## 1 Introduction  
A hollow-core photonic crystal fiber (HC-PCF) has periodical microstructures of air holes surrounding a hollow core where light is confined [1]. Because the light is trapped in HC-PCF by a photonic bandgap in the cladding that is made of spaced air holes instead of internal reflection, it is possible to guide light in a gas-filled core [2]. In addition, its long interaction length can realize resonance and near-resonance light-light and light-matter interactions [3]. Due to its excellent characteristics in gas sensing, it has been extensively studied for gas detection. To realize an all-fiber gas sensor, single-mode fiber (SMF) and HC-PCF are usually utilized for coupling, which has the advantages of a compact structure, easy miniaturization, light weight, anti-interference, and long working range [4; 5; 6]. However, the assembly of SMF and HC-PCF has a low coupling efficiency, which will reduce the output light intensity and thus reduce the sensitivity of the detection system according to Lambert-Beer law [7].  
Many efforts have been made to improve the coupling efficiency. In one proposed method, the structure or fiber mode of HC-PCF [8; 9] is specifically selected, or the micropore collapse effect [10] is reduced, but with limited improvement of the coupling efficiency. In another proposal, the SMF is wedged into HC-PCF by special cutting, to ensure an ultra-high coupling efficiency [11]. However, the structure is too compact and prevents the gas from entering the HC-PCF, resulting in a poor response time of the sensor. In view of this, the coupling efficiency can only be improved by shortening the distance between HC-PCF and SMF. In order to obtain a higher coupling efficiency, HC-PCF should be as close as possible to SMF in consideration of the rapid divergence of SMF-emitted beams. By controlling the distance between SMF and HC-PCF, it is shown that the coupling efficiency is highest when the coupling length is 7.618 \(\upmu\)m [12]. However, due to this short distance, the gas diffuses into the HC-PCF very slowly [13], thereby reducing the response time of the sensor. Additionally, the coupling gap is difficult to control for such a short distance.  
In view of this, a coupling method that can achieve a high coupling efficiency at a long coupling distance is proposed. By adding a GRIN fiber probe to the SMF, the coupling efficiency can be substantially improved over the desired coupling distance. Compared to the all-fiber structure for gas detection using a GRIN lens with a large volume [14], a GRIN fiber probe is an all-fiber optical lens composed of a single-mode fiber, no-core fiber (NCF), and GRIN fiber. It has an ultra-small structure size and good focusing performance [15]. It has been widely used in the field of optical coherent tomography (OCT) [16; 17; 18] and interference sensing measurement [19; 20]. The light emitted from the GRIN fiber probe has the characteristics of focusing first and then diverging, which can obtain a smaller beam waist spot at a longer distance, thus overcoming the shortcoming of the short working distance of SMF. This excellent characteristic can be used in the study of HC-PCF gas sensors: a smaller beam waist size helps to improve the coupling efficiency of the probe and HC-PCF, while a longer working distance can maintain a long gap between the two, which is conducive to the entry of gas into HC-PCF, improving the response time of the sensor.