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Abstract
We demonstrate high-sensitivity vibrational absorption spectroscopy in the 2-micron wavelength range by using a mode-locked Cr:ZnS laser. Interferometric subtraction and multichannel detection across the broad laser spectrum realize simultaneous background-free detection of multiple vibrational modes over a spectral span of >380 cm−1. Importantly, we achieve detection of small absorbance on the order of 10−4, which is well below the detection limit of conventional absorption spectroscopy set by the detector dynamic range. The results indicate the promising potential of the background-free method for ultrasensitive and rapid detection of trace gases and chemicals.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Vibrational absorption spectroscopy is potentially useful for detection of trace gases and chemicals and has a wide range of applications, such as atmospheric environment monitoring [1], industrial chemical control [2], breath analysis [3] and astrochemistry [4]. However, conventional absorption spectroscopy in the transmission or reflection geometry, or direct absorption spectroscopy (DAS), intrinsically faces the challenge of detecting a small absorption dip in a large background light. The background light has a negative effect on the detection sensitivity mainly in two ways. First, the intensity noise of the background light directly limits the minimum detectable absorbance, though this limitation is relaxed by monitoring the spectrum of the light source during the sample transmittance measurement. Second, the saturation of the detector due to the background light does not allow us to increase the incident optical power for enhanced transmission dips. As a result, the detection sensitivity is limited by the dynamic range of the detector, namely, the ratio of the saturation level to the noise level [5].
A few strategies have been proposed to eliminate the background light in absorption spectroscopy. The first strategy is to use an ultrashort pulsed laser as a light source and filter out the background light in time. Here, the incident femtosecond pulses resonantly excite multiple vibrational modes, which emit radiations in the form of the free-induction decay (FID). Then, the temporally-short background light is filtered out by a time gate based on nonlinear wave mixing [6–9]. This time-gating approach, however, requires highly energetic, ultrashort laser pulses for nonlinear wave mixing to produce detectable signals.
The second strategy is to cancel the background light in a coherent manner by exploiting interferometry [10]. By setting an interferometer with the destructive interference condition and by placing a sample in one of the optical arms, molecular absorption can be extracted with an eliminated background. This interferometer-based background-free spectroscopy (BFS) has been demonstrated with a thermal tungsten lamp [11], a wavelength-tunable diode laser [12], and a quantum cascaded laser [13]. For multispecies trace gas sensing, however, laser sources with broadband emission spectra are beneficial because the broad spectral coverage enables the rapid, simultaneous detection of multiple vibrational transition lines and guarantees quantitative accuracy even under an unexpected change in the optical spectrum [14,15]. Recently, interferometer-based BFS has been implemented with a few-cycle erbium-fiber pumped laser system [16] and a mid-infrared dual-comb source based on thulium-fiber pumped subharmonic GaAs OPO [17]. However, a small absorbance measurement on the order of $10^{-4}$ or less has not yet been achieved in vibrational BFS.
Here, we develop a broadband BFS in the 2-micron wavelength range by using a high brightness, low noise, mode-locked Cr:ZnS laser. Interferometric subtraction across the broad laser spectrum and the multichannel acquisition realize the simultaneous background-free detection of the multiple vibrational modes over a spectral span of $> 380$ cm$^{-1}$. With appropriate balances of loss and phase delay between two interferometer arms, we experimentally demonstrate detection of small absorbance on the order of $10^{-4}$ with a 1 ms integration time. The demonstrated sensitivity is well beyond the limit for conventional DAS determined by the dynamic range of the detector. The current work makes significant progress in broadband BFS regarding detectable absorbance, indicating promising potential for the ultrasensitive, rapid detection of trace gases and chemicals.
2. Experimental setup
As a broadband infrared source, we use a homemade mode-locked Cr:ZnS oscillator [18–20], which emits 40 fs pulses with a center wavelength of 2270 nm and an average power of 200 mW at a repetition rate of 40 MHz. Cr-doped chalcogenide lasers are useful for vibrational spectroscopy because of their broad emission ranges in the infrared [21,22]. In fact, our Cr:ZnS laser spectrum covers the first overtones and the lower-order combination bands of various industrial gas molecules, as shown in Fig. 1(a), while existing at an atmospheric window.
Fig. 1. (a) A mode-locked Cr:ZnS laser spectrum on a logarithmic scale (red) and absorption lines of several industrial gases (black). (b) The experimental setup of broadband BFS. VOA: variable optical attenuator, M: a gold mirror, DM: a dichroic mirror, BS: a beamsplitter, PD: a Si photodiode.
