# Microchannel-Embedded D-Shaped Photonic Crystal Fiber-Based Highly Sensitive Plasmonic Biosensor
## 2 The Structure of the Sensor  
The illustration of the proposed PCF-based plasmonic biosensor is demonstrated in the transverse plane in Figure 1a that contains silica as background material. The refractive index \(n\) as a function of wavelength \(\lambda\) of the PCF background material silica is evaluated by the following Sellmeier equation:  
\[n^{2}(\lambda)=1+\frac{A_{1}\lambda^{2}}{\lambda^{2}-B_{1}}+\frac{A_{2}\lambda ^{2}}{\lambda^{2}-B_{2}}+\frac{A_{3}\lambda^{2}}{\lambda^{2}-B_{3}}. \tag{1}\]  
The values of the coefficients A and B in Equation(1) are the same as those in [30]. In the proposed PCF, four air-hole layers are organized in a hexagonal lattice with an optimized pitch constant \(\Lambda=2\)\(\upmu\)m. The stack preform of the PCF is shown in Figure 1b. Figure 1b shows that selected air holes around the center are replaced by silica's solid rods to form a single core and leakage path for light to create an evanescent electric field that reaches the plasmonic material to excite free electrons. Figure 1 shows that a microchannel with a larger air hole of diameter d\({}_{\text{ch}}=2.2\Lambda\) is inserted in the PCF to contain the analyte. The air holes with a shrunk diameter d\({}_{\text{s}}=0.6\Lambda\) and enlarged diameter d\({}_{1}=0.9\Lambda\) control the interaction of light with the plasmonic film and the analyte channel. All other air holes in the PCF have a diameter d = 0.8\(\Lambda\). It should be noted that the structural parameters used in the model are optimized to detect analyte RI from 1.33 to 1.44 with very high sensitivity. The preform structure shows that a thick silica tube is used for the smallest air hole, and thin silica tubes are used for the larger air holes. The dimensions of air holes considered in this model are larger than the smallest air hole of the PCF fabricated in Ref. [31]. Therefore, the stack preform of the hexagonal lattice-based proposed sensor indicates that the manufacturing process of PCF can be achieved by following the stack-and-draw fiber drawing technique [31]. In order to easily fill up the analyte into the microchannel, the PCF is polished by side-polishing technique as described in Ref. [19], starting from the top of the PCF to the polishing boundary as shown in Figure 1b, which leads to the formation of the D-shaped PCF sensor and opens a microchannel. The wider channel reduces the distance between the core of the PCF and the plasmonic film that leads to the strong resonance and efficient energy exchange of the coupled modes. After opening the microchannel, 6 nm of TiO\({}_{2}\) is deposited inside the open channel to work as an adhesive layer, and on top of that, 40 nm gold is deposited as a plasmonic medium. In this modified D-shaped PCF sensor, the flat surface is not required to be smooth because the plasmonic layer (gold) is deposited on the inner plane of the larger air hole. Moreover, the inner wall of the larger air hole has a smooth surface by itself; therefore, no additional efforts are necessary to make the sensing layer smooth, such as in the case of the flat surface of a D-shaped sensor. A high-quality thin film of the plasmonic and adhesive layer can be deposited inside the open-air hole by using physical vapor deposition (e.g., sputtering, electron beam evaporation) and chemical vapor deposition process (e.g., atomic layer deposition) [32; 33]. Moreover, a long-lasting immobilized uniform gold layer can be deposited by using the nano particle-layer-deposition (NLD) process, even in the case of uneven circular silica capillary [34]. In addition, the Tollens' reaction chemical coating method can be used to deposit metal in the inner plane of the open channel [35]. The permittivity of gold is found by the following the Drude-Lorentz model:  
\[\varepsilon_{Au}=\varepsilon_{\infty}-\frac{\omega_{D}^{2}}{\omega(\omega+j \gamma_{D})}-\frac{\Delta\varepsilon\Omega_{L}^{2}}{\left(\omega^{2}-\Omega_ {L}^{2}\right)+j\Gamma_{L}\omega} \tag{2}\]  
where \(\omega\) is the angular frequency.