## 3 Discussion
To optimize the visual clarity and mitigate potential overlap of the resonance dips, the spectra are intentionally offset along the Y-axis, strategically enhancing the distinctiveness of each resonant feature. The rate of the change in the resonance wavelength versus the refractive index unit (RIU) is plotted in Figure 4b. The slope of the line is estimated by applying a linear regression method. The importance of the linear regression method in establishing the slope of a line cannot be overstated, as it provides a methodical and quantitative framework for comprehending the connection between variables. Through the application of a linear equation to a dataset, this method measures the influence of variations in an independent variable on the dependent variable. The line's slope, denoted by the coefficient'm' in the equation \(y=\text{mx}+\text{b}\), assumes a pivotal role as a parameter that signifies the rate of the change in the dependent variable for every unit alteration in the independent variable. The bulk sensitivity of the device is determined as follows [36; 41]:  
\[\text{S}_{\text{bulk}}=\frac{\Delta\lambda}{\Delta\text{n}}; \tag{4}\]  
Figure 3: (**a**) Transmission spectrum of RRs with R = 50 \(\upmu\)m, 75 \(\upmu\)m, and 100 \(\upmu\)m; (**b**) FSR of the resonance dip obtained at 1543.84 nm; (**c**) image of the RR structure captured during the measurement via IR camera in on-resonance state. where \(\Delta\lambda\) and \(\Delta\)n are the change in the resonance wavelength and the change in the ambient refractive index, respectively. The device's sensitivity, obtained through both experimental and numerical computations, stands at 112.5 nm/RIU and 110 nm/RIU, respectively. This minimal difference yields a relative percent error (\(\frac{Experiment-numerical}{Experiment}\times 100\)) of merely 2.2%, underscoring the precision and reliability of the results. Table 1 briefly presents the numerical and experimental findings detailed in this paper, accompanied by the corresponding relative percent errors for comprehensive clarity. The linearity of an RR sensor refers to its ability to produce a linear response to changes in the parameter it measures, such as the refractive index [42]. In practical terms, this means that as the refractive index of the surrounding medium changes, the resonance wavelength changes in a predictable and proportional manner. The linear correlation coefficient quantifies this relationship mathematically, providing a measure of how closely the sensor's output follows a straight-line trend with changes in the measured parameter [43]. Our sensing device has a correlation coefficient close to +1, which indicates a strong positive linear relationship, implying that the sensor is highly sensitive and exhibits minimal deviations from linearity over its operating range. Ensuring high linearity and a strong correlation coefficient enhances the sensor's accuracy and effectiveness in various practical scenarios. The limit of detection (LOD) within an optical RR-based sensor denotes the smallest discernible change in the measured parameter, such as the refractive index or concentration, that the sensor can reliably identify and can be determined as follows [36]:  
\[\text{LOD}=\frac{\lambda_{\text{res}}}{\text{Q}-\text{factor}.\text{S}} \tag{5}\]  
where \(\lambda_{\text{res}}\), Q factor, and S are the resonance wavelength, quality factor, and sensitivity of the device, respectively. Attaining a low LOD holds paramount significance in enhancing