# Comparison of the Sensitivity of Various Fibers in Distributed Acoustic Sensing
## 2 Approach
### Samples  
Six different types of non-standard optical fibers and a standard single-mode fiber were available for this study (Table 1). Corning SMF-28 Ultra was used as a reference due to its widespread use in telecommunications and DAS applications. Generally, fibers produced by MCVD exhibit a slightly higher attenuation coefficient than those produced by OVD. So, \"Fiber 6\" was selected to investigate whether it has a higher acoustic sensitivity than \"Fiber 1\", as the primary difference between them is the production method. \"Fiber 2\" is represented by Corning SMF-28 with a multilayer coating [40], where the Young's modulus \(E\) of the inner layer is slightly higher than that of the outer layer, with both being lower than the modulus of acrylates. This fiber is more than three times larger in diameter than \"Fiber 1\", making it important to study which parameter--diameter or modulus--has a greater impact on acoustic sensitivity. The effect of multilayer coating was also a subject of interest. In contrast, \"Fiber 3\" has a smaller outer diameter but higher \(E\) values for each coating layer. Additionally, the speed of sound in metals is relatively high, so this fiber was chosen to explore how these characteristics influence its acoustic sensitivity compared to \"Fiber 1\". Polyimide coatings provide higher tensile strength, have similar \(E\) values to acrylate and are known to induce bend losses. However, if an acoustic wave modulates the fiber's micro- and macro-bends, polyimide-coated fibers may exhibit enhanced acoustic sensitivity. Two types of polyimide-coated fibers were available in this study; one of these had coating defects, including inhomogeneities, caverns and embedded bubbles. These minor coating imperfections could potentially resonate with specific acoustic frequencies, increasing the fiber's acoustic sensitivity. It was also decided to include the anisotropic \"Fiber 7\" in the study because of its smaller outer diameter and reduced glass cladding diameter (see Figure 2). An acoustic disturbance induces mechanical waves in the fiber core and could lead to polarization mode coupling, resulting in the transfer of light between modes. This phenomenon could enhance the fiber's acoustic sensitivity. However, fibers like \"Fiber 7\" are inherently anisotropic, exhibiting intrinsic strain that provides additional resistance to bend losses, which may offset the sensitivity benefits provided by its other features, potentially resulting in lower acoustic sensitivity compared to \"Fiber 1\". During testing, \"Fiber 7\" was probed with a fiber optic polarizer to direct all the probing light to the fiber's \"fast\" polarizing mode. To evaluate the estimated acoustic sensitivities of the FUTs, the \(kL\) parameter was used, assuming known [PERSON]'s moduli \(E\) for the coating materials, along with known diameters of fiber claddings and coatings. Here, \(L\) is consistent across all fibers, as is the stiffness coefficient \(k\) of the uncoated fibers (Table 2):  
\[kL=0.25\pi E(D_{o}^{2}-D_{i}^{2}), \tag{5}\]  
where \(D_{o}\) is the outer coating diameter and \(D_{i}\) is the inner coating diameter. Lower values of \(kL\) indicate higher sensitivity. For fibers with multilayer coatings, \(kL\) was calculated as follows:  
\[kL=(kL)_{1}\frac{S_{1}}{S_{1}+S_{2}}+(kL)_{2}\frac{S_{2}}{S_{1}+S_{2}}, \tag{6}\]  
where \((kL)_{1}\) and \((kL)_{2}\) represent the \(kL\) parameters of the first and second coating layers, \(S_{1}\) and \(S_{2}\) are their cross-sectional areas. The final \(kL\) value for the multilayer-coated fiber was determined by weighting each layer's \(kL\) value according to its cross-sectional area relative to the total cross-sectional area of the coating.