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Abstract
We modified our 910-m long path THz system to increase the signal-to-noise ratio (S/N) with a nanostructure plasmonic THz transmitter (Tx) chip and a seven-mirror array reflector with 1 m diameter. When the THz pulse propagates the 910-m distance in the atmosphere, the S/N is up to 1170:1, which made the THz pulse measurable at a high water vapor density (WVD) of up to 25.2 g/m3. The time shift of the THz pulse according to the WVD measured for each meteorological season was matched well with the theoretical result. Due to the modified long-distance THz system, we were able to measure for the first time the resonances of N2O gas, which is located 455 m away from the Tx and receiver (Rx) chips and contained in a 1.5-m diameter rubber balloon under atmospheric pressure. Seven resonances can be detected except for one overlay of resonant frequency by water vapor.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
When THz electromagnetic waves propagate into the atmosphere, attenuation is caused by the rotational lines of mainly water molecules and the continuum absorption of the atmosphere, which is proportional to the square of the frequency [1–3]. This attenuation increases by accumulating with longer propagation distances and by increasing the water vapor content of the atmosphere. The content of water vapor, expressed as water vapor density (WVD), is determined by temperature and humidity. Recently, THz attenuation and phase delay measurements were performed according to the WVD in the atmosphere and environmental changes such as snow and rain [4,5]. In addition to atmospheric attenuation, another factor reducing THz propagation efficiency is the THz beam size. Because the diameter of the Gaussian THz beam increases with a longer propagation distance, a portion of the THz beam is clipped if any of the mirrors are not large enough. When the THz beam propagates into the atmosphere, the beam diameter is inversely proportional to the frequency [6]. As the frequency decreases, the attenuation by the atmosphere decreases, but the diameter of the THz beam increases. Therefore, mirrors with bigger diameters are needed to cover the large diameter of the Gaussian beam.
Recently, we developed a long distance THz time-domain spectroscopy (THz-TDS) system to propagate 186 and 910 m distances in the atmosphere [4,5]. Due to the continuum absorption of the atmosphere, the frequency bandwidth was only 0.1 to 0.4 THz for the 910 m propagation distance. Moreover, due to a limited THz beam power and small size of the retro-reflector mirror, the S/N was only 160:1, which is not enough to detect a THz pulse at the high WVDs of the summer season in Korea. However, in this study, we were able to improve the THz system and obtain an S/N of up to 1170:1, which is enough to measure the THz pulse even in the high WVDs of the summer season.
Meanwhile, remote gas sensing using THz has been attempted [7–9]. The first remote gas detection system that used pulsed THz-TDS was studied with a chamber corresponding to a 5.4 m round trip filled with CH3CN gas [7]. The total THz round trip path was only 6.7 m, although it had a high S/N and detected strong gas resonances. Remote N2O gas sensing using continuous THz wave was also studied with a chamber corresponding to a 2 m round trip out of a 7.2 m total THz round trip path [8,9]. The remote gas sensing was carried out at a very close distance from the Tx and Rx chips. The distances of CH3CN and N2O gases were only 3.35 and 3.6 m. However, with our modified THz long-distance system, we can detect N2O gas resonances with a 1.5 m diameter gas balloon, which is located 455 m away from Tx and Rx chips, corresponding to a 910 m round trip path.
