## 3 Results and Discussion
### Fabrication and Sensing Experiment of Uniformly Etched TMFBG
#### 3.3.2 Refractive Index-Sensing Characteristics  
NaCl solutions with different concentrations (5%, 10%, 15%, 20%, 25%) were prepared by dissolving solid NaCl into distilled water. The corresponding refractive indices were determined (to be 1.332, 1.346, 1.353, 1.361, and 1.371, respectively) with an Abbe refractometer. The different concentrations of NaCl solutions were kept at room temperature for two hours to avoid the influence of temperature changes on the experiment. The refractive index measurement system is composed of an amplified spontaneous emission (ASE, working wavelength: 1525-1610 nm) and an optical spectrum analyzer (OSA). Three sizes of TMFBG structures, obtained after uniform etching, are studied at room temperature. After each measurement, the TMFBG structure is repeatedly cleaned with alcohol and dried to prevent the interference of the residual solution on the grating surface. The transmission spectra of the TMFBGs with different diameters in solutions with different refractive indices are recorded and compared in Figure 7.  
As shown in Figure 8a, as the refractive index increases from 1.332 to 1.371, the resonance dip wavelength of the cladding mode increases. The wavelength shift of the TMFBG with a diameter of 30 \(\upmu\)m is more obvious than that of the 70 \(\upmu\)m and 125 \(\upmu\)m TMFBGs. In addition to the wavelength shift, the resonant depth of the cladding modes also changes with the refractive index. When the refractive index continues to increase, the smaller-diameter etched TMFBG exhibits a greater wavelength shift and a smaller transmission depth for the cladding mode. As shown in Figure 8b, there are three core modes whose wavelength does not drift with the change in the refractive index. The transmission intensity of the core mode also does not change. The experimental results reveal that the core mode is insensitive to changes in the external refractive index, while the cladding mode shows the opposite effect. The refractive index-sensing characteristic curves of the uniformly etched TMFBGs with the diameters of 125 \(\upmu\)m (unetched), 70 \(\upmu\)m, and 30 \(\upmu\)m are shown in Figure 8. For the higher-order cladding mode at 1538 nm, when the diameter increases from 125 to 30 \(\upmu\)m, the sensitivity is improved from 0.964 nm/RIU to 6.368 nm/RIU, as shown in Figure 9a. A smaller diameter corresponds to higher sensitivity. Compared with the raw TFBG, the refractive index sensitivity is increased more than six times. As shown in Figure 9b, the sensitivity of the low-order cladding mode at 1546 nm is low, and the sensitivity of the untreated TFBG is only 0.294 nm/RIU. When the cladding diameter is reduced to 30 \(\upmu\)m, this sensitivity is increased to 2.353 nm/RIU, being approximately eight  
Figure 8: Transmission spectra of uniformly etched TMFBGs with different sizes, including their (**a**) local cladding mode and (**b**) core mode. times higher. For the low-order cladding mode, the reduction in the cladding diameter has a more obvious effect in terms of improving the sensitivity. The binding ability of the optical fiber to the high-order cladding mode is weaker than that of the core mode, so the sensitivity of the low-order cladding mode is far lower than that of the high-order cladding mode. However, for both the low-order and high-order cladding modes, the decrease in the cladding diameter will improve their sensitivity to the refractive index change. High-sensitivity refractive index sensing can be achieved by measuring the wavelength shift of the higher-order cladding mode in the cladding mode. In order to promote the proposed TMFBG sensor for monitoring building structural health and biological objects, the TMFBG can be encapsulated in flexible polymer materials with a large elasto-optic coefficient. The structural stress will directly affect the polymer encapsulation layer, leading to a change in its refractive index.