## 3 Sensing Performance Tests and Discussions
### Temperature Dependence of Refractive Index of Water  
It is well known that the RI of transparent liquids and solids are functions of temperature. Taking a direct determination of the temperature dependence of water's RI as an example, the ability of simultaneous measurement of the RI and temperature may be verified by using the hybrid grating in an RDF. Based on the water-bath method, the hybrid grating was immersed in the distilled and deionized water, and the temperature was controlled with a heater and monitored with a thermometer. When the water was heated, there were two effects occurring, including the thermo-optic and thermal expansion effects of the hybrid grating itself, and the RI change of the water. Figure 5a shows the experiment results. The Bragg resonance had the same temperature response coefficient as that of air because it was not affected by the surrounding RI change. However, it is worth noting that the resonant wavelength of the cladding mode did not monotonically shift with the increase in temperature. We can employ the temperature calibration relationship of Bragg and cladding mode resonances to eliminate the inherent thermo-optic and thermal expansion effects of the grating induced by the temperature change. The result is shown in Figure 5b. It can be seen that the wavelength shift of the cladding mode after calibration was much larger than that before calibration. So, with the temperature rising from 25-80 \({}^{\circ}\)C, the wavelength shift above 2.5 nm was caused by the dominated negative d\(n\)/d\(T\) of water, showing a monotonic change. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sensing Structure** & **Sensitivity** & **RI Region** \\ \hline LPG with a small period [8] & 312.5 nm/RIU & 1.315–1.395 \\ LPG in hollow eccentric fiber [9] & 1005 nm/RIU & 1.422–1.441 \\
10\({}^{\circ}\) TFBG [13] & \(\sim\)556 nm/RIU & 1.315–1.360 \\ Tilted moiré FBG [14] & -574.2 nm/RIU & 1.390–1.445 \\ Multi-angle TFBG [16] & 500 nm/RIU & 1.15–1.45 \\ Multi-mode TFBG [39] & \(\sim\)570 nm/RIU & 1.41–1.44 \\ Gold-coated TFBG [22] & 510.5 nm/RIU & 1.335–1.432 \\ Gold-coated TFBG in polymer fiber [23] & \(\sim\)550 nm/RIU & 1.408–1.428 \\ Silver nanowires-coated TFBG [24] & \(\sim\)651 nm/RIU & 1.330–1.347 \\ ZnO-coated TFBG [26] & 210 nm/RIU & \(\sim\)1.39 \\ \(>\)80\({}^{\circ}\) Ex-TFG [29, 33] & 340 nm/RIU & \(\sim\)1.33 \\ Hybrid grating in RDF (This work) & \(\sim\)1224 nm/RIU & \(\sim\)1.38 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of sensitivity between fiber grating-based RI sensors. As mentioned before, each wavelength of the cladding mode corresponds to a specific RI value of surrounding medium after the removal of inherent thermal effects of the grating. And then, we can calculate the corresponding RI values at each temperature by the calibration results plotted in Figure 4b. The obtained RI decreased nonlinearly with increasing temperature, and the fitting curve shows a nonlinear RI change of water in the temperature range of 25 \({}^{\circ}\)C\(\sim\)80 \({}^{\circ}\)C, which is very similar to the relationships from the previous reports [42; 43; 44]. The exponential relationship of water RI versus temperature in Celsius was \(n=-0.00233\)-exp(7/42.74454) + 1.33755, with the R-square of 0.99945. In view of the above results, the contributions of the hybrid structure composed of two gratings in RDF are as follows: a) The sharp Bragg resonance of the FBG produced a stable temperature response that was exempt from surrounding RI change; b) The Ex-TFG provided an accessible evanescent field to enhance the interaction between light and the surrounding medium; and c) The use of RDF can help to enhance this effect and then the RI sensitivity. Meanwhile, although the temperature dependence of water RI as an example was investigated, to demonstrate simultaneous sensing performance of dual-parameter, the actual applications could be extended to the dynamic and static high-sensitivity measurement of RI and temperature.