## 1 Introduction  
Natural gas hydrates (NGHs) are formed on the seabed under low-temperature and high-pressure conditions [1]. Compared to traditional energy, such as coal and petroleum, NGHs as an alternative energy source have the characteristics of clean, high-efficiency, and abundant reserves. To accelerate the utilization rate of NGHs, many efforts were made in the exploration of such energy sources, and the most important thing is to accurately identify the distribution area. Stable isotope compositions of volatiles bound in the formation of NGHs are due to physical processes and chemical reactions [2, 3]. Therefore, the isotope compositions can be used to identify and even quantitatively analyze the source or settlement position of NGHs. At present, a very effective method for detecting deep-sea natural gas hydrate is measuring the gas dissolved in the seawater. The type of gas measured mainly includes carbon dioxide (CO\({}_{2}\)) and its carbon isotope ratio. So far, high-precision chemical element measured methods mainly include mass spectrometry [4], chromatography [5], flame ionization [6], etc. However, these detection methods are complex in structure and poor in long-term measurement stability, which are not suitable for detection in a complex seabed environment. Recently, the tunable diode laser absorption spectroscopy (TDLAS) [7; 8; 9; 10; 11] technique was applied in many non-contact gas detection applications, such as environmental, industrial, biology, and safety applications, as a consequence of its high sensitivity and high resolution. In 2006, [PERSON] et al. measured the CO\({}_{2}\) isotopic ratio under the conditions of 45 Torr and a light path length of 100.9 m using a distributed feedback laser in the absorption spectrum of 1.6 \(\upmu\)m, achieving the precision of \(\pm\)1.0% at 3000 ppm [12]. In 2008, AERODYNE RESEARCH, Inc. proposed a CO\({}_{2}\) isotope monitor using a mid-infrared absorption spectroscope with optical path lengths up to 76 m to achieve 0.10% precision for \(\delta^{13}\)C at 1 s [13]. In the same year, [PERSON] described in situ, continuous, and high-precision isotope ratio measurements of atmospheric CO\({}_{2}\) using a quantum cascade laser-based absorption spectrometer, and achieved isotope ratios of ambient CO\({}_{2}\) with precision of 0.03 at 100 s of integration time [14]. In 2012, [PERSON] illustrated a laser spectrometer based on a continuous-wave thermoelectrically cooled distributed feedback quantum cascade laser at 2308 cm\({}^{-1}\) for the measurement of \({}^{13}\)CO\({}_{2}\)/\({}^{12}\)CO\({}_{2}\) isotopic ratio changes in exhaled breath samples. Typical short-term \(\delta^{13}\)C precisions of 1.1% (1 s integration time) and 0.5% (8 to 12 s integration time) were estimated from the Allan variance plots of recorded data [15]. In 2018, a vertical cavity surface emitting laser was utilized by [PERSON] et al. in the detection of CO\({}_{2}\) isotopic ratio collected from exhaled small samples of CO\({}_{2}\) (0.1 L) with a resolution of about 0.2% [16]. Although these instruments achieved good carbon isotope detection performance, they cannot meet the requirement of deep-sea natural gas hydrate exploration (\(\delta^{13}\)C of \(\sim\)0.01%). Moreover, these sensing systems are bulky, which makes them unsuitable for CO\({}_{2}\) gas detection on the seabed with compact requirements.