2. Experimental results
Previous THz long-range propagation experiments used a telescope mirror, which is a 31.7 cm diameter spherical mirror with a 317.5 cm focal length, to collimate the THz beam [4,5,10–12]. We used the same spherical mirror M2 (see Fig. 2) in this setup. If the focal length does not match and the THz beam is not incident to the spherical mirror along its optic axis, the reflected THz beam is not fully collimated. Even if the two conditions are satisfied, when the Gaussian beam is incident to a spherical mirror, the beam waist of the reflected beam still depends on the diameter of incident beam, propagation distance, and wavelength. Therefore, the diameter of the THz beam will continue to grow during the propagation of hundreds of meters. In this THz long-distance systems, the spherical mirror had to be 8.6 degrees tilted to reflect in a different direction from the incident beam [4,5]. Because the incidence angle is very small, any resulting aberrations are also very small. When we measured the THz beam in front of the spherical mirror, the THz beam had a Gaussian distribution as shown in Fig. 1(a). The yellow area indicates that the THz beam is slightly clipped because of the limited spherical mirror radius. The dashed line indicates the 1/e field of the Gaussian beam. Because the spherical mirror radius is bigger than the 1/e radius of the field, most of THz beam is reflected by the spherical mirror. After the spherical mirror, the beam travels ∼90 m to mirror M6 (see Fig. 2). Assuming unclipped Gaussian beam propagation, Fig. 1(b) plots the calculated 1/e waist radius of the field plotted at every location from the Tx to M6. Given the large propagation distance following the spherical mirror, the beam expands significantly. Even at the highest frequencies, the beam becomes about twice the size of M6, whose transverse extent is 35 × 35 cm. This suggests that clipping is significant at M6 and the Gaussian beam approximation no longer holds thereafter. Since the beam becomes so large, it can be loosely regarded as uniform over M6, an approximation that becomes increasingly accurate with lower frequency. In this approximation, the beam size at the position of the original retro-reflector (now the seven-mirror-array) can be calculated with Fraunhofer diffraction theory [13], where a square aperture of the same extent as M6 has been assumed. The beam profile at this position is shown in Fig. 1(c). The waist radiuses are 2.18 and 0.44 m at 0.1 and 0.5 THz because a lower frequency has more diffraction. A retro-reflector mirror composed of two 60 × 40 cm flat mirrors covers only 1.1 and 28.0% of the THz beam at 0.1 and 0.5 THz, respectively [5], which is one of the reasons a small THz signal was originally measured.
Fig. 1. (a) Measured Gaussian THz beam field profile in front of the spherical mirror that is located 3.2 m away from the Tx chip. The amplitude data is the relative magnitude at 0.13 THz, the maximum amplitude of each measured THz pulse. The yellow area and dashed line indicate the clipped THz beam and 1/e field of the Gaussian beam, respectively. (b) Frequency dependent THz beam waist between Tx and M6. The transverse half-width of mirror M6 is indicated by the dashed line. The kink at ∼3 m is due to the collimating effect of the spherical mirror. (c) Normalized Fraunhofer diffraction field patterns at position of seven-mirror-array. The solid black line indicates the 1/e field level.
Fig. 2. Schematic of the 910 m long-path setup with seven-mirror array which is located at the return point (455 m away from Tx and Rx chips) of the long-path. The photograph shows the seven-mirror array on a concrete block.
We tried two things to increase the small THz signal. First, we used a nanostructure plasmonic THz Tx chip, which emitted a strong THz beam although it had low frequency components [14,15]. The nanostructure plasmonic THz Tx chip achieved a THz pulse 77 times larger than the signals generated using the previous photoconductive Tx chip. It also improved the S/N by 2.6 times. A Ti:Sapphire mode-locked laser with a pulse repetition rate of 84.01 MHz was used to excite the THz pulses with an average laser power of 300 mW on a 300 × 300 µm2 nanostructure antenna of the Tx chip. A 32 kHz AC bias of 20 Vpp was applied to the antenna. We also used a 200 µm-long dipole antenna Rx chip on an LT-GaAs substrate to detect the low frequency THz signal with an average laser power of 12 mW on the dipole antenna. Another reason for using these Tx and Rx chips with low frequency characteristics is that when the THz beam propagates through the atmosphere, only low frequencies propagate a long distance because high frequencies have excessive loss. Second, the retro-reflector mirror of previous work [5] was replaced with an array mirror that had seven mirrors totaling a 1 m diameter to increase the reflecting areas as shown in the inset photo of Fig. 2. Instead of horizontally shifting the THz beam by the retro-reflector mirror about 44.8 cm, the seven-mirror array reflected the THz beam without shifting, which increased the reflective area. The reflective area for the seven-mirror array was increased 460% over that of the retro-reflector mirror. Each of the seven mirrors is precisely adjustable such that the array behaves as a single, focusing optic for the reflected THz beam. The seven-mirror array works as a 1 m diameter spherical mirror with a focal length of ∼452 m. The THz beams reflected by the seven-mirror array are reflected by M7 (60 × 40 cm), M8 (35 × 35 cm, which is the same dimension as M5), and M4 (55 × 41 cm), again focused on the spherical mirror (M3) as shown in Fig. 2. Both, the in-coming and out-going THz beams to the seven-mirror array minimize the clipping and reduce diffraction losses.
