# SARS-CoV-2 Detection Using Optical Fiber Based Sensor Method
## 5 Proposed Experimental Testbed
### The Wavelength-Refractive Index Relation  
The sensitivity of the refractive index to wavelength is discussed in this section. A leakage mode arises in the bending zone of an optical fiber with a bend radius small enough that when light enters the bending region, total reflection is no longer maintained at the interface between the core and cladding layers, according to [PERSON] et al. [36] and [PERSON] et al. [37]. As a result, certain light rays from the core layer can leak or be released to the cladding layer, reflecting at the interface between the external medium and the cladding layer, generating a whispering gallery mode \((\mathrm{WGM})\). After then, the light beams would be linked back to the core layer. Due to the two separate transmission paths, interference is created when light beams couple via the WGM from the cladding layer to the core layer. As a result, a unique WGM wavelength spectrum is created, with various peaks and troughs visible.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline \multirow{4}{*}{Laser} & Wavelength = 530 nm \\  & Electrical Power = 3100 mW \\  & Output Power = \(\left\{\begin{array}{c}3.2 mW @200 \mu\mathrm{m}\\ 9.6 mW @500 \mu\mathrm{m}\end{array}\right.\) \\ \hline \multirow{2}{*}{Optical Fiber} & Type = POF \\  & Diameter = 200 and 500 \(\mu\mathrm{m}\) \\ \hline \multirow{2}{*}{Photodiode} & Responsivity = 0.34 A/W \\  & Bandwidth =2 GHz \\ \hline \hline \end{tabular}
\end{table}
Table 2: Testbed parameters.  
The interference spectrum light source intensity of the WGM can be represented by Equation (6) [38].  
\[I=I_{co}+I_{w}+2\sqrt{I_{co}+I_{w}}\ cos(\phi) \tag{6}\]  
where \(I_{co}\) and \(I_{w}\) are the light intensities in the fiber's core mode and WGM, respectively, and \(\phi\) is the phase difference between the core mode and the WGM. It is well understood that increasing the refractive index changes the effective refractive index difference between the core and cladding, as well as the position of the wavelength at the point of loss. Based on the refractive index fluctuations in the external environment, the wavelength sensitivity can be stated as:  
\[\frac{d\lambda_{D}}{dn_{ext}}=-\frac{\lambda_{D}}{\Delta n_{eff}}\frac{\partial _{neff}^{cl,m}}{\partial n_{ext}}\left/\left[1-\frac{\lambda_{D}}{\Delta n_{ eff}}\left(\frac{\partial_{neff}^{co}}{\partial\lambda}-\frac{\partial_{n eff}^{cl,m}}{\partial\lambda}\right)\right]\right. \tag{7}\]  
The equations presented above linking the refractive index and sensitivity reveal that when the external refractive index changes, the effective refractive indices of the core and cladding modes should change, causing wavelength shifts. The core of a typical single-mode optical fiber has a higher effective refractive index than its cladding, and its effective refractive index equation is \(n_{eff}^{co}-n_{eff}^{cl,m}>0\).  
Furthermore, when \(\frac{\lambda_{D}}{\Delta n_{eff}}\left(\frac{\partial_{neff}^{co}}{\partial \lambda}-\frac{\partial_{neff}^{cl,m}}{\partial\lambda}\right)<\)1, the wavelength sensitivity to refractive index fluctuations is negative, implying that any increase in the refractive index decreases the wavelength.  
Based on this explanation in this section, in case of a specimen with infection, it is observed that for a smaller diameter of 200 \(\upmu\)m PoF, the intensity curve is much stronger compared to the case when 500 \(\upmu\)m diameter PoF is utilized. This shows that the correlation of the specimen with a smaller-diameter probe is better as the intensity is higher due to better exposure and higher total internal reflection. Similarly, the bending in terms of U-shaped fiber is better compared to D- or T-shaped probe fiber.