Figure 1 depicts a schematic diagram of the spectrometer. The DFG source consists of a ridge-waveguide PPLN (NEL, model WD-3360-000-A-B-C) with a conversion efficiency of 5 %/W, a 1.55 μm distributed feedback (DFB) laser diode module (Anritsu, model AB5A1102M521D) with a pigtail fiber output as a signal source, and a 1.064 μm DFB laser diode (Hamamatsu Photonics, model LA0927LP) as a pump source. The pump and signal lasers are each connected to an injection-current-temperature controller (ILX Lightwave, model LDC-3744B). The pump laser is mounted on a laser mount (Thorlabs, model LDM21) with a Peltier element, a thermistor, and a collimation lens.

The pump wave passes through an optical isolator (OFR, model IO-2.5-1064-VLP) and then an anamorphic prism pair (Thorlabs, model PS879-C), which transforms the beam shape from elliptical to circular for efficient coupling with an optical fiber. Half- and quarter-wave plates adjust the polarization of the pump wave for efficient wavelength conversion. The pump wave is then coupled with a polarization-maintaining (PM) single-mode fiber by a spatial-beam fiber coupler. The parallel-polarized signal (5 mW) and pump (30 mW) waves are combined by a PM fiber coupler and fed into the PPLN module through a pigtail fiber. A Peltier element and a thermistor in the PPLN module are connected with a temperature controller (ILX Lightwave, model LDT-5412) for phase matching. The generated 3.4 μm idler wave of 7.5 μW is sufficient for linear absorption spectroscopy, even though the total wavelength conversion efficiency is reduced due to loss at the spatial-beam fiber coupler, the PM fiber coupler, and three fiber connectors. The mid-infrared source is compact in dimension: the housings individually mounting the two DFB lasers and the PPLN are smaller than 100 cm³. The current sources and the temperature controllers used are typical commercially available products for low power consumption, and optical fibers reduce the number of mirror mounts and amount of space for optical alignment. The temperature tuning range of the individual laser device is 15 cm⁻¹ without any frequency gap; therefore, the DFG source is tunable from 2,950 to 2,980 cm⁻¹. The phase-matching condition of the PPLN is attained by temperature-tuning, and the single ridge-waveguide PPLN operates in the wavenumber range of 60 cm⁻¹.

The idler wave is collimated by a sapphire lens and passes through a quartz wedge separating one tenth of the power level from the idler wave. The main beam enters a 150-cm-long absorption cell fitted with CaF₂ windows, and the 470 cm³ volume is filled with 80 μmol of pure methane at a pressure of 400 Pa. The transmitted idler wave is sent back to the cell by a flat mirror, then reflected and focused onto a liquid-nitrogen-cooled InSb photodiode (Hamamatsu Photonics, model P5968-100) with the pump and signal waves removed by a 3.4 μm bandpass filter. The separated beam is immediately detected by another similar detector in order to monitor variations in the incident power level. The idler frequency is swept and modulated by superposing a 0.1 Hz triangle signal and a 5 kHz sinusoidal signal on the injection current of the 1.55 μm DFB laser. The modulation frequency is set at the highest response frequency of the detector [23,24]. The corresponding modulation depth is 250 MHz peak-to-peak, comparable with the absorption line width for obtaining a large signal without significant modulation broadening.

The detected signals are demodulated at 5 kHz (1f detection) by two lock-in amplifiers (Stanford Research Systems, model SR810) with a time constant of 10 ms. The 1f signals as well as the sweep signal are stored by the lock-in amplifiers at the acquisition rate of 500 Hz, corresponding to 2,500 data points in the up/down sweep of the idle frequency. The 1f signals are recorded ten times by the lock-in amplifiers, and the averaged spectrum is stored in a PC. The frequency sweep rate is limited by the time constant, the acquisition time, and the memory size of the lock-in amplifiers. The absorption cell is connected with a molecular turbo pump, an absolute pressure gauge (Edwards, 655AB) with an accuracy of 0.15 %, and two gas containers for exchanging sample and working standard gases. Neither the absorption cell temperature nor the room temperature is stabilized.

Line selection has been discussed and analyzed [10,22,25,26]. Table 1 lists a pair of ¹²CH₄ and ¹²CH₃D lines with asterisks suitable for precisely measuring the isotope ratio together with the adjacent absorption lines having a line intensity exceeding 1.0 × 10⁻²⁵ cm⁻¹/(molecule·cm⁻²) [27]. The ν₄ ^pP(7, 6) line is one of the strongest lines of the less abundant ¹²CH₃D. It does not seriously overlap the lines of ¹²CH₄ and ¹³CH₄, and it has a transition frequency and absorption intensity similar to those of the ν₂ + ν₄ R(6) F₁⁽¹⁾ line of ¹²CH₄, which are favorable characteristics for measuring the isotope ratio. Therefore, the weak overtone band transition is chosen for the major isotope [10,22]. The absorption coefficient depends on temperature of −0.066 and −0.14 %/K at 295 K for the ¹²CH₃D ν₄ ^pP(7,6) and ¹²CH₄ ν₂ + ν₄ R(6) F₁⁽¹⁾ lines; therefore, the ratio has a low temperature dependence of 0.074 %/K, which is another advantage of the present pair.