Figure 3 shows the effect of the seven-mirror array, which consists of a central mirror with an area of 962 cm2 and six external mirrors with a combined area of 6 × 1149 cm2. After we measured the THz pulse reflected by only the central mirror as shown in the lowest THz pulse of Fig. 3(a), we added the external mirrors one by one until we included all seven mirrors. The topmost THz pulse shows the THz pulse reflected by the entire array. The peak-to-peak amplitudes of the reflected THz pulses by the central mirror and the entire array are 7.6 and 43.3 nA, respectively. Therefore, the average signal increase by each of the six mirrors is about 6.0 nA. Although the area of the central mirror is 0.84 times that of an external mirror, the peak-to-peak amplitude of the THz pulse is 1.3 times bigger. As mentioned, the THz beam 451.8 m away from the spherical mirror is clipped by M6. Therefore, the 1 m diameter of the seven-mirror array is still not enough to cover the entire THz beam, except perhaps at higher frequencies (>0.5 THz), as shown in Fig. 1(c). However, we can increase the reflected THz pulse 5.7 times using the entire seven-mirror array rather than using only the central mirror.
Fig. 3. (a) Measured THz pulses reflected in each mirror combination of the seven-mirror array. The lowest THz pulse indicates the reflected THz pulse by only the central mirror (A0). The upper pulses are measured with the addition of external mirrors one by one (from A1 to A6). The topmost THz pulse shows the reflected THz pulse by the entire mirror. The average relative humidity and temperature in the THz beam path were 19.7% and 8.7° (water vapor density 1.7 g/m3), respectively. (b) Corresponding amplitude of spectra for the pulses. The inset figure shows the peak-to-peak amplitude of THz pulses according to number of mirrors. The dots and solid line indicate the measured data and fitted line, respectively.
The S/N of the reflected THz pulse by the seven-mirror array and the plasmonic Tx chip was 1170:1, which is 7.3 times larger than that of the retro-reflector mirror and GaAs Tx chip with two parallel transmission lines used in previous work. The inset of Fig. 3(b) shows the peak-to-peak amplitude of the THz pulses according to number of mirrors. As the reflective area increases, the THz signal linearly increases, suggesting a symmetric illumination of the array. Figure 3(b) shows the corresponding amplitude spectra of the pulses. As shown in the THz pulses, the amplitude spectra increase with an increasing reflected area of the seven-mirror array. The handbook water line at 0.183 THz clearly appears but the water line does not have clean line shapes, especially in the small amplitude spectrum. The water line frequency shifts slightly due to consequent pulse jitter caused by unstable relative humidity and temperature [4,5]. The spectra have narrow, low-frequency bandwidths from 0.05 to 0.4 THz because of the high frequency attenuation loss for the long path. Two additional water lines at 0.325 and 0.380 THz are weakly evident in the spectrum.
The measured output THz pulses in this measurement for the lowest (2.1 g/m3) and the highest (25.2 g/m3) WVDs are shown in Fig. 4(a). The time delay (shift) between the two THz pulses is 231.4 ps, which is determined by comparison for the first maximum of the THz pulses. Comparing the amplitude of the measured THz pulses with a WVD of 2.1 g/m3, the maximum to minimum amplitude of 20.9 nA is 2.2 times bigger than the pulse with a WVD of 25.2 g/m3, corresponding to 9.5 nA. The amplitudes of THz pulses in Fig. 3(a) are larger than those of Fig. 4(a) because the seven mirrors were modified with screws that could adjust the angle very precisely and widely before the measurement in Fig. 3(a). Therefore, we can increase the THz pulse by very accurately adjusting the positions of the seven mirrors. However, the amplitude of THz pulses does not affect the time shift measurement because the time shift is related only to the phase of the THz pulses. It is very difficult to precisely determine the time shift between two THz pulses with different WVDs in the time-domain, due to dispersion and oscillation of the pulses. Therefore, we measured the time shift by the relative phase shift at 0.25 THz, which was the frequency used in Ref. [5]. The phase (ΦWVD) in radians of the spectral components of the measured pulses with different WVDs are shown in Fig. 4(b). The phase linearly increases because the refractive index of air is mostly constant within this frequency range. The time shift (Δttot Meas) is measured from the relative phase delay (ΔΦ=ΦWVD-Φref) as Δt=ΔΦ/(2πf) where f is the frequency and Φref is the reference phase at the lowest WVD (2.1 g/m3). The measured time shift derived by the phase difference for the lowest WVD (reference) and the highest WVDs at 0.25 THz was 242.9 ps which was very close to the time shift measured by the time-domain THz pulses.