The experimental setup is shown in Fig. 1(b). To eliminate the background light, we use a Michelson interferometer composed of a 5 mm thick, wedged CaF$_2$ beam splitter with a single-side coating (Thorlabs BSW511) and Au mirrors. We place a 10 cm long gas cell with a 1.5 mm thick MgF$_2$ window on each end. To balance the energy throughput and the phase delay between the two arms, we place two 1.5 mm thick MgF$_2$ windows and a 5 mm thick CaF$_2$ window in one of the arms. This CaF$_2$ window has an anti-reflection coating on one side (Thorlabs W510D) so that both the number of Fresnel transmission and that of Fresnal reflection are balanced between the two arms. The resulting group-delay dispersion (GDD) proves to be well balanced according to spectral interferometry analysis (see the Supplement for more details). The interferometer output or the molecular response signal is dispersed by a monochromator (SOL Instruments MS5204i) and detected by an InGaAs arrayed sensor (512 pixels, Hamamatsu Photonics G9208-512WB). In this way, the full background-free absorption spectrum is obtained simultaneously without any mechanical scan.
To stabilize the interferometer, we use a He-Ne CW laser with a wavelengh of 632.8 nm. The He-Ne laser is collinearly combined with the Cr:ZnS laser by the first dichroic mirror to be sent into the interferometer. The interferometer output of the He-Ne laser is bounced off by the second dichroic mirror and sent into a homemade ’dithering and locking’ feedback loop [23]. This feedback loop consists of a Si photodetector, a lock-in amplifier (NF LI5650), a PI servo, and a piezoelectric transducer. The amplitude and frequency of the dithering is 5 nm and 401 Hz, respectively, and the time constant for the lock-in amplifier is 20 ms. As a result, the interferometer is stabilized to represent the RMS phase variation of $\pi /70$ for 100 seconds for the He-Ne laser wavelength (which corresponds to $\pi /250$ for the Cr:ZnS laser wavelength).
3. Results and discussion
3.1 Background-free absorption spectrum
Figures 2(a) and (b) show the measured power spectra of the interferometer output, namely, the background-free absorption spectra (red lines) for a 10 cm long gas cell (the effective interaction length is 20 cm because of the double pass geometry) filled with 0.28 atm CH$_{4}$ and 0.6 atm CO, respectively. The spectra are measured with an input laser power of 27 mW, a detector integration time of 1 ms, and an averaging number of 50. The entrance slit width is set to 20 $\mu$m so that the spectral resolution is 0.4 cm$^{-1}$.
Fig. 2. The measured background-free absorption spectra (red lines) for (a) methane (a 10 cm cell with a 0.28 atm pressure) and (b) carbon monoxide (a 10 cm cell with a 0.6 atm pressure). The reference absorbance spectra calculated from the HITRAN data are shown as gray lines with reversed signs. The two arrows in (a) indicate the bands at 2312 nm and 2330 nm, which are investigated in Fig. 3.
For CH$_4$, the rovibrational transition lines of the combination tones of the symmetric CH stretching and scissoring vibrations and the second overtone of the scissoring vibration are observed. For CO, the rovibrational transition lines of the first overtone of the CO stretching vibration are observed. In both cases, the measured spectra match well the reference absorbance spectra (shown as gray lines with reversed signs), which are calculated using the HITRAN data [24] and the experimental spectral resolution. Here, we note that the spectrometer is calibrated by using the absorption lines of CO, acquired in the normal transmission geometry.
The measured optical power spectra represent peak structures with a well-suppressed background, which indicates that the destructive interference condition is satisfied for a broad spectral range from 2200 to 2400 nm, which corresponds to a spectral span of $> 380$ cm$^{-1}$.
