## 4 Conclusions  
In this work, an FP cavity-assisted RWG on the tip of a single-mode fiber was studied theoretically for refractive index sensing. In contrast to a uniform RWG directly on the fiber facet, the total grating length can be restricted to a small area around the fiber core while the resonant reflection peak intensity was enhanced by approximately three times, reaching more than 70%. This improved peak intensity is crucial for practical sensing applications as it increases signal-to-noise ratio, thus allowing for a more accurate read-out of peak information. The average sensitivity of the designed fiber-tip RWG sensor is 158 nm/RIU for the refractive index range from 1.33 to 1.43. The improved FOM promises significant application potential in multi-channel biochemical sensing and for real-time medical diagnostics. Such multi-channel sensing can be realized using multi-core fibers, where the compact size of our resonant RWG sensor allows for, e.g., measurements of blood composition changes. In the case of a multiplexed sensor with many RWG sensing elements, the restriction of leaky mode propagation within limited regions around separate cores is important to eliminate cross response between different channels, which is crucial for both spatial and wavelength multiplexing. Furthermore, the new design strategy is preferable for the development of high-performance RWG wavelength filters on a single-mode fiber tip, which may find applications in fiber lasers. Figure 6: (**a**) Mode reflectance (blue), total reflectance (magenta) for a 3D fiber RWG, mode reflectance for a 2D model (green) and mode reflectance of uniform grating (red); (**b**) Spectral response for different ambient refractive indices. **Author Contributions: Y.Y. : Conceptualization, Methodology, Writing--Original Draft; Y.X. : Software, Data Curation; N.-K.C. : Supervision; I.P. : Software, Formal analysis; S.S.: Formal analysis, Writing--Review and Editing; D.K. : Supervision, Writing--Review and Editing; Y.R. : Writing--Review and Editing. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported in part by the National Natural Science Foundation of China under Grants 61875247 and 11874243, by Natural Science Foundation of Shandong Province under Grants ZR2020 QF086 and ZR2020 QA068, by Liaocheng University under Grants 318051411, 319190301 and 31805180101, and by Deutsche Forschungsgemeinschaft (DFG Ki482/19-1). **Acknowledgments: [PERSON] acknowledges the support of Introduction and Cultivation Plan of Youth Innovation Talents for Universities of Shandong Province. Conflicts of Interest: The authors declare no conflict of interest. References References
* [PERSON] and [PERSON] (2016) [PERSON]; [PERSON] Fiber-optic chemical sensors and biosensors (2013-2015). Anal. Chem. **2016**, _88_, 203-227. [CrossRef]
* [PERSON] et al. (2019) [PERSON]; [PERSON]; [PERSON]; [PERSON] Tapered optical fibre sensors: Current trends and future perspectives. Sensors**2019**, _19_, 2294. [CrossRef] [PubMed]
* [PERSON] and [PERSON] (2014) [PERSON]; [PERSON] [PERSON] High resolution, all-fiber, micro-machined sensor for simultaneous measurement of refractive index and temperature. Opt. Express**2014**, _22_, 16241-16253. [CrossRef]
* [PERSON] et al. (2017) [PERSON]; [PERSON]; [PERSON]; [PERSON] Fiber-integrated refractive index sensor based on a diced Fabry-Perot micro-resonator. _Appl. Opt._**2017**, _56_, 9139-9143. [CrossRef] [PubMed]
* [PERSON] et al. (2021) [PERSON]; [PERSON]; [PERSON] Fiber-optic sensor measuring spatial distributions of refractive index and temperature. _Appl. Opt._**2021**, _60_, 1428. [CrossRef]
* [PERSON] (1941) [PERSON] The theory of anomalous diffraction gratings and of quasi-stationary waves on metallic surfaces (Sommerfeld's waves). _J. Opt. Soc. Am._**1941**, _31_, 213-222. [CrossRef]
* [PERSON] (1965) [PERSON]; [PERSON] A new theory of Wood's anomalies on optical gratings. _Appl. Opt._**1965**, \(4\), 1275-1297. [CrossRef]
* [PERSON] et al.