet provided by isotope ratio measurements using absorption spectroscopy. They developed a stable spectrometer and accomplished the small uncertainty by accumulating the data over 200 s. Uehara et al. also achieved the relative uncertainty of 0.3 ‰ [16]. They employed a long absorption length and a wavelength-modulation technique. In contrast, the present spectrometer is very simple because the 3.3-μm band of methane is two orders of magnitude stronger than the 1.67-μm band observed by Uehara et al. [16]. This enables us to use a short absorption cell, select a weakly allowed transition of 12CH4, and eliminate the need for modulation techniques. Similar 3 μm DFG sources were developed for observing methane in ambient gas, and the ratio of 12CH4 to 12CH3D was determined with the relative uncertainty of 4 ‰ [23, 24].
5.3 Allan variance
To evaluate temporal stability of the measurement system, Allan variance analysis was introduced to absorption spectroscopy of trace gas [25]. Following the pioneering work, we recorded twenty 64-averaged spectra such as Fig. 6 every 30 s. They were fit to the Gaussian profile to yield the absorption coefficients and eventually the absorption coefficient ratios in Eq. (6). In chronological order, the i-th ACR is denoted as Ri, and the Allan variance is given by
where T is the time separation between the adjacent measurements, and N is the number of the ACRs. Note that this definition does not consider the dead time of the measurements. Figure 8 depicts the obtained Allan variances in red. They are about 5 × 10−7 for an integration time of 30 to 210 s. The ACRs of the sample X in Fig. 7 gave the Allan variance of 7.0 × 10−7 for an integration time of 1 hour. We also recorded nineteen single-shot spectra every 6 s in order to investigate the short-time stability. The Allan variances are indicated in blue in Fig. 8. They decrease as the integration time and smoothly connect with the red curve. Some data points are not depicted in Fig. 8 because their degrees of freedom are less than 3 and thus the expected uncertainties are large. Conclusively, the present spectrometer is the most sensitive when the integration time is taken about 60 s. It is also quite stable for the order of hour because appreciable drifts are not observed.Fig. 8 Allan variance of absorption coefficient ratio, R13CH4. The red and blue curves are drawn for 64-averaged and shingle-shot spectra.
5.4 Pressure dependence
We examined the sample-pressure dependence of the ACR for sample X. Figure 9 shows the R13CH4 values determined for various pressures together with the uncertainties denoted by bars. The values were almost constant except for that at pressure of 10 Pa, and the weighted average and the standard deviation of means are 0.5492 ± 0.0013. This is not inconsistent with the values in Table 2. Figure 10 shows the pressure dependence of the absorbance for transitions A and B. At a pressure of 10 Pa, the absorbance of the transition B is only 1.7%, which is too small to determine the R13CH4 value with the relative uncertainty of 0.7 ‰ similar to that of other measurements at higher sample pressures. The lower limits for sample pressure can be improved by employing a longer absorption cell.
Fig. 9 Pressure dependence of R13CH4. Sample X is used. The large error bar (pressure is 10 Pa) is caused by the poor signal-to-noise ratio in the spectrum. The red line shows the weighted average value.
Fig. 10 Pressure dependence of absorbance for transitions A and B. Squares (blue) and diamonds (red) denote transitions A and B, respectively.
The sample pressure increased up to 270 Pa, where the absorbance was 51% and 32% for the transitions A and B. Because the absorption signals are considerably larger than the noise level, the ACR value is determined with a small uncertainty. At higher pressure, the line profiles deviate from the Gaussian because of the exponential dependence of Beer’s law and the pressure broadening. The absorption coefficient is thereby correlated with the other adjustable parameters, and the uncertainty considerably increases. Therefore, the sample pressure is adjusted so that the absorbance is smaller than 70% in particular for the isotope ratio measurements.
5.5 Temperature dependence
We investigated the temperature dependence of the ACR for sample X. For comparisons, we also measured that between the transition B and the (ν3 + ν4)−ν4 band R(6) A2 transition of 12CH4, which is shown as C in Fig. 2. The energy of the lower level of transition C is 1300 cm–1 higher than that of transition B. The absorption cell was wound with a ribbon heater. The temperature between the ribbon heater and the cell surface was monitored with a thermometer. The Doppler width determined from the fitting of the observed spectra suggests a sample temperature about 70°C when the thermometer indicates 125°C.
Figure 11 shows the temperature-induced deviations of δ 13CH4,sB (s = A, C) from the value at a temperature of 20°C. It is evident that the temperature dependence of δ 13CH4,AB is negligible whereas that of δ 13CH4,CB is very large. Even though a quantitative analysis is difficult because the sample gas temperature is not measured precisely, the pair of target transitions, A and B, requires no temperature control unless the relative uncertainty of δ 13CH4,ss' is greatly improved.
Fig. 11 Temperature dependence of R13CH4 for sample X. Squares (blue) and diamonds (red) denote pairs of the transitions A and B and of the transitions B and C, respectively.
6. Conclusion
In this paper, we described a dual wavelength mid-infrared spectrometer designed to determine the 13CH4 to 12CH4 isotope abundance ratio. The wide tunability of the DFG sources enabled us to record spectra of the best pair transitions one after the other rapidly. We examined the repeatability and the pressure- and temperature-dependences and obtained a relative uncertainty of 0.7 ‰. The widely tunable DFG sources are also promising for the remote sensing of multiple trace gases.
Acknowledgments
We are grateful to Drs N. Yoshida, K. Yamada, and K. Tsuji of the Tokyo Institute of Technology for providing us with two methane samples and for determining the isotope ratios using mass spectrometry.
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