3.2 Formulation of signal-to-noise ratio
For the discussion of sensitivity in absorbance measurements, we formulate the signal-to-noise ratio (SNR) in terms of absorbance $A$ and the field unbalanced factor $\delta$ between the two arms [16]. The electric-field amplitude at the detector for the light which traveled through the path with and without the gas sample is described as
respectively, where the inverse sign in Eq. (1) denotes the destructive interference condition. Then, the optical power of the interferometer output is described asThe noise equivalent power in the background-free measurements can be described as [16,25],
By defining the signal as the optical power that reflects molecular absorption $A$ in Eq (3), we can describe SNR as
For small absorbance $A \ll 1$ and negligible optical shot noise, Eq. (6) is rewritten as
3.3 Experimental signal-to-noise ratio
We investigate how the SNR depends on the optical power $P_0$ and the field unbalanced factor $\delta$. In the experiments described below, we change $\delta$ by rotating the compensation window and then estimate $\delta$ by fitting the measured absorption line of methane at 2312 nm with Eq.3 (See supplement “Influence of the field unbalanced factor”)
Figure 3(a) shows the experimental SNR (markers) as a function of the employed optical power per spectral element $P_0$, measured for a band at 2330 nm that exhibits an absorbance of $A=0.054$. Here, the field unbalanced factors are set to $\delta =0.067$ and $0.089$. Here, we note that the experimental power per spectral element is calculated by neglecting both the reflection loss inside the monochromator and the transmission loss at the entrance slit. The SNRs scale almost linearly with the optical power, indicating the detector-noise dominant range (see Eq. (8)). Figure 3(b) shows the same data but plotted against $\delta$. Figure 3(c) shows the experimental SNR (markers) as a function of the optical power, measured for a band at 2312 nm that exhibits $A=0.23$. We see that the SNRs tend to become saturated with the employed optical power, indicating the intensity-noise dominant range (see Eq. (9)). Figure 3(d) shows the corresponding $\delta$-dependence of the SNR.
Fig. 3. (a)(c) The experimental SNR (markers) as a function of the employed optical power per spectral element for (a) a band at 2330 nm that exhibits an absorbance of $A=0.054$ and (c) a band at 2312 nm that exhibits $A=0.23$. The corresponding theoretical curves calculated using Eq. (6) are shown as solid lines. (b)(d) The same data and theoretical curves are plotted against $\delta$. The optical power per spectral element of 5.6 $\mu W$ corresponds to the input laser power of 56 mW.
Figures 3(a-d) also display the theoretical curves (solid lines) based on Eq. (6), calculated with the experimentally evaluated values of $\sigma _r = 0.6\%, \Delta f = 0.5$ MHz, and $P_\mathrm {d} = 4.2 \times 10^{-4}$ $\mu$W. The theoretical curves agree with the measured SNR well. From the theoretical curves shown in Figs. 3(b,d), we see that the SNR increases with $\delta$ and then decreases at an optimum $\delta$ and that the optimum $\delta$ depends on $P_0$ and $A$.
To evaluate the sensitivity, we define the limit of detection (LOD) as the absorbance $A_{\textrm {min}}$ that satisfies SNR=1. This definition could be termed the noise equivalent absorbance (NEA). Figure 4 shows the LOD calculated from Eq. (6) with the experimentally evaluated parameters of $\sigma _{\textrm {r}}$ and $\Delta f, P_{\textrm {d}}$, plotted against the relative input power $P_0/P_\mathrm {d}$ and the field unbalanced factor $\delta$. The white area indicates the condition where the detector is saturated. The white dashed line represents the optimal unbalanced factor $\delta _\textrm {opt}$ that gives the minimum LOD for a given relative input power $P_0/P_\mathrm {d}$. For a small absorbance ($A \ll \delta$) and negligible optical shot noise, the LOD is calculated from Eq. (7) as
Fig. 4. The calculated LOD plotted against the relative input power $P_\textrm {0}/P_\textrm {d}$ and the field unbalanced factor $\delta$. $\sigma _{r}$ is set to our typical value of $0.6\%$. The white-dashed line shows the optimal $\delta$ that achieves the minimum LOD for a given relative input power $P_\textrm {0}/P_\textrm {d}$. The white area indicates the condition where the detector is saturated.
This LOD map indicates that the minumum LOD is obtained with $\delta _\textrm {opt}=0.105$ for the employed optical power of $P_0 = 5.6$ $\mu$W or the relative power of $P_0/P_\textrm {d}=1.4 \times 10^{4}$. If we fully utilize the laser output power of 200 mW and set the width of the entrance slit to a 45 $\mu$m (corresponding spectral resolution is 0.6 cm $^{-1}$), the relative optical power reaches ${P_0 }/{P_{\textrm {d}}} = 2.3 \times 10^{5}$. With this increased laser power, $A_\textrm {LOD} = 2.3 \times 10^{-4}$ can be achieved with $\delta _\mathrm {opt}$ of 0.027. To obtain even higher sensitivity with the same $\sigma _{r}$, one may increase the laser power to have larger ${P_0 }/{P_{\textrm {d}}}$ and then choose the optimal $\delta _\mathrm {opt}$, although it may require more effort to achieve $\delta _\mathrm {opt}$ that is smaller than $10^{-2}$.
