# A Novel Dual-Wavelength Method for Evaluating Temperature Effect in Fiber-Optic SPR Sensors
## 4 Experimental Results and Discussion  
Based on the above-mentioned dual-wavelength method, the approach can be directly applied to the conventional fiber-optic SPR sensor. A proof-of-concept experiment is carried out with a typical transmission-based fiber-optic SPR sensor. The schematic of the transmission-based fiber-optic SPR is shown in Figure 8. Two laser diodes with the center wavelengths of 520 nm and 635 nm light up in turns. The light beams interflow into the two exiting directions through a semi-permeable mirror. One direction of the light is directly recorded by a photoelectric detector as the reference to eliminate the influence caused by the fluctuation of light source. The other one is the detecting light coupled into the optical fiber with the lens 3. The light passes through the SPR sensing probe portion and is detected with a fiber-optic power meter (PM20A, Thorlabs). A step index multimode fiber (core: 200 \(\upmu\)m, 0.37 NA) is used as the light transmission medium with cladding of 10 mm length removed. Then, the unclad fiber core is coated with gold film of a thickness of 50 nm using vacuum magnetic sputtering rotary technique. Figure 8: Schematic of the transmission-based fiber-optic SPR experimental setup. The experimental platform can provide an exact measurement of transmission power variation caused by SPR sensing at the two detecting wavelengths. Different concentrations of aqueous NaCl solution are used as the analytes and confirm the RI with an Abel refractive index-measuring instrument in the experiment. The change of temperature is controlled by a hot plate. Therefore, a proof-of-concept experiment is carried out to demonstrate the capability of the proposed dual-wavelength method after the optical arrangement. Figure 9 depicts the relationship between the output signal versus analyte RI when the temperature is fixed at 30 \({}^{\circ}\)C. Obviously, there is a significant linear relationship between output signal and the RI. With the RI changing from 1.3407 RIU to 1.3462 RIU, the signal at \(\lambda_{2}=635\) nm decreases from 35.7258 uuv to 30.9591 uuv while the signal at \(\lambda_{1}=520\) nm increases from 29.6735 uuv to 31.7652 uuv, corresponding to the slopes of \(-873.0231\) uuv/RIU and 383.0945 uuv/RIU, respectively. Figure 10 shows the dual-wavelength signals' variation versus temperature with the RI of 1.3448 RIU. With the increase in temperature, both of the output signals decrease slightly, resulting in the detectable slopes of \(-0.0240\) uuv/\({}^{\circ}\)C for \(S(\lambda_{2})\) and \(-0.0138\) uuv/\({}^{\circ}\)C for \(S(\lambda_{2})\), respectively. Due to the fitting lines measured in the calibration progress, the sensitivity matrix can be obtained with the linear coefficients. Therefore, with the proposed dual-wavelength technique and the inverse of linear sensitivity matrix, both the RI and temperature variations can be measured as:  
\[\left( \begin{array}{c}\Delta n\\ \Delta T\end{array} \right)=\mathrm{K}^{-1}\left( \begin{array}{c}\Delta S( \lambda_{1})\\ \Delta S(\lambda_{2})\end{array} \right)=\left( \begin{array}{cc}5.2593&-9.1466 \\ -33.2716&-14.6001\end{array} \right)\left( \begin{array}{c}\Delta S(\lambda_{1 })\\ \Delta S(\lambda_{2})\end{array} \right) \tag{25}\]  
Here, \(\Delta n\) and \(\Delta T\) are the RI variation and temperature change of the analyte in units of \(10^{-4}\) RIU and \({}^{\circ}\)C. \(\Delta S(\lambda_{1})\) and \(\Delta S(\lambda_{2})\) are the variations of defined output signals at \(\lambda_{1}=520\) nm and \(\lambda_{2}=635\) nm, respectively. For the experimental setup used to verify the new technique, the sensor works in the intensity-interrogation mode. The detection limit is dependent on the composite resolutions of the fiber intensity detector, metal thickness, and RI detecting range. In general, a conventional SPR sensor based on multimode fiber has the RI resolutions of \(7.69\times 10^{-5}\) RIU with the wavelength sensitivity of 2600 nm/RIU and spectrometer resolutions of 0.2 nm [41].