Fig. 4. (a) Measured time-delay between the THz pulses with the lowest and highest WVD. (b) Phase shifts of the measured THz pulses using the seven-mirror array with different WVDs at 0.25 THz (vertical dashed line). (c) Comparison time shift caused by water vapor in the outdoor atmosphere: theoretical calculation (Δtwater; blue color) and experimental measurement (Δtwater Meas; red color). The black color indicates the measured time shift (Δttot Meas) caused by water vapor and dry air in the outdoor atmosphere. The circles and dots indicate the previous measured data [5] and new measured data from this research, respectively. The horizontal arrows indicate the meteorological seasons in Korea during the measurements. The solid lines indicate the fitted lines.
Figure 4(c) shows the measured total time shift (Δttot Meas) that was caused by the outdoor water vapor and dry air as a function of WVD. Because the time shift linearly increases with increasing the WVDs, the measured time shift slope should be started (linear shifted) from zero WVD [11]. The new measured time shift data between 2.1 g/m3 and higher WVD are added to the previous measured data. The black circles and dots indicate the previous measured data [5] and new measured data by the modified THz long-distance system, respectively. The yellow area of the figure indicates a correction time shift after removing the time shift caused by dry air. The corrected time shift should be added to the total time shift so that there is only the time shift (ΔtWater Meas) caused by water vapor in the outdoor air, as shown in the red circles and dots. Meanwhile, the theoretical total time shift can be calculated from the refractivity of the outdoor water vapor and dry air as shown in the simple formula based on the following Essen and Froome equation [16]:
The theoretical time shift (Δtwater) caused by outdoor water vapor can be calculated by subtracting the theoretical time shift by dry air from the theoretical total time shift. The theoretical calculation (Δtwater) and experimental measurement (Δtwater Meas) of the time shift caused by water vapor agreed very well for all the WVDs. Due to the additional data from this measurement, the line fitted to the Δtwater Meas is very close to the theoretical calculation. The fitted line slopes for the theoretical calculation and experimental measurement are 16.5 and 16.1 ps/(g/m3), respectively. The standard deviation of the measured time shift to the fitted line is 12.3 ps, which indicates the system is very stable, although we measured the time shift according to the season. One of the reasons for the time shift variation is the WVD changes during measurement [4]. The atmosphere during wet season (summer in Korea) has a higher water vapor and less dry air than the dry season (winter in Korea). Thanks to the modified THz long distance system, we can measure the time shift not only in the dry season but also in the wet season as shown by the “summer (red dots)” in the figure.
Thanks to the increased S/N, we were able to measure the resonance of N2O gas, which is located 455 m from the Tx and Rx chips. Instead of a gas container, we used a rubber balloon with a diameter of 1.5 m by injecting it with air or gas. The balloon was placed in front of the seven-mirror array as shown in the insert of Fig. 5(a). The black lines in Fig. 5(a) show the THz pulse through an air-filled balloon for measuring the reference (input) and red lines show the THz pulse through a balloon filled with N2O gas for measuring the output. The WVD in this measurement is 2.1 g/m3. The reshaped and attenuated excitation pulse is followed by a series of coherent transients, which rapidly decay because of the collisional broadening [19]. The relative amplitude of the first transient (echo pulse) is 1/8.7 compared to that of the excitation pulse, and a well-defined picosecond coherent transient appears at 40 ps from the main THz pulse as shown by the first arrow. The second transient weakly appears at 40 ps from the first transient THz pulse as shown by the second arrow. The temporal spacing between the coherent transients corresponds to the inverse frequency spacing (approximately 25 GHz) of the rotational absorption resonances of N2O.
Fig. 5. Measurement of N2O gas located 455 m away from the Tx and Rx chips. (a) Measured THz pulses with air (black line) and N2O gas (red line) in a gas balloon. The black arrows indicate picosecond coherent transient THz pulses. The inset figure shows a schematic of the gas balloon in front of seven-mirror array. (b) The corresponding amplitude of the spectra for the pulses. The red arrows indicate detected N2O gas resonance. (c) Absorbance of N2O gas. The green curve indicates the calculated absorption coefficient of N2O gas.