3.4 Validation of sensitivity
To experimentally validate the LOD, we measure the absorption lines of gaseous CO (10 cm long cell, 0.6 atm). As shown in Fig. 2(b), CO molecules exhibit well-separated, rovibrational transition lines of the first overtone of the stretching mode in the measured spectral range. Importantly, each of the P- and R-branches represents an infinite number of rovibrational transition lines with varied absorption strengths. Here, we validate the sensitivity by targeting a transition line that has the smallest detectable absorbance.
Figure 5(a) shows the measured background-free absorption spectrum as a blue solid line. This measurement is performed with a detector integration time of 1 ms without any further averaging procedure and a relative optical power of ${P_{\textrm {0}}}/{P_{\textrm {d}}} \approx 2.3 \times 10^{5}$. In the wavelength range below 2304 nm, we clearly see multiple peaks of the R-branch rovibrational lines, R($J$)’s with $J \geqq 28$. There is also an unwanted jagged pattern originating from the pixel-by-pixel sensitivity variation of the arrayed sensor. The amplitude of the jagged pattern ($\sim$ 600 counts) is more than 3 times larger than the fluctuating noise ($\sim$ 170 counts) and does not decrease with increasing integration time. Here, we remove this pattern to obtain the smoothed spectrum shown as a red solid line in Fig. 5(b) by the sensitivity calibration and a simple low-pass filter.
Fig. 5. (a) The measured background-free absorption spectrum of the rovibrational transition lines in the R-branch of CO measured with an 1 ms integration time. The spectrum is normalized by the detector saturation level. (b) The spectrum after removal of the jagged pattern (a red solid line) and the fitted curve (a gray dashed line) indicate detection of the R(34) transition line, which has an absorbance of 4$\times 10^{-4}$. The shows a vertically magnified plots of the R(34) transition line. (c) The wavelength-dependent field unbalanced factor $\delta$ that gives the best fit to the measured background-free absorption spectrum.
The smoothed spectrum is numerically fitted with Eq. (4), as shown by the gray dashed lines in Figs. 5(a,b). Here, the absorption spectrum taken from the HITRAN database is convoluted with our instrumental function, and $\delta$ is expressed as a fifth-order polynomial with respect to the wavelength, as shown in Fig. 5(c). Note that the instrumental function is determined by the experimental spectral resolution and the cutoff frequency of the filtering procedure. We see that the R(34) line ($J=34 \rightarrow 35$) at 2299.1 nm that exhibits an absorbance of $4\times 10^{-4}$ is successfully detected. This is by far the highest sensitivity ever reported for broadband BFS [16,17]. The detected absorbance is well below the value $1.7\times 10^{-3}$, which is the LOD for DAS set by the the dynamic range of the detector ($600$). Note that the measured amplitude of the R(34) line corresponds to the detector count of $240$, which is larger than the detector fluctuating noise of 50.
It is, however, difficult to distinguish the transition lines beyond the R(34) line because of the disturbance from the jagged pattern. The unwanted pattern mainly originates from the variation in the detector sensitivity, as well as some ‘etalon fringes’. Assuming that the unwanted pattern are removed, the sensitivity would be governed by the fluctuating noise and improved with increasing integration time.
To investigate the statistical character of temporal fluctuation, we measure the Allan deviation $\sigma _\textrm {A}$ of the interferometer output power measured with $\delta = 0.044$ at a wavelength of 2324 nm, as shown in Fig. 6. The horizontal axis is the detector integration time and any molecular resonance is absent at the measured wavelength. Here, Allan deviation $\sigma _\textrm {A}$ is normalized by the averaged signal level ($\sim P_0 \delta ^{2}$). As we see from Fig. 6, $\sigma _\textrm {A}$ is 0.0068 at a detector integration time of 1 ms. According to Eq. (10), the LOD in terms of absorbance is determined as $A_\textrm {LOD} = \textrm {Noise} /(P_0 \delta ) = \sigma _\textrm {A} \delta = 0.0068 \times 0.044 = 3.0 \times 10^{-4}$, which is consistent with the value $4.0 \times 10^{-4}$ demonstrated above. Correspondingly, the LOD for a 1 s integration time is estimated as $9.5 \times 10^{-6} \textrm {Hz}^{-1/2}$.
