## 3 Results and Discussion
The system layer was coated on the microscope glass slide, and it was attached to the prism using index matching gel. The SPR signal was separately registered for each thickness in the presence of DDW (n = 1.3323). Figure 3b,c shows the SPR results to test the refractive index of the layers and baseline. The refractive index of the layer was achieved by analysis of the SPR signal using [PERSON]'s theory for the multilayer system when the refractive index of the gold layer was 0.237 + 3.335i. [PERSON]'s theory predicts the reflection coefficient (\(r\)) from dielectric and metal medium such as the gold layer. The matrix form that was presented in ref. [33; 34] is used for the multilayer system. The reflectance (\(R\)) is equal to \(r\times r\). If the refractive index (\(n\)) and accurate thickness (\(t\)) of layers are unknown, they can obtain from the minimum root square of the difference between the theory and experimental value of reflectance as follows [26; 27]:  
\[\Psi\ =\ \sum_{\theta}\left[R_{Theory}(\theta,n,t)-R_{Exp}(\theta,n,t)\right] \tag{2}\]  
where \(R_{Theory}\) and \(R_{Exp}\) are the theoretical and experimental value of reflectance, respectively. Figure 3: _Cont._  
According to the SPR signals analysis, the accurate thickness of layers was in the range of 3.6 nm to 94.2 nm, and the refractive index of the PPy-Chi-BaFe\({}_{2}\)O\({}_{4}\) was in the range of 1.67571 + 0.139i to 1.57072 + 0.164i. Figure 3c shows the SPR signal at the baseline when the baseline was obtained at 53.948 using the PPy-Chi-BaFe\({}_{2}\)O\({}_{4}\) layer with 7.3 nm of thickness. The variation of real (\(n\)) and imaginary (\(k\)) parts of the refractive index were demonstrated in Figure 4a,b, respectively. Consequently, the real (\(n\)) part of the refractive index decreased, and the imaginary (\(k\)) part of the PPy-Chi-BaFe\({}_{2}\)O\({}_{4}\) increased when the thickness of the layer increased. The pertinent parameters were listed in Table 1. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & **Thickness (nm)** & **Thickness (nm)** & **Refractive** & **Resonance** & **Reflectance** \\  & **(Profilometer)** & **(SPR Analysis)** & **Index** & **Angle** & **Reflectance** \\ \hline
1 & 3 & 3.6 & 1.67571 + 0.139i & 53.126\({}^{\circ}\) & 0.045 \\
2 & 7 & 7.3 & 1.66191 + 0.141i & 53.948\({}^{\circ}\) & 0.088 \\
3 & 18 & 18.5 & 1.64183 + 0.144i & 56.668\({}^{\circ}\) & 0.216 \\
4 & 94 & 94.2 & 1.57072 + 0.164i & 68.131\({}^{\circ}\) & 0.658 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The thickness, refractive index, resonance angle, and reflectance of SPR signal related to PPy–Chi–BaFe\({}_{2}\)O\({}_{4}\) sensing layer  
Figure 4: Variation of (**a**) real (\(n\)) and (**b**) imaginary (\(k\)) parts of the refractive index of PPy–Chi–BaFe\({}_{2}\)O\({}_{4}\). Figure 3: (**a**) Variation in the thickness of layer with increasing the cycle; (**b**) The SPR signal related to obtaining the refractive index of the PPy–Chi–BaFe\({}_{2}\)O\({}_{4}\) composite layer in the different thickness; (**c**) The SPR signal at the baseline. The PPy-Chi-BaFe\({}_{2}\)O\({}_{4}\) with 7.3 nm thickness was used to measure and detect the low concentration of glucose, sucrose, and fructose. The experiment was separately carried out in the presence of 0.005 ppm (0.0005 mg/dL), 0.05 ppm (0.005 mg/dL), 0.5 ppm (0.05 mg/dL), 5 ppm (0.5 mg/dL), 15 ppm (1.5 mg/dL), and 25 ppm (2.5 mg/dL) of glucose, sucrose, and fructose. The SPR signals were registered, and the variation of resonance angle shift was achieved during 420 s. Figure 5a-c shows the resonance angle shift with time (sensorgram) for the glucose, fructose, and sucrose, respectively. As a result, the experimental values fit well with the first order Langmuir formula (\(\Delta\theta\ =\ \Delta\theta_{sat}(1-\exp(-k_{at}t))\)) [35; 36]. The concentration of sugars that attached the sensing layer was tested using UV-vis spectroscopy.