# Highly Sensitive Liquid M-Z Waveguide Sensor Based on Polymer Suspended Slot Waveguide Structure
## 5 Data Analysis and Comparison of MZI  
The optimization analysis of the overall MZI structure was subsequently performed. The device was designed with branch interval of 10 \(\upmu\)m, arm length of 2045 \(\upmu\)m, and branch span of 700 \(\upmu\)m. Furthermore, we investigated the device sensitivity (\(S_{d}\)) of the suspended MZI with the slot waveguide (Figure 6a), the suspended MZI with the strip waveguide (Figure 6c), the MZI with the strip waveguide on the substrate (Figure 6d). All their cladding is liquid, the structures in Figure 6a,d show the adopted slot waveguide, the structures in Figure 6b,c show the adopted strip waveguide. The structures on substrates with the refractive index of 1.33 are shown in Figure 6c,d. The device sensitivity \(S_{d}\) can be described as:  
\[S_{d}=\frac{\partial_{Lust}}{\partial_{n_{c}}}=\frac{2\pi L}{\lambda}\cdot \sin\left(\frac{2\pi L}{\lambda}\Big{(}N_{eff1}-N_{eff2}\Big{)}\right)\cdot \left(\frac{\partial_{N_{eff1}}}{\partial_{n_{c}}}-\frac{\partial_{N_{eff2}}}{ \partial_{n_{c}}}\right) \tag{2}\]  
where \(S_{d}\) is the sensitivity of the sensor and \(n_{c}\) is the refractive index of the test medium. \(L\) is the length of the branched arm, \(\lambda\) is the operation wavelength. \(N_{eff1}\) and \(N_{eff2}\) are the effective refractive indexes of two branched arms. We selected salt solution as the liquid  
Figure 4: (**a**) Schematic of the coupling structure. (**b**) \(I_{out}\) and \(\eta\) corresponding to different slot cross-section sizes. Figure 5: \(\eta\) for the device with the substrate. analyte to be tested. When the mass fraction of the salt solution varied from 12.5% to 17.5%, the reflective index changed from 1.33 to 1.34. The schematic of different structures is shown in Figure 6, and the connections between \(I_{out}\) and \(n_{c}\) are illustrated in Figure 7. The suspended MZI sensor with a slot waveguide has an average sensitivity of 972.1 dB/RIU and an average detection resolution of 1.6 \(\times\) 10\({}^{-6}\) RIU. The suspended MZI sensor with a strip waveguide has an average sensitivity of 652.3 dB/RIU and an average detection resolution of 1.5 \(\times\) 10\({}^{-6}\) RIU. The average sensitivity of an MZI sensor with a strip structure on a substrate is 460.1 dB/RIU, and the average detection resolution is 2.2 \(\times\) 10\({}^{-6}\) RIU. The MZI sensor with a slot structure on the substrate has an average sensitivity of 601.6 dB/RIU and an average detection resolution of 1.6 \(\times\) 10\({}^{-6}\) RIU. It can be concluded that the average detection resolution of the suspended MZI sensor based on the slot structure we designed is about 1.5 times higher than that of the suspended strip waveguide structure, 1.6 times higher than that of the non-suspended slot structure, and 2.1 times higher than that of the non-suspended strip waveguide structure. Figure 8 illustrates the simulated optical field of different structures. Figure 6: Schematics of the devices: (**a**) the suspended MZI with a slot waveguide; (**b**) the suspended MZI with a strip waveguide; (**c**) the MZI with a strip waveguide on a substrate; and (**d**) the MZI with a slot waveguide on a substrate. Figure 7: The connections between \(I_{out}\) and the \(n_{c}\) of the suspended MZI with a slot waveguide, the suspended MZI with a strip waveguide, the MZI with a slot waveguide on a substrate. Regarding polymer slot waveguides, the variation in sensing accuracy with wavelength change is significantly higher than that of ridge waveguides and silicon slots. One of the main reasons is that its mode changes with wavelength, and the other is that the polymer has a high sensitivity to wavelength change owing to its low refractive index. Therefore, we analyzed the relationship between the normalized output energy with the refractive index for the structure at different wavelengths near the communication wavelength of 1550 nm.