The corresponding amplitude of spectra for the reference and output pulses are shown in Fig. 5(b) as black and red lines, respectively. The amplitude of the output spectrum is smaller than that of the reference spectrum due to absorption by the N2O gas. Due to the transient of the time-domain THz pulse, rotational absorption resonances indicated by arrows are also seen in the output spectrum. The first resonance is at 0.151 THz. Although the first resonance frequency is at the maximum amplitude of the spectrum bandwidth, the resonance depth is very weak because of the small N2O gas resonance at that frequency. Figure 5(c) shows absorbance of the N2O. Theoretically calculated N2O gas resonances are shown by the green line in the figure [20]. The grey regions indicate no-signal areas, caused by the strong water vapor absorption line (0.182 THz) and very small amplitude of the spectrum. The resonance amplitudes in the low frequency region are very weak compared to the higher frequency range for the measured spectrum bandwidth. Therefore, we can detect a very small resonance depth at 0.151 THz. The second resonance is not clearly shown at 0.176 THz because the resonance frequency is very close to a strong water line, which is at 0.182 THz. However, the 3rd to 8th resonances are clearly shown in the spectrum. Although the 8th resonance frequency overlaps with the water line, the resonance depth is stronger than the water line in the reference spectrum because the resonance of N2O gas at that frequency is relatively strong compared to the resonances in the low frequency range as shown in the theoretically calculated green line.
3. Summary and conclusion
We modified our 910-m long path THz system to increase the S/N with a nanostructure plasmonic THz Tx chip and a seven-mirror array reflector 455 m away from the Tx and Rx chips. When the THz pulse propagates 910-m distance in the atmosphere, the S/N obtained by the improved system is 7.3 times better than the S/N obtained from the previous system. In particular, the THz pulse reflected by all seven mirrors with an area of 7,853 cm2 is 5.7 times larger than that for a central mirror with an area of 962 cm2. Due to the increased S/N, we can measure THz pulses that have propagated 910 m in the atmosphere even in the summer season when there is high WVD, which could not be measured by the previous system. The time shift of the THz pulse according to the WVD measured for each season matched the theoretical result well. We also measured the resonances of N2O gas located 455 m away from the Tx and Rx chips. Seven N2O resonances were detected in the measured bandwidth, while one expected resonance was not, due to coincidence with a stronger water vapor resonance. This measurement was performed on a low WVD. More gas and higher S/N are required for gas sensing in high WVD. These studies show that the THz long distance system can detect dangerous gas and monitor pollutants in the atmosphere.
Funding
National Research Foundation of Korea (2016R1A2B4012523, 2019R1A2B5B01070261).
References
1. Y. Yang, M. Mandehgar, and D. Grischkowsky, “Broad-band THz pulse transmission through the atmosphere,” IEEE Trans. Terahertz Sci. Technol. 1(1), 264–273 (2011). [CrossRef]
2. V. B. Podobedov, D. F. Plusquellic, K. E. Siegrist, G. T. Fraser, Q. Ma, and R. H. Tipping, “New measurements of the water vapor continuum in the region from 0.3 to 2.7 THz,” J. Quant. Spectrosc. Radiat. Transfer 109(3), 458–467 (2008). [CrossRef]
3. D. M. Slocum, E. J. Slingerland, R. H. Giles, and T. M. Goyette, “Atmospheric absorption of terahertz radiation and water vapor continuum effects,” J. Quant. Spectrosc. Radiat. Transfer 127, 49–63 (2013). [CrossRef]
4. E.-B. Moon, T.-I. Jeon, and D. Grischkowsky, “Long-path THz-TDS atmospheric measurements between buildings,” IEEE Trans. Terahertz Sci. Technol. 5(5), 742–750 (2015). [CrossRef]
5. G.-R. Kim, T.-I. Jeon, and D. Grischkowsky, “910-m propagation of THz ps pulses through the atmosphere,” Opt. Express 25(21), 25422–25434 (2017). [CrossRef]
6. O. Svelto, Principles of Lasers, 5th ed. (Springer, 2010).
7. J. S. Melinger, Y. Yang, M. Mandehgar, and D. Grischkowsky, “THz detection of small molecule vapors in the atmospheric transmission windows,” Opt. Express 20(6), 6788–6807 (2012). [CrossRef]
8. N. Shimizu, H.-J. Song, Y. Kado, T. Furuta, A. Wakatsuki, and Y. Muramoto, “Gas detection using terahertz waves,” NTT Technical Review 7(3), 1 (2009).
