Chinese Journal of Chemical Physics  2020, Vol. 33 Issue (1): 37-42

The article information

Bo Fang, Na-na Yang, Chun-hui Wang, Wei-xiong Zhao, Xue-zhe Xu, Yang Zhang, Wei-jun Zhang
方波, 杨娜娜, 王春晖, 赵卫雄, 徐学哲, 张杨, 张为俊
Detection of Nitric Oxide with Faraday Rotation Spectroscopy at 5.33 μm
5.33 μm处磁旋转吸收光谱NO分子探测研究
Chinese Journal of Chemical Physics, 2020, 33(1): 37-42
化学物理学报, 2020, 33(1): 37-42

Article history

Received on: October 21, 2019
Accepted on: November 13, 2019
Detection of Nitric Oxide with Faraday Rotation Spectroscopy at 5.33 μm
Bo Fanga,b , Na-na Yanga,b , Chun-hui Wanga,c , Wei-xiong Zhaoa , Xue-zhe Xua , Yang Zhanga , Wei-jun Zhanga,c     
Dated: Received on October 21, 2019; Accepted on November 13, 2019
a. Laboratory of Atmospheric Physico-Chemistry, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China;
b. University of Science and Technology of China, Hefei 230026, China;
c. School of Environmental Science and Optoelectronic Technology, University of Science and Technology of China, Hefei 230026, China
Abstract: We report the development of a static magnetic field Faraday rotation spectrometer for NO detection. A 5.33 μm continuous-wave quantum cascade laser was used as the probing laser. Line absorption at 1875.81 cm$^{-1}$ ($^2\Pi_{3/2}$Q(3/2), $v$=1$\leftarrow$0) was chosen for the detection. By using a Chernin type multipass cell, a detection precision of 1.15 ppbv (1$\sigma$, 1s) was achieved with an absorption pathlength of 108 m. This value was reduced to 0.43 ppbv by increasing the data-acquisition time to 15 s.
Key words: Faraday rotation spectroscopy    Mid-infrared    Laser spectroscopy    Nitric oxide    

Atmospheric nitric oxide (NO) is an important compound of atmospheric reactive nitrogen. It is mainly formed in the combustion process carried out by human activities [1], and plays important roles in controlling the photochemical production of ozone (O$_3$), in determining the concentration of the hydroxyl radical (OH$\cdot$), and in contributing to the formation of secondary organic aerosols (SOA) as well as acid precipitation [2, 3]. High-precision measurement of ambient NO is thus critical for environmental pollution and atmospheric chemistry research.

Laser spectroscopy technique provides an attractive and powerful chemical-free tool for NO measurement with high time resolution and good precision. A wide range of laser spectroscopy methods, such as quartz-enhanced photoacoustic spectroscopy [4], differential optical absorption spectroscopy [5], tunable diode laser absorption spectroscopy [6], cavity based techniques (integrated cavity output spectroscopy [7], cavity-enhanced absorption spectroscopy [8], cavity ring down spectroscopy [9]), and Faraday rotation spectroscopy (FRS) [10], have been used for NO measurement. The reported detection precision ranged from several tens of pptv (parts per trillion by volume) to several ppbv (parts per billion by volume) levels.

FRS is a spectroscopic technique that relies on the magneto-optic effect (Zeeman split) for paramagnetic species [11-13]. The background signals from the absorption of diamagnetic compunds are largely suppressed [14], thus providing a useful method for high sensitive measurement of NO [10, 14-34]. There are two ways to modulate the Zeeman splitting of the absorption line: (ⅰ) an alternating magnetic field (AC-field) produces varying magnetic circular birefringence; (ⅱ) a static magnetic field (DC-field) combined with wavelength modulation spectroscopy (WMS) of the laser frequency to effectively vary the magnetic circular birefringence [35]. The FRS signal is then generated from the demodulation of the modulated magnetic circular birefringence with a phase-sensitive lock-in amplifier. Compared with AC-FRS method, DC-FRS method provides an alternative FRS scheme with excellent performance. The use of permanent magnet instead of AC magnetic coil has potential to reduce the power consumption, and the low frequency noise can be reduced by using high frequency modulation (in AC-FRS method, the demodulation frequency is usually limited by the resonant frequency of RLC circule) [36].

In this work, DC-FRS technique was studied for NO detection at 5.33 µm (1875.81 cm$^{-1}$, $^2\Pi_{3/2}$Q(3/2), $v$=1$\leftarrow$0) with a continuous-wave (CW) quantum cascade laser (QCL). A Chernin type multipass cell was used to increase the absorption pathlength. Performance evaluation is presented and discussed.


