# Microchannel-Embedded D-Shaped Photonic Crystal Fiber-Based Highly Sensitive Plasmonic Biosensor
## 3 Performance Analysis and Numerical Results  
To numerically explore the optical properties of the proposed sensor, finite element method (FEM)-based commercial software COMSOL Multiphysics is used. For computational purposes, we use a circular perfectly matched boundary to attenuate all electromagnetic radiation that arrives at the boundary. Maximum mesh size is found by \(\lambda/6n\) for the entire geometry, where \(n\) is the mesh size parameter that increases up to 1 and \(\lambda\) is the operating wavelength. Figure 2 shows the confinement loss and the maximum number of elements as a function of \(n\). In this model, the region of silica is much larger compared with the air-gap regions. From Figure 2, it can be seen that confinement loss remains almost constant for \(n\)\(<\) 0.6. Therefore, to make the computation process faster, we use 100,168 elements. Asymmetrical structure of the PCF results in the existence of birefringence. Therefore, light propagating inside the fiber shows \(x\)-and \(y\)-polarizations of the fundamental and SPP modes, as shown in Figure 3a-d.The field distribution of these modes is shown for the analyte RI = 1.43 at the resonant wavelengths. Figure 3e demonstrates the RI and confinement loss as a function of wavelength for the fundamental and the SPP modes for both \(x\)- and \(y\)-polarizations. It is seen that resonance occurs at the phase-matching wavelength that results in maximum energy transfer from the fundamental modes to the SPP modes, and confinement loss becomes maximum for both polarized lights. For example, phase matching or resonant wavelengths are 1250 nm for \(x\)-polarization and 1080 nm for \(y\)-polarization. Additionally, the peak confinement losses at the resonant wavelengths are 97.04 and 12.89 dB/cm for \(x\)-and \(y\)-polarizations, respectively. As the operating wavelength, red/blue shifts far from the resonant wavelength, and the confinement loss approaches its tail from the peak loss. From Figure 3, it is noted that at the resonant condition, energy transmission increases significantly from the core to the SP for the \(x\)-polarized field compared with the \(y\)-polarized field because of efficient excitation of metal electrons by the evanescent wave. As a result, we consider sensor optical characteristics for \(x\)-polarization. Figure 2: Confinement loss and maximum number of elements as a function of mesh size parameter. The propagation loss spectra of the \(x\)-polarized fundamental mode are shown in Figure 4a due to the medium placed in the channel with RI ranging from 1.33 to 1.44. The increase in the analyte RI results in the reduction in core-cladding index contrast; as a result, resonant wavelength redshifts and peak confinement loss raises. The resonant wavelengths and peak confinement losses are shown in Table 1 for different analyte RI. The loss spectrum for higher analyte RI (e.g., 1.44) shows multiple resonance peaks at longer wavelengths similar to the Ref. in [38], where only the largest peak loss is considered to find the resonant wavelength. The higher peak loss is considered due to larger energy transmission from the core mode to SPP mode compared with the other subpeaks. Figure 3: Electric field distribution of \(x\)-polarized (**a**) core, (**b**) SPP mode, \(y\)-polarized (**c**) core, and (**d**) SPP mode; (**e**)confinement loss spectrum for both \(x\)- and \(y\)-polarization as a function of wavelength for analyte RI of 1.43; dispersion relation of core and SPP mode for both \(x\)- and \(y\)-polarization.