# Simultaneous Measurement of Refractive Index and Flow Rate Using a Co\({}^{2+}\)-Doped Microfiber
## 3 Results  
The sensing characteristics of the proposed 16.7 \(\upmu\)m diameter Co-MFBGS for temperature (20-140 \({}^{\circ}\)C), surrounding LRI (1.32-1.44 RIU) and LFR (0-0.98 \(\upmu\)L/s) changes have been tested as described in the following section. The temperature characteristics of the Co-MFBGS were tested first by putting the sensor into a chamber whose temperature could be adjusted in the range of 20-140 \({}^{\circ}\)C in steps of 10 \({}^{\circ}\)C and a resolution of 0.1 \({}^{\circ}\)C. The temperature experimental result of the wavelength interval (\(\lambda_{\text{a-b}}\)) change between \(\lambda_{\text{a}}\) and \(\lambda_{\text{b}}\) of the Co-MFBGS is shown in Figure 3a, which is clearly showing that \(\lambda_{\text{a-b}}\) is almost free from temperature perturbations. So, the temperature cross-sensitivity of LRI measurements can be neglected. The LRI measurement experiment of the Co-MFBGS was conducted at room temperature (25 \({}^{\circ}\)C). In each measurement, the aqueous glycerin solutions, with concentrations whose RI changed from 1.32 to 1.44 RIU in steps of 0.02 RIU, were injected into the microfluidic channel. After the aqueous glycerin solution had flowed to surround the entire Co-MFBGS, the reflection spectrum was interrogated several times by the OSA until almost no change was observed, and then the spectrum was recorded, so the reliable measuring values can be obtained. The experimental results of the proposed Co-MFBGS wavelength shift with different LPIs are shown in Figure 3b-d. Figure 3b-d shows the value change of \(\lambda_{\text{a}}\), \(\lambda_{\text{b}}\) and \(\lambda_{\text{a-b}}\) with different LPIs, respectively. It is clear that the core mode wavelength of the proposed Co-MFBGS does not shift, which means it is insensitive to the LRI. Meanwhile, the cladding mode is exceedingly sensitive to the LRI; its wavelength shift decreases by 0.69 nm with the LRI changes from 1.32 to 1.44 RIU. So, the value change of \(\lambda_{\text{a-b}}\) is almost the same with the value change of \(\lambda_{\text{b}}\), and it can be fit to a quadratic non-linear equation with LRI change (1.32-1.44 RIU). The equation indicates that the maximum LRI sensitivity of the proposed Co-MFBGS wavelength interval is about \(-7.85\) nm/RIU, Figure 3d. Figure 3: (**a**) Wavelength interval change with different temperatures; (**b**) value change of \(\lambda_{\text{a}}\); (**c**) value change of \(\lambda_{\text{b}}\); (**d**) wavelength interval change with different LPIs. Before beginning the LFR measurement experiment, the Co-MFBGS was heated by using pumped laser powers of 250, 350 and 450 mW at a wavelength of 1480 nm, as the Co-MFBGS can be heated by pump laser due to the light absorption of cobalt. Figure 4f shows the wavelength shift of the core mode (\(\lambda_{\text{a}}\)) at different pumped laser powers, which clearly shows that \(\lambda_{\text{a}}\) has a redshift while increasing pumped laser power, and the sensitivity increases significantly with increasing heating power. That means the temperature of Co-MFBGS is increased, so, when the Co-MFBGS is used for LFR sensing, the heat of Co-MFBGS will be carried away by the flowing liquid, the temperature of Co-MFBGS will be decreased, and \(\lambda_{\text{a}}\) will has a blueshift. During the LFR measurement experiment of the proposed Co-MFBGS, the LFR was varied in 0-0.98 \(\upmu\)L/s by using a commercial electronic-controlled syringe pump to inject an aqueous glycerin solution with a constant concentration into the microfluidic channel; meanwhile, the pumped laser power was set to 450 mW. A PZT flow sensor was used to calibrate the LFR. The experimental results are shown in Figure 4.  
With increasing LFR, both \(\lambda_{\text{a}}\) and \(\lambda_{\text{b}}\) experience a blueshift due to the decreasing temperature of the Co-MFBGS; reflection spectra corresponding to different flow rates are shown in Figure 4a.