# Terahertz Rotational Spectroscopy of Greenhouse Gases Using Long Interaction Path-Lengths
## 3 Results and Discussion
### Intra-Cavity THz Measurements of CF\({}_{4}\)  
In the previous sections, we showed that multi-pass cells provide higher sensitivity for the measurements of weak rotational resonances or small number of absorbing molecules leading to THz line with low intensities. However, these cells are limited by a significant attenuation of the input THz power and generally require large volumes to reach distances exceeding 100 m. An alternative approach is to adapt the intra-cavity techniques developed in the IR domain to the longer wavelengths of the THz/submm-wave spectral domains. In 2019, our group challenges this feat by developing a THz resonator based on a low-loss oversized corrugated waveguide closed with highly reflective photonic mirrors made from silicon discs [17]. The length of the cavity is finely adjusted using piezo-electric actuators to move the mirrors by up to 250 \(\upmu\)m, a control loop locks the cavity length to the THz frequency. With Fabry-Perot THz absorption spectroscopy (FP-TAS), we were able to perform gas phase measurements with a finesse better than 3000 in the 620 GHz frequency range. With such high-finesse, an equivalent interaction length of 1 km is estimated with a cavity of 48 cm long. It was demonstrated by measurements on a low abundant OCS isotopologue that FP-TAS is clearly able to measure transitions with intensities of about \(10^{-27}\) cm\({}^{-1}/(\text{molec cm}^{-2})\). A scheme and a picture of the THz FP cavity is given in Figure 5. We can notice that the quality of the cavity should be optimised and must remain stable to perform quantification. The measured signal is not directly the molecular absorption it is the second harmonic of a frequency modulated THz. It indicates the strength and width of the cavity mode as it scans across the molecular line. The absorption by the molecule causes a reduction in the signal allowing the line centre to be reliably determined and quantification undertaken for a given cavity configuration. For all these reasons, a step of calibration is still required. Figure 4: Left: Simulation of the rotational absorption in the 575–625 frequency region of N\({}_{2}\)O and O\({}_{3}\) at tropospheric (330 ppb) and stratospheric (7.5 ppm) concentrations, respectively, for a THz pathlength of 200 m. Right: 400 ppm of N\({}_{2}\)O at \(P=0.7\) mbar and 200 ppm of O\({}_{3}\) at \(P=1.0\) mbar measured in CHARME with the MultiCHARME setup in a 4 \(\times\) 5 Chernin configuration providing a THz pathlength of 200 m (black open circles). Both lines have been measured with an amplitude modulated at 4.5 kHz. An additional frequency modulation at 50 kHz with a 1.1 MHz depth was added to limit the baseline oscillations. The red solid lines correspond to Voigt profiles simulated with HITRAN2016 tabulated frequencies, linewidths and intensities. In the present article, we present new measurements performed with this cavity on CF4 a very stable GHG, with a high greenhouse warming potential (>6500) [2]. As for CH4, CF4 is not polar and only rotational transitions induced by centrifugal distortion or vibrational anharmonicity may be observed. Compared to CH4, the heavier CF4 molecule exhibits ground state pure rotational transitions at lower frequencies with a maximum intensity around 650 GHz. According to ab initio parameters [35], the distortion-induced dipole is estimated to only 0.324 \(\upmu\)D. Therefore, all the THz lines are very weak with intensities never exceeding \(10^{-27}\) cm\({}^{-1}/(\text{m{olec}}\) cm\({}^{-2})\). At room temperature, rotational transitions belonging to the hot band \(v_{3}=1\) are slightly more intense compared to the ground state transitions. Rotational clusters in the \(R\) branch of this band were measured by FT-THz spectroscopy based on synchrotron source with a path-length of 150 m in the White-type cell shown in Figure 1 (right part) [36].