The article information
 Akiko Nishiyama, Grzegorz Kowzan, Dominik Charczun, Ryszard S. Trawiński, Piotr Masłowski
 Nishiyama Akiko, Kowzan Grzegorz, Charczun Dominik, Trawiński Ryszard S., Masłowski Piotr
 Optical Frequency CombBased CavityEnhanced FourierTransform Spectroscopy: Application to Collisional LineShape Study
 基于光梳的腔增强傅里叶变换光谱：在碰撞线形研究中的应用
 Chinese Journal of Chemical Physics, 2020, 33(1): 2330
 化学物理学报, 2020, 33(1): 2330
 http://dx.doi.org/10.1063/16740068/cjcp1911192

Article history
 Received on: November 1, 2019
 Accepted on: November 27, 2019
Optical frequency combs (OFCs) have spectrum consisting of millions of equally spaced narrow modes that can be stabilized to radio frequency (RF) or optical frequency standards. They have been adopted as reliable optical frequency rulers in the fields of metrology and precise spectroscopy [1, 2]. Using OFCs as spectroscopic light sources led to development of such techniques as: virtuallyimaged phasedarray (VIPA) spectroscopy [3, 4], dualcomb spectroscopy [57] and OFCbased Fouriertransform spectroscopy (FTS) [8, 9]. These directcomb spectroscopy techniques have been intensely developed in recent years because of their high potential for applications in various fields, including highresolution molecular and atomic spectroscopy [1013], remote sensing [14], and breath analysis [4]. In directcomb spectroscopy, it is possible to extract spectral information from a large number of comb modes.
If the comb modes are resolved, then the frequency resolution is determined by comb mode linewidth, which makes it on par with conventional highresolution spectrometers using continuous wave (cw) lasers. OFCs stabilized to primary frequency standards offer stateoftheart frequency accuracy and precision that transfers directly to frequency accuracy of directcomb spectroscopy. Furthermore, thanks to the broadband spectrum of OFCs, spectral acquisition over a wide wavelength range can be performed instantaneously.
Dualcomb spectroscopy needs two OFCs and requires them to be highly phasestable relative to each other. Alternatively, the intrinsic phase instability can be accounted for in postprocessing but this requires sophisticated phase correction algorithms. VIPA spectrometers usually require filtering the OFC to increase comb mode spacing due to insufficient resolution and their bandwidth is strongly limited by the physical size of the photodetector array. In contrast, OFCbased FTS is simple, inexpensive and versatile because it is based on simple Michelson interferometer like in traditional Fouriertransform infrared (FTIR) spectroscopy. From the principle of Fourier transform, the resolution in traditional FTIR spectroscopy is limited by the maximum delay range (
Additionally, the high spectral brightness and coherence of OFC led high signaltonoise ratios (SNR) in recording times orders of magnitude shorter than that in conventional FTIR. Furthermore, directcomb spectroscopy can be successfully combined with cavityenhanced techniques. The enhancement cavity increases the interaction length between the intracavity sample and the resonant light, and provides high detection sensitivity. There have been reports of directcomb versions of cavityringdown spectroscopy (CRDS) [16], cavitymode width spectroscopy (CMWS), and cavitymode dispersion spectroscopy (CMDS) [17, 18], however, the most established OFCbased cavity spectroscopy is cavityenhanced absorption spectroscopy (CEAS) [4, 10, 11, 17, 1923]. In CEAS the absorption information is determined directly from attenuation of the transmitted light. In OFCbased CEAS, many comb modes in a wide wavelength range are resonant with the cavity and their intensities are detected simultaneously.
Precise spectroscopic lineshape parameters, such as accurate center frequencies or pressure broadening and shift coefficients, are important for a variety of astrophysical and terrestrial atmosphere observations. They are also crucial for verifying intermolecular interaction potentials by comparing ab intio lineshape parameters with experimental ones. HITRAN and other databases provide spectroscopic data for many molecules, but the accuracy of the data is in many cases insufficient [24]. Atmospheric CO plays an important role in the carbon cycle [25] and can be a useful probe for astronomical observations [26, 27]. Since CO perturbed by Ar is a relatively simple system, precise lineshape measurements of this system are useful for comparison of the experimental and theoretical lineshape profiles [2831]. There have been several reports of collisional lineshape parameters of transitions in the fundamental band and the first overtone band of CO perturbed by Ar, but only a few articles reporting the line broadening parameters of the second overtone (03) band so far [3234]. Our group performed precise lineshape measurements of the 03 band employing a cwCRDS spectrometer referenced to an OFC [33], however, since this measurement involved step scanning the spectrum with a cw laser, parameters of only several lines in the P branch were determined.
