# Highly Sensitive Liquid M-Z Waveguide Sensor Based on Polymer Suspended Slot Waveguide Structure
## 4 Optimization of Slot Waveguide  
For the device, the sensing accuracy (\(S_{w}\)) depends on the slope of the phase difference and the change in the cladding refractive index. The waveguide sensitivity \(S_{w}\) can be described as:  
\[S_{w}=\frac{\partial_{N_{eff}}}{\partial_{n_{c}}} \tag{1}\]  
where \(N_{eff}\) is the mode effective refractive index, \(n_{c}\) is the refractive index of the upper cladding (the sensing liquid). \(S_{w}\) depends on the distribution of the optical field in the test fluid, i.e., the integral share of the light in the test liquid. \(\eta\) represents the cladding optical field energy divided by the total energy. \(\eta\) is affected by the width of both the slab and theslot, which are analyzed respectively. The relationship between the integration ratio and the slot width as well as the relationship between \(S_{w}\) and the slot width are analyzed for the slab widths of 0.1, 0.2, and 0.3 \(\upmu\)m.  
Relationships between \(\eta\) and slot width with different slab sizes are shown in Figure 3a, indicating that when the slot widths vary from 0.2 to 0.9 \(\upmu\)m, the corresponding values of \(\eta\) for slab sizes of 0.1, 0.2, and 0.3 \(\upmu\)m range from 0.76118 to 0.94623, 0.71795 to 0.90513, and 0.67193 to 0.84676, respectively. The value of \(\eta\) reaches 0.94623 when the slot width is 0.9 \(\upmu\)m with slab thickness of 0.1 \(\upmu\)m, surpassing that of the other two slab sizes. Secondly, \(S_{w}\) corresponding to different structures were explored when the slot widths vary from 0.2 to 0.9 \(\upmu\)m. The \(S_{w}\) of the changed slot widths under different slab thicknesses is illustrated in Figure 3b, \(S_{w}\) for slab sizes of 0.1, 0.2, and 0.3 \(\upmu\)m varies from 0.5571 to 0.9532, 0.5127 to 0.8953, and 0.4673 to 0.8000, respectively. It can be concluded that the thinner the slab, the higher the \(S_{w}\). Thus, combined with previous studies, the slab of 0.1 \(\upmu\)m was adopted for further exploration. In brief, it can be concluded that as the slot width keeps increasing, \(S_{w}\) and \(\eta\) are rising. However, with the increase in slot width, the limitation of the optical field decreases, so the structure was adopted with a slab thickness of 0.1 \(\upmu\)m and a slot width of 0.7 \(\upmu\)m for further study. The increase in the value of \(\eta\) means the decreasing limitation of the optical field and larger coupling loss during the coupling process. Hence, the coupling structure was optimized using the finite element method for simulation, and the coupling structure we designed is illustrated in Figure 4a. Subsequently, the normalized output energy (\(I_{out}\)) and \(\eta\) corresponding to the width of waveguide on both sides of slot (w in Figure 4a) were calculated. The results are shown in Figure 4b. When \(\w\) is between 0.15 and 0.65 \(\upmu\)m, the value of \(\eta\) varies from 0.93848 to 0.71262 and \(I_{out}\) increase from 0.69720 to 0.97826. Consequently, it can be obtained that \(S_{w}\) is positively correlated with \(\eta\). To maximize device performance, taking slot parameters the posterior end of oraconaris length (s) = 2 \(\upmu\)m, the fore part of oraconaris length (r) = 0.8 \(\upmu\)m, the length of oraconaris (c) = 75 \(\upmu\)m, the length of the syntaxial waveguide (d) = 25 \(\upmu\)m, the length of coupling point (e) = 135 \(\upmu\)m, the slot width (f) = 0.7 \(\upmu\)m, the slot length (g) = 500 \(\upmu\)m, and the waveguide width on both sides of the slot (w) = 0.25 \(\upmu\)m, the normalized output energy (\(I_{out}\)) of 0.8768 corresponds the value of \(\eta\) = 0.9095. In addition, we calculated \(\eta\) of the structure using a substrate material with a refractive index of 1.33, and the results are illustrated in Figure 5, from which it can be found that with a substrate, the maximum \(\eta\) can only reach up to about 55%, which is lower than that of the suspended structure. Figure 3: (**a**) Relationships between the value of \(\eta\) and the slot width with different slab sizes.