For weak absorption and small rotation angle ($\varphi$, the angle offset the cross position between two polarizers), the laser power ($P$) emerging from the analyzer can be expressed as [11]:

$ \begin{eqnarray} P(\varphi)=\frac{P_0}{2}\left(1-\cos2\varphi+R_\Delta L\sin2\varphi\right) \end{eqnarray} $ (1)

where $P_0$ is the laser incident power, $L$ is the absorption path length inside the magnetic field, and $R_\Delta$ is the differential between the refraction indices ($n$) of the medium for the right- (RHCP, +) and left-handed (LHCP, $-$) circularly polarized light. $R_\Delta$=$k_0$($n_+$$-$$n_-$), where $k_0$ is the wave vector, responsible for the FRS signal ($F$):

$ \begin{eqnarray} F=\frac{P_0}{2}R_\Delta L\sin2\varphi \end{eqnarray} $ (2)

$R_\Delta$ contains line shape information, which can be calculated as the sum of all allowed Zeeman sublevel transition components (as shown in FIG. 1) [37]:

$ \begin{eqnarray} R_\Delta=\frac{NS\sqrt{\ln 2}}{\pi\gamma_\textrm{D}}\sum\limits_{M'_JM''_J}(-1)^{M'_J-M''_J}\textrm{Re}[Z(z)] \end{eqnarray} $ (3)
FIG. 1 Zeeman splitting energy pattern for Q$_{3/2}$(3/2) of NO molecule. The $\Delta M_J$=$\pm$1 transitions are indicated by arrows

where $N$ is the molecule concentration in molecule/cm$^3$, $S$ is the line absorption intensity in cm$^{-1}\cdot$molecule$^{-1}\cdot$cm$^{2}$, $\gamma_\textrm{D}$ is the Doppler width (HWHM) in cm$^{-1}$, $M_J'$ and $M_J''$ are the magnetic quantum numbers for the upper and lower states, and $Z(z)$ is the plasma dispersion function with $z$=$x$+$iy$:

$ \begin{eqnarray} Z(z)&=&\frac{1}{\sqrt{\pi}}\int_{-\infty}^{+\infty}\frac{\exp(-t^2)}{t-z}\textrm{d}t \end{eqnarray} $ (4)
$ \begin{eqnarray} x&=&\sqrt{\ln 2}\frac{\nu-\nu_{M'M''}}{\gamma_\textrm{D}} \end{eqnarray} $ (5)
$ \begin{eqnarray} y&=&\sqrt{\ln 2}\frac{\gamma_\textrm{C}}{\gamma_\textrm{D}} \end{eqnarray} $ (6)

where $\gamma_\textrm{C}$ is the collisional width in cm$^{-1}$, $\nu$ is the laser frequency, and $\nu_{M'M''}$ is the line center frequency in the magnetic field.

The total noise can be expressed as the following by adding the noise term with the extinction ratio ($\xi$) term of the analyzer [18]:

$ \begin{eqnarray} N_{\textrm{tot}}=\frac{P_0}{2}\left(1-\cos2\varphi+P_0\xi\right) \end{eqnarray} $ (7)

which is a function of the offset angle $\varphi$ [37]:

$ \begin{eqnarray} N_{\textrm{tot}}(\varphi)=\sqrt{{N_0}^2+{N_1}^2(\sin^2\varphi+\xi)+{N_2}^2(\sin^2\varphi+\xi)^2}\\ \end{eqnarray} $ (8)

Among these noise sources, the detector noise $N_0$ is independent of $\varphi$. For small $\varphi$, the shot noise $N_1$($\sin^2\varphi$+$\xi$)$^{1/2}$ is proportional to $\varphi$, and the laser noise $N_2$($\sin^2\varphi$+$\xi$) is proportional to $\varphi^2$. As the FRS signal is proportional to $\varphi$, there is a maximum signal-to-noise ratio (SNR) at an optimal rotation angle $\varphi_{\rm{opt}}$ depending on the contribution of each noise source.