9. N. Shimizu, N. Kukutsu, A. Wakatsuki, and Y. Muramoto, “Remote detection of hazardous gases in full-scale simulated fire by using terahertz electromagnetic waves,” NTT Technical Review 10(2), 1 (2012).
10. Y. Yang, A. Shutler, and D. Grischkowsky, “Measurement of the transmission of the atmosphere from 0.2 to 2 THz,” Opt. Express 19(9), 8830–8838 (2011). [CrossRef]
11. Y. Yang, M. Mandehgar, and D. Grischkowsky, “Time domain measurement of the THz refractivity of water vapor,” Opt. Express 20(24), 26208–26218 (2012). [CrossRef]
12. Y. Yang, M. Mandehgar, and D. Grischkowsky, “Determination of the water vapor continuum absorption by THz-TDS and molecular response theory,” Opt. Express 22(4), 4388–4403 (2014). [CrossRef]
13. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Co. Publishers, 2005).
14. K. Moon, I.-M. Lee, N. Kim, H. Ko, S.-P. Han, and K. H. Park, “Nano-gap electrode large area THz emitter for the enhanced emission efficiency and heat dissipation,” in Proceedings of 39th International Conference on Infrared, Millimeter, and Terahertz waves (IRMMW-THz, 2014), pp. R3/B-31.5.
15. K. Moon, I.-M. Lee, J.-H. Shin, E. S. Lee, N. Kim, W.-H. Lee, H. Ko, S.-P. Han, and K. H. Park, “Bias field tailored plasmonic nanoelectrode for high-power terahertz photonic devices,” Sci. Rep. 5(1), 13817 (2015). [CrossRef]
16. L. Essen and K. D. Froome, “The refractive indices and dielectric constants of air and its principle constituents at 24,000 Mc/s,” Proc. Phys. Soc., London, Sect. B 64(10), 862–875 (1951). [CrossRef]
17. B. H. Sang and T.-I. Jeon, “Pressure-dependent refractive indices of gases by THz time-domain spectroscopy,” Opt. Express 24(25), 29040–29047 (2016). [CrossRef]
18. Union International Telecommunication, “The radio refractive index: its formula and refractivity data,” Recommendation ITU-R P.453–12, (2016).
19. H. Harde, R. A. Cheville, and D. Grischkowsky, “Terahertz studies of collision-broadened rotational lines,” J. Phys. Chem. A 101(20), 3646–3660 (1997). [CrossRef]
20. I. E. Gordon, L. S. Rothman, C. Hill, R. V. Kochanov, Y. Tan, P. F. Bernath, M. Birk, V. Boudon, A. Campargue, K. V. Chance, B. J. Drouin, J.-M. Flaud, R. R. Gamache, J. T. Hodges, D. Jacquemart, V. I. Perevalov, A. Perrin, K. P. Shine, M.-A. H. Smith, J. Tennyson, G. C. Toon, H. Tran, V. G. Tyuterev, A. Barbe, A. G. Császár, V. M. Devi, T. Furtenbacher, J. J. Harrison, J.-M. Hartmann, A. Jolly, T. J. Johnson, T. Karman, I. Kleiner, A. A. Kyuberis, J. Loos, O. M. Lyulin, S. T. Massie, S. N. Mikhailenko, N. Moazzen-Ahmadi, H. S. P. Müller, O. V. Naumenko, A. V. Nikitin, O. L. Polyansky, M. Rey, M. Rotger, S. W. Sharpe, K. Sung, E. Starikova, S. A. Tashkun, J. V. Auwera, G. Wagner, J. Wilzewski, P. Wcisło, S. Yu, and E. J. Zak, “The HITRAN2016 molecular spectroscopic database,” J. Quant. Spectrosc. Radiat. Transfer 203, 3–69 (2017). [CrossRef]
