# Wave-Shaped Microstructure Cancer Detection Sensor in Terahertz Band: Design and Analysis
## 2 Numerical Analysis  
The proposed biosensor has been designed and analyzed using the FEM, which is the primary approach employed in this study. The steps involved in biosensor design and performance evaluation are illustrated in Figure 1. Initially, the Global Variables (GVs) and Structure Variables (SVs) were declared in COMSOL Multiphysics 5.5 software, followed by the design of the probable PCF sensor structure. Materials were then assigned to different parts of the sensor, including Zeonex to PML and Strut of the fiber sensor, air holes in the cladding, and six cell type analytes (in both normal and cancerous forms) in the core for analysis purposes. Boundary and initial conditions were applied, and the designed fiber was meshed and solved using partial differential equations. The optical parameter data were then collected and transferred to MATLAB for further analysis. Different results were analyzed, and the relationship between the operating frequency and various optical parameters was observed. If the results were not satisfactory, the GVs and SVs were adjusted, and the entire process was repeated until the desired results were achieved. A list of different optical properties, such as relative sensitivity, effective area, numerical aperture, CL, effective material loss (EML), etc., seems necessary to check the biosensor's functionality. These parameters, i.e., performance indices, will be investigated through simulation using the software while injecting an analyte into the core of the proposed sensor using a capillary injection strategy. In actuality, though, this function will be fulfilled by an optical spectrum analyzer. For each analyte, the full procedure will be repeated. The FEM with a Perfectly Matched Layer (PML) boundary condition is a commonly used framework for solving problems numerically. For investigating optical properties and removing leaks, a PML is utilized. A meshing technique is used to partition the proposed PCF into homogeneous triangular sub-spaces. Modal analysis and frequency transmission through the Z-direction of fiber can be used to determine the performance of waveforms  
Figure 1: The step-by-step process involved in designing and analyzing the model in this study. spanning 1.5-3 THz in an x-y cross-section. The following equation can be obtained using the Maxwell equations [27]:  
\[\Delta\times[s]^{-1}\times E-k_{0}^{2}n^{2}[s]E=0 \tag{1}\]  
In this context, \(s\) represents the PML matrix of \(3\times 3\) and \([s]^{-1}\) is the inverse of \(s\). Electric field vector \(E\), domain refractive index \(n\), free-space wave number \(K_{0}\), and operational wavelength \(\lambda\) are all represented by the symbol. In this simulation, the fiber is split into 2,920,397 triangular segments. One-fourth of the PML layer computation window is used to display Figure 2 for the recommended PCF structure. How sensitive a terahertz PCF is to an analyte depends on how much light interacts with matter. This is dependent on a particular coefficient of frequency absorption. The Beer-Lambert law can be used to explain it [8],  
\[I(f)=I_{0}(f)e^{[-\pi n_{\text{eff}}]} \tag{2}\]  
where the symbols for the optical intensity in the presence and absence of the desired material are \(I(f)\) and \(I_{0}(f)\), respectively. In this case, the channel range is \(lc\), the relative sensitivity is \(r\), the optical frequency is \(f\), and the absorption factor is \(\alpha_{m}\). The formula for the absorbance (A) is  
\[A=\log\frac{I}{I_{0}}=-r\alpha_{m}l_{c} \tag{3}\]  
Now, relative sensitivity depicts the amount of light that interacts with the analyte. The sensitivity of the PCF must be measured in order to examine its sensing efficiency, which can be achieved using [8],  
\[r=\frac{n_{r}}{n_{\text{eff}}}\times Y \tag{4}\]  
where the RI (real) of the analyte to be detected is \(n_{r}\), and the RI (effective) of the guided mode is \(n_{\text{eff}}\) (ERI).