Ⅲ. EXPERIMENTS A. Experimental setup

The schematic diagram and the corresponding photograph of the experimental setup are shown in FIG. 2. A 5.33 µm room temperature continuous-wave (CW) quantum cascade laser (QCL, Thorlabs), controlled by a laser diode controller (ITC4002QCL, Thorlabs), was used for probing the Faraday rotation effect via measurement of the Q$_{3/2}$(3/2) line of NO at 1875.81 cm$^{-1}$ (with a line strength of 3.76$\times$10$^{-20}$ cm$^{-1}\cdot$molecule$^{-1}\cdot$cm$^{2}$). The output of the laser was collimated by an aspheric lens with an effective focal length of 1.873 mm. The collimated laser beam was then directed to FRS setup: (ⅰ) a Rochon type polarizer used to "clean-up" a polarization state of the probe laser, (ⅱ) a Chernin type multipass cell used for increasing the absorption pathlength and improving the detection sensitivity, and (ⅲ) a second Rochon type polarizer acted as an polarization analyzer. The laser intensity emerging from the analyzer was detected with a thermoelectrically cooled photodetector (PIP-4TE-8, Vigo System).

FIG. 2 Schematic diagram and corresponding photograph of the experimental setup. DAQ: data acquisition, PC: personal computer

Laser wavelength scan was realized by feeding an external voltage ramp from a function generator (Agilent 33622A) to the injection laser diode current at a rate of 100 Hz. An internal reference sinusoidal signal ($f_{\rm{m}}$=33 kHz) from a lock-in amplifier (SR850, Stanford Research) was added to the ramp for wavelength modulation. The FRS signal was demodulated (second harmonic, $2f$ detection) by the lock-in amplifier with a time constant of 100 µs.

B. Chernin type optical multipass cell

The light path diagram and actual light spot pattern of the Chernin type optical multipass cell [38-41] are shown in FIG. 3 (a) and (b) respectively. The cell consisted of two rectangular filed mirrors (FIG. 3(c), with dimensions of 75 mm$\times$15 mm and 105 mm$\times$90 mm), and three circular objective mirrors (FIG. 2(d), 45 mm in diameter). All mirrors had the same radius of curvature (ROC=1500 mm), which was equal to the base length of the cell. The mirrors were coated with protected silver with a reflectivity of $\sim$97%. Field and objective mirrors were mounted on their own back plates. Each mirrors could be adjusted independently, which had good stability to vibrations [41]. Arbitrary rows with even columns spot patterns on the field mirrors were easily achievable (as shown in FIG. 2(b), an example of 6 rows$\times$6 columns spot pattern). This configuration offered an effective use of the surface of the field mirror compared with the common used White type cell.

FIG. 3 The Chernin type optical multipass cell. (a) Ray tracing simulation of the cell using TracePro. (b) 6 rows$\times$6 columns spot pattern. A pathlength of 108 m was achieved under this pattern. (c) Three-dimension rendering models of the field and (d) objective mirrors. The golden color of the mirror surfaces is only used to distinguish between the mirrors and the mount
C. Superconducting magnet

The static magnetic field was provided by a superconducting wires (NbTi) wrapped coil [38]. In order to maintain superconducting sate, the magnet coil was sealed in a Dewar vessel (with 1280 mm long, and 500 mm inner diameter), and was cooled to temperature below 5 K with a He-cycle cryocooler (SHI F-50, Sumitomo Industries). The intensity of the magnetic field intensity was adjustable (17.9 Gauss/A) with a resolution of 2 Gauss. The maximum field intensity tested was about 1800 Gauss, which was limited by the current source. The intensity could be further increased as the excitation current increased.

Ⅳ. RESULTS AND DISCUSSION A. Optimization of magnetic field and rotation angle

To maximize the FRS signal in the experimental pressure of 100 mbar, a series of experiments were performed to determine the optimum magnetic field strength ($B_{\rm{opt}}$, as shown in FIG. 4(a)). The intensity of $2f$ signal (peak-to-peak value of the spectrum) initially increased with the increment of $B$, and when it reached a certain value, it began to decrease with the increment of $B$. The largest FRS $2f$ signal was found at 107 Gauss. The FRS signals at three different magnetic field strengths ($B$) are shown in FIG. 4(b). The magnet current of 0 A meant a zero $B$, which corresponded to WMS only. A current of 6 A corresponded to the optimum field. With a current of 13 A, split of the $2f$ signal was observed, which was caused by the large Zemman splitting energy level. The measured total noise of the system and SNR as a function of $\varphi$ is shown in FIG. 5. The maximum SNR was achieved at a rotation angle of 7$^\circ$ with a total noise of 3.70 µV$\cdot$Hz$^{-1/2}$.