Fig. 6. The measured Allan deviation of the detector signal for the interferometer output (normalized by the averaged signal level) plotted against the detector integration time. An optimum integration time of 6 s indicates the minimum detectable absorbance of $7.0 \times 10^{-6}$. The red dashed line denotes the dependence expected for the case accompanied only by the white noise.
The measured $\sigma _\textrm {A}$ follows the dependence of random fluctuation, $(\textrm {integration time})^{-1/2}$, at shorter integration time, as indicated by a red dashed line, but deviates from it at longer integration time. This deviation may arise from non-stochastic interferometer displacement, temperature drift, etc. (see the Supplement for more details). The optimum integration time of approximately 6 s results in the least Allan deviation of $1.6 \times 10^{-4}$, which corresponds to an LOD of 7.0$\times 10^{-6}$. This value indicates a detection sensitivity of 517 ppbV for CO and 381 ppbV for CH$_4$, assuming the same interaction length of 20 cm. Here, we target a rovibrational transition line that has the largest cross-section within the spectral range covered by our mode-locked Cr:ZnS laser for each of CO and CH$_4$. Note that this sensitivity is high enough to detect CH$_4$ in the natural atmosphere ($\sim$1900 ppbv) with a 20 cm interaction length.
It is worthwhile to compare our detection sensitivity with that of DAS. When exploiting DAS based on the Fourier transformation method with a mode-locked Cr:ZnSe laser [21], the NEA at one second averaging per spectral element was $({\textrm {SNR}})^{-1}\times (T/M)^{1/2} = 1.7\times 10^{-5}( \textrm {Hz}^{-1/2})$. Here, $T$ and $M$ denote the integration time and the number of spectral elements, respectively. DAS using ytterbium-doped fiber dual-combs [26] and that using two OPO combs [27] showed NEA at one second averaging per spectral element of $(\textrm {SNR})^{-1}\times (T/M)^{1/2} =$ $1.3 \times 10^{-6} (\textrm {Hz}^{-1/2})$ and $5.1 \times 10^{-5} (\textrm {Hz}^{-1/2})$, respectively. Our measured value of $A_{\mathrm {LOD}}=4 \times 10^{-4}$ (shown in Fig. 5(b)) for an integration time of 1 ms and 512 spectral elements corresponds to $({\textrm {SNR}})^{-1}\times (T/M)^{1/2} = 5.3\times 10^{-7}( \textrm {Hz}^{-1/2})$, which is more superior than the values listed above for the previous DAS. We also evaluate an LOD of DAS by using our mode-locked Cr:ZnS laser, and confirm more than 40 times higher sensitivity for BFS.
4. Conclusion
In summary, we demonstrate vibrational BFS in the 2-micron range that enables simultaneous detection of multiple vibrational modes over a spectral span of $> 380$ cm$^{-1}$ with an absorbance sensitivity on the order of $10^{-4}$, well below the limit set by the dynamic range of the detector, with a 1 ms integration time. This is by far the highest sensitivity ever reported in the previous broadband BFS [16,17]. One of the keys is the use of the infrared mode-locked Cr:ZnS laser, which supports high brightness and low intensity noise at the same time. The other key is the suppression of the imbalances of loss and phase delay between the two interferometer arms. Allan deviation measurements suggest the potential LOD in terms of absorbance of $7.0{\times }10^{-6}$ with a 6 s integration time. We also develop an LOD map that indicates the optimal field unbalanced factor and the achievable sensitivity.
The presented results indicate the promising potential of the BFS method based on emerging infrared mode-locked lasers for the ultrasensitive, rapid detection of trace gases and chemicals. It is worthwhile to note that our demonstrated setup potentially allows a single-shot measurement of the background-free absorption spectrum, which would be useful for monitoring chemical reaction processes. To push the sensitivity limit further, we can increase the employed laser power while paying effort to achieve $\delta$ smaller than $10^{-2}$. Another interesting challenge toward detecting low concentration gases is to integrate BFS with a multiple-pass cell or a resonant cavity to increase the effective path length.
Funding
Japan Society for the Promotion of Science (20H02651, 20J22067, 20K20556, 21K14584); Core Research for Evolutional Science and Technology (JP20348765).
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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