# Microchannel-Embedded D-Shaped Photonic Crystal Fiber-Based Highly Sensitive Plasmonic Biosensor
## 3 Performance Analysis and Numerical Results
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**RI** & \(\lambda_{\text{res-}}\) & \(\alpha_{peak}\) & \(\mathbf{S_{\lambda}}\) & **Resolution** & \(\mathbf{S_{\lambda}}\) & **FWHM** & **FOM** \\ \hline  & **nm** & **dB/cm** & **nm/RIU** & **RIU** & **RIU\({}^{-1}\)** & **nm** & \\ \hline
1.33 & 590 & 3.05 & 1000 & \(1.00\times 10^{-04}\) & 106.64 & 42 & 24 \\ \hline
1.34 & 600 & 3.70 & 1000 & \(1.00\times 10^{-04}\) & 145.89 & 40 & 25 \\ \hline
1.35 & 610 & 4.42 & 2000 & \(5.00\times 10^{-05}\) & 194.74 & 38 & 52 \\ \hline
1.36 & 630 & 5.43 & 3000 & \(3.33\times 10^{-05}\) & 272.29 & 37 & 82 \\ \hline
1.37 & 660 & 6.72 & 3000 & \(3.33\times 10^{-05}\) & 381.55 & 36 & 84 \\ \hline
1.38 & 690 & 8.40 & 3000 & \(3.33\times 10^{-05}\) & 529.83 & 35 & 85 \\ \hline
1.39 & 720 & 10.85 & 5000 & \(2.00\times 10^{-05}\) & 751.41 & 35 & 142 \\ \hline
1.40 & 770 & 14.21 & 8000 & \(1.25\times 10^{-05}\) & 968.03 & 37 & 215 \\ \hline
1.41 & 850 & 18.58 & 12,000 & \(8.33\times 10^{-05}\) & 1182.50 & 46 & 259 \\ \hline
1.42 & 970 & 26.26 & 28,000 & \(3.57\times 10^{-06}\) & 1439.00 & 59 & 471 \\ \hline
1.43 & 1250 & 97.04 & 63,000 & \(1.59\times 10^{-06}\) & 343.59 & 75 & 839 \\ \hline
1.44 & 1880 & 110.07 & NA & NA & NA & NA & NA \\ \hline \end{tabular}
\end{table} 
Table 1: Performance of sensor for analyte RI from 1.33 to 1.44. Figure 4: Sensor characteristics for analyte RI ranging from 1.33 to 1.44: **(a)**confinement loss as a function of wavelength, **(b)**different analytes’ amplitude sensitivity as a function of wavelength, **(c)**resonant wavelength and their polynomial fitting as a function of analyte RI, and **(d)** FWHM and FOM as a function of analyte RI. The increase in analyte RI results in the redshift of the resonant wavelengths that are used to find the wavelength sensitivity by the following equation  
\[\mathrm{S}_{\lambda}(\mathrm{nm/RIU})=\Delta\lambda_{\mathrm{resonance}}(n_{a})/ \Delta n_{a} \tag{5}\]  
where \(\Delta\lambda_{\mathrm{resonance}}\) is the amount of redshift of the resonant wavelengths in nm for the difference of analyte RI of \(\Delta n_{a}\)[11]. Since \(\Delta n_{a}=0.01\) is constant in our analysis, wavelength sensitivity \(\mathrm{S}_{\lambda}\) shows higher values for larger \(\Delta\lambda_{\mathrm{resonance}}\). For example, the resonant wavelength changes from 590 nm to 600 nm as \(n_{a}\) changes from 1.33 to 1.34, which results in the wavelength sensitivity of 1000 nm/RIU. Similarly, for the increase in \(n_{a}\) from 1.43 to 1.44, the change of \(\lambda_{\mathrm{resonance}}\) is maximum (i.e., from 1250 nm to 1880 nm), which leads to the maximum wavelength sensitivity of 63,000 nm/RIU. The wavelength sensitivities are listed in Table 1 for other analytes' RI. The sensitivity parameter termed as the resolution of a sensor detects the minimum change in RI and can be found as follows:  
\[R_{\lambda}(\mathrm{RIU})=\Delta n_{a}\times\Delta\lambda_{\mathrm{min}}/ \Delta\lambda_{\mathrm{resonance}} \tag{6}\]  
where \(\Delta\lambda_{\mathrm{min}}=0.1\) nm is the minimum spectral resolution [11]. Table 1 shows sensor resolutions for analytes' RI from 1.33 to 1.43. The Table 1 shows that as analyte RI changes from 1.43 to 1.44, the sensor resolution is minimum (i.e., \(1.59\times 10^{-06}\) RIU), corresponding to the highest wavelength sensitivity of 63,000 nm/RIU. The smallest resolution \(1.59\times 10^{-06}\) RIU in Table 1 indicates the detector's ability to discriminate between analytes' RI that are close enough. There is another important sensor parameter known as amplitude sensitivity, which is measured by the amplitude interrogation method. The amplitude sensitivity analysis is a low-cost sensitivity measurement process compared with wavelength sensitivity because this method does not engage spectral manipulation.