Figure 2 plots the observed spectrum involving these transitions. The absorption lines have a dispersion-like shape because of the 1f detection in wavelength-modulation spectroscopy. The thin red curve is drawn on a scale 300 times larger than the thick blue curve, and the vertical scale is indicated on the right side of Figure 2. Most small variations in the spectral curves come from the weak absorption lines partially listed in Table 1. The signal-to-noise ratio is limited by some periodic distortion with a typical magnitude of 0.001 V, which will be discussed in Section 3.2. The absorbance is 6 % for the ¹²CH₃D ν₄ ^pP(7,6) line and 40 % for the ¹²CH₄ ν₂ + ν₄ R(6) F₁⁽¹⁾ line at a sample pressure of 400 Pa. These values lie in the desirable range for sensitivity and signal linearity. The idler wave changes in output power as the injection current of the 1.55 μm DFB laser, and the power level at the ¹²CH₃D ν₄ ^pP(7,6) line is 1.5 times higher than that at the ¹²CH₄ ν₂ + ν₄ R(6) F₁⁽¹⁾ line. Therefore, residual amplitude modulation (RAM) inducing asymmetries in signal line shapes on wavelength modulation spectroscopy affects the 1f signal differently for the ¹²CH₃D and ¹²CH₄ lines. These asymmetries, however, do not affect the signal amplitude or detection sensitivity [24].

Here we define the signal ratio R as: (1) R   12 CH 3 D = I 1 f   12 CH 3 D / I 1 f   12 CH 4where I_1f is the peak-to-peak amplitude of the 1f signal. The values of R for the working standard (WS) and the sample are alternately measured. The δ value of the isotope ratio is then determined by: (2) δ 12 CH 3 D Sample-WS = ( R Sample   12 CH 3 D − R WS   12 CH 3 D ) / R WS   12 CH 3 D

Here, the value of R_WS is the average of the working-standard measurements immediately before and after the particular sample measurement to eliminate the effect of uniform signal drift discussed in Section 3.3.

The hydrogen isotope ratio is reported as a value relative to the international standard Vienna Standard Mean Ocean Water (VSMOW) for δD. The value of δ¹²CH₃D_Sample-WS is converted to that of δ¹²CH₃D _Sample-VSMOW as follows: (3) δ 12 CH 3 D Sample-VSMOW = 1 + δ 12 CH 3 D Sample-WS 1 + δ 12 CH 3 D WS-VSMOW − 1

We measured the isotope ratio of the sample and the working standard of pure methane gas whose δD_VSMOW was determined to be −289.9 ± 2.8 and −183.2 ± 1.5‰ using a gas chromatograph high-temperature conversion IRMS (GC/ TC/IRMS, Delta XL, Thermo Finnigan, Bremen, Germany).

The value of δ¹²CH₃D (the isotopomer ratio) determined from the present laser measurements is easily converted to that of δD-CH₄ (the hydrogen isotope ratio of methane), because we use isotopically natural methane, for which the effects of other isotopomers (e.g., ¹³CH₃D and ¹²CH₂D₂) are extremely small [28].

To evaluate the spectrometer sensitivity, we recorded the 1f signal for an evacuated cell. We found a periodic distortion in the baseline with a period of 0.05 cm⁻¹. This interference fringe is caused by weak reflection at the anti-reflection-coated interfaces of the 5-cm-long PPLN with a refractive index of 2.1. We reduced the distortion by dividing the mid-infrared beam into two, using a quartz wedge, and subtracting the 1f signal without any sample from that with the sample. In this way, spectra such as Figure 2 were recorded, attaining a detectable absorbance of < 1 × 10⁻⁴ with an effective signal averaging time of 100 ms. Accordingly, the signal-to-noise ratio was enhanced from 100 to 1,000 for the ¹²CH₃D ν₄ ^pP(7,6) line. The resultant signal still had another smaller periodic distortion in the baseline with a period of 0.2 cm⁻¹, probably because of the Brewster windows of the absorption cell. Distortion amplitude was sensitive to optical alignment and wavelength, limiting the minimum detectable coefficient to 4 × 10⁻⁹ cm⁻¹·Hz^−1/2. The sensitivity satisfied the necessary condition for determining the isotope ratio at an uncertainty level of 1 ‰.

Figure 3 illustrates the pressure dependence of the signal ratio R^CH₃D of Equation (1). The sample pressure is measured with the pressure gauge to an accuracy of 2 Pa. The large pressure dependence of 0.4 ‰/Pa at a pressure of 300 Pa is due to the difference of 5 to 1 in absorbance of ¹²CH₄ to ¹²CH₃D, and the exponential relation in the Lambert Beer's law between the absorbance and the pressure. Therefore, the pressure of the sample and the working standard must be identical with an uncertainty of 2.5 Pa for a 1-‰-level measurement.

The absorption cell is alternately refilled with the working standard and the sample methane. The gas pressure is carefully set at (400 ± 1) Pa, and the value remains constant within ±1 Pa from the initial value during the measurement. Figure 4 depicts the temporal variation of the alternate isotope ratio measurements.

The plots of the sample and the working standard similarly drift by a relative magnitude of 0.46 and 0.36 % on a time scale of an hour, probably because of the temperature variation. If it were due to only the temperature dependence of the absorption coefficient ratio discussed in Section 2.2, the room temperature would change by 6 K. Since it is one order of magnitude larger than the actual condition, we attribute it to the other slow variations of the optical alignment and the electric circuits. To remove the slow effect, we use the averaging procedure described in Section 2.3. The values of δ¹²CH₃D _Sample-VSMOW are then determined to be −294.2, −295.6, −293.7, and −293.5‰, yielding an average of −294.2‰ and the standard deviation of 0.8‰. The averaged δ¹²CH₃D_Sample-VSMOW value is a little lower than the value of −289.9 ± 2.8‰ determined by a mass spectrometer. The difference is slightly beyond experiment uncertainty. This is the first report of the isotope ratio measurements by the present spectrometer. The result is tentative, and further measurements are required for comparison between laser spectroscopy and mass spectrometry.