FIG. 4 (a) The largest FRS $2f$ signal was found at an current of 6 A, which corresponded to an optimum magnetic field strength $B_{\rm{opt}}$ of 107 Gauss. (b) The FRS $2f$ signals at three different magnetic field strengths $B$. Split of the $2f$ signal was observed at high $B$ condition
FIG. 5 (a) The measured total noise and (b) SNR as a function of rotation angle
B. Performance evaluation

The linear relationship between FRS $2f$ signal and NO concentration is shown in FIG. 6. The linear fit uncertainty was less than 3%. Different NO concenrations were obtained by diluting 1000 ppmv NO cylinder gas with high purity N$_2$. A commercial NO-NO$_2$-NO$_x$ analyzer (Thermo Modeal 42i) was used for the measurement of the concentration of the mixed gas. The linear relationship with a correlation coefficient $R^2$ of 0.998 demonstrates that the FRS system has a good response for NO measurement.

FIG. 6 Linear relationship between FRS-$2f$ signal and NO concentration

Performance comparison between FRS and WMS was taken to depict the improvement of DC-FRS, as shown in FIG. 7. Continuous time series measurement of NO with the two methods are shown in FIG. 7(a, b). The time resolution of the data was 1 s (wavelength scanning with a 100 Hz ramp, and 100 spectral averaging). Measurement fluctuations ($1\sigma$ standard deviation) over 5000 s were 1.45 ppbv for FRS, and 7.06 ppbv for WMS, respectively.

FIG. 7 Comparison between (a, c, e) FRS and (b, d, f) WMS. Time series measurement of NO concentration with (a) FRS and (b) WMS. Frequency distribution of the mixing ratio with (c) FRS and (d) WMS. Allan deviation plots for NO measurement with (e) FRS and (f) WMS

A histogram plot of time series depicting an approximate normal distribution around the mean value is plotted in FIG. 7(c, d), which was used to assess the measurement repeatability. A Gaussian profile was fitted to the distribution histogram, resulting in a half-width at half-maximum (HWHM) of 1.71 ppbv and 8.32 ppbv, and a $\sigma_{\rm{Gaussian}}$ (a measure of actual precision) of 1.45 ppbv and 7.51 ppbv for FRS and WMS respectively.

The stability and precision were investigated using Allan deviation analysis, which is shown in FIG. 7(e, f). For FRS, the measurement precision was 1.15 ppbv with a 1 s data acquisition time, and was improved further to 0.43 ppbv with averaging time of 15 s. For WMS, the precision over 1 s was 3.12 ppbv, and may be improved to 1.28 ppbv in 150 s. The precision for FRS was several times better than WMS.

A comparison of the detection precision with some literature report results is shown in Table Ⅰ. Though further improvement can be made, the achieved precision in this work with DC-FRS was comparable to AC-FRS methods combined with laser frequency locking [10, 22], heterodyne-enhanced [23], dual-modulation [34], and cavity enhanced methods [32].

Table Ⅰ Comparison of the NO detection precision of some FRS systems

An experimental study was carried out on NO detection with DC-FRS method. By using a Chernin type multipass cell, a precision of 1.15 ppbv in 1 s data-acquisition time was achieved. This precision was reduced to 0.43 ppbv by increasing the sampling time to 15 s. The experimental system in this work can be further miniaturized by using a compact multipass cell and a small solenoid magnet or a permanent magnet to make it suitable for field application.


This work was supported by the National Key Research and Development Program of China (No.2016YFC0202205), the National Natural Science Foundation of China (No.41805104, No.41875151, and No.41627810), the Natural Science Foundation of Anhui Province (No.1508085J03), the Youth Innovation Promotion Association CAS (No.2016383), and the CASHIPS Director's Fund (YZJJ2018QN7, BJPY2019B02).

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5.33 μm处磁旋转吸收光谱NO分子探测研究
方波a,b , 杨娜娜a,b , 王春晖a,c , 赵卫雄a , 徐学哲a , 张杨a , 张为俊a,c     
a. 中国科学院安徽光学精密机械研究所,大气物理化学研究室,合肥 230031;
b. 中国科学技术大学,科学岛分院,合肥 230026;
c. 中国科学技术大学环境科学与光电技术学院,合肥 230026
摘要: 本文基于直流磁场的磁旋转吸收光谱技术探测研究一氧化氮分子的痕量.使用5.33 μm连续波量子级联激光器作为探测光源,结合Chernin型光学多通池,在1875.81 cm$^{-1}$($^2$$\Pi$$_{3/2}$(3/2),$\nu$=1$\leftarrow$0)波长处进行探测. 108 m吸收光程下,实现了1.15 ppbv的探测极限(1s,1$\sigma$).当采样时间延长到15 s,探测极限可提高至0.43 ppbv.
关键词: 磁旋转吸收光谱    中红外    激光光谱    一氧化氮