We measured P and R branch transitions of the 03 band of CO perturbed by Ar using an OFCbased cavityenhanced FTS. The measurements spanned the wavenumber range from 6270 cm
Our experimental setup is illustrated in FIG. 1(a). A modelocked Erdoped fiber laser (Menlo System FC1500) is used as the OFC. The repetition rate (
FIG. 2(a) displays transmission spectra of highfinesse cavity obtained at COAr gas pressure of 100 Torr. Spectral range of the transmission depends on dispersion of cavity mirrors, cavity finesse and FSR, and comb mode width. The cavity dispersion includes both the molecular and mirror coatings' dispersion, thus depending on total pressure of samples. In contrast to comb mode structure, which has equal mode spacing over the whole emission spectrum, the FSR of a cavity varies with wavelength due to the cavity dispersion [20]. In our setup it limits the transmission range to about 100 cm
Calibration of the frequency axis in OFCbased FTS was performed following the methods introduced in Refs.[9, 35]. To acquire an ILSfree spectrum, the OFC interferogram is resampled at zerocrossings of HeNe laser interferogram, resulting in sample spacing of
In the optical frequency region, this difference is multiplied by comb mode number (
$ \begin{aligned} S_{\mathrm{FTS}}(\nu) &=\\ \mathrm{abs}\{&\left.\mathrm{FFT}\left[P(\Delta) \exp \left(\frac{i 2 \pi\left(f_{0}+f_{\mathrm{shift}}\right) \Delta}{c}\right)\right]\right\} \end{aligned} $  (1) 
In order to obtain an accurate value of
FIG. 4(a) shows a normalized spectrum of the P6 line observed at 10 Torr with point spacing of 50 MHz obtained by interleaving (black). The frequency axis calibration was performed as described above. The lineshape function obtained by leastsquares fitting of the VP is also shown in the same plot (red). We used cavity transmission equation [22] containing dispersion part of the molecular transition to describe the asymmetric line shape. Details of fitting functions are written in the next paragraph. In this pressure region, Doppler broadening is dominant and the line shape is well described by the VP. The full Doppler width was calculated from the room temperature and fixed to 442 MHz; the fitted collisional broadening was less than 10% of the Doppler width. Halfwidth at half maximum (HWHM) of the line is smaller than
Following the report by Foltynowicz et al. [22], the intensity of cavity transmission is written as:
$ \begin{array}{l} \frac{{{I_t}(\nu )}}{{{I_0}(\nu )}} = \\ \;\;\;\frac{{{T^2}{{\rm{e}}^{  2\delta (\nu )L}}}}{{1  {R^2}{{\rm{e}}^{  4\delta (\nu )L}}  2R{{\rm{e}}^{  2\delta (\nu )L}}{\rm{cos}}[2\phi (\nu )L + \varphi (\nu )]}} \end{array} $  (2) 
where,
$ \begin{eqnarray} \delta(\nu)=\frac{Sn_\textrm{A}}{2}{\rm Re}\chi(\nu) \end{eqnarray} $  (3) 
$ \begin{eqnarray} \phi(\nu)=\frac{Sn_\textrm{A}}{2}{\rm Im}\chi(\nu) \end{eqnarray} $  (4) 
Here,
We analyzed the observed spectra by fitting Eq.(2) with an appropriate lineshape profile substituted for
$ \begin{eqnarray} \gamma_L(x) = \gamma_LB_w(x)=\gamma_L[1+a_w(x^23/2)] \end{eqnarray} $  (5) 
where
FIG. 5 shows the experimental data of P4 and P6 lines at each pressure (black dots), fitted line profiles (red), residuals of VP (green), and SDVP fits (blue), and fitted etalon (magenta) for the lines at 450 Torr and 700 Torr. The quality factors (QFs) shown under the residual plots are calculated from the ratio of absorption peak to standard deviation of residuals. The residuals of VP fits show systematic wshaped discrepancies due to the neglected speed dependence of broadening. The SDVP significantly improves residuals and better agreement for both lines at all pressures is obtained. This results show that the OFCbased cavityenhanced Fouriertransform spectrometer allows for accurate line shape measurements exceeding the accuracy of the VP even in the case that line shapes have strong asymmetry. The center frequency at zero pressure (
In the line shapes in FIG. 5, as the FTS axis has been calibrated according to the procedure described above, the influence of ILS has been removed. Nonetheless, the residuals of P4 and P6 lines at 100 Torr show large discrepancies near the line center. FIG. 6 shows the P15 line obtained in the same measurement and with the same calibration. The P15 line has smaller asymmetry because the transition was close to one of the twopoint lock wavelengths, and the SDVP fit residuals show smaller discrepancies and a higher QF value than that for P4 and P6 lines. This leads us to conclude that the larger fitting uncertainties of P4 and P6 lines are most likely caused by fluctuations of the cavitycomb offset during the measurement, as the lines with larger asymmetry have larger discrepancies. Asymmetric line shapes are due to the cosine part, which depends on the cavitycomb offset term as shown in Eq.(2), therefore, the combcavity offset fluctuation at larger absolute values has significant influence on the distortion of measured line shapes. In this case, the combcavity offsets of P4 and P6 were
In conclusion, an OFCbased cavityenhanced Fouriertransform spectrometer was constructed and it was proved that the system is valuable for lineshape studies. We adopted a high finesse cavity for the observation of second overtone band of CO and a highly sensitive measurement was performed with detectable absorption per spectral element of 1.3
With a stepscanned cwlaser CRDS setup, it is in practice difficult to acquire spectral data of a large number of lines, but our system enabled us to acquire 40 lines in P and R branches in a short amount of time and with high sensitivity. Moreover, accurate narrow line shapes that conventional FTIR cannot be measured due to that the ILS was observable with our system. Based on the discussion about uncertainty of obtained line shapes mentioned above, we estimate that the precision of the line shape parameters will be improved by introducing low dispersion mirrors. In the ongoing experiments, we will derive the spectroscopic parameters of a large number of rovibrational lines, and soon they will be available for the application in various fields such as astronomy and atmospheric science.
Ⅴ. ACKNOWLEDGMENTSThis work was supported by National Science Center, Poland Projects No.2016/23/B/ST2/00730, 2016/21/N/ST2/00334. Grzegorz Kowzan was supported by National Science Center, Poland Scholarship No.2017/24/T/ST2/00242.
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