## 4 Optimization of LT-MZI Structure  
In this section, the LT-MZI structure undergoes optimization to ascertain the spectral characteristics of the device. At this stage, the LT-MZI structure is examined in its bare form, devoid of any PHMB polymer covering on the sensing arm, and lacks an upper cladding in this particular configuration. Initially, the impact of variations in \(\mathrm{L_{DC}}\) on both interference dips and the free spectral range (FSR) is thoroughly investigated which is a fundamental parameter that defines the spacing between consecutive resonance frequencies within the device. It represents the spectral range over which the resonator can operate without encountering spectral overlap between adjacent resonances. Essentially, the FSR determines the resolution or spacing capability of the resonator's spectral response. It is  
Figure 2: Transmission of a directional coupler segment versus \(\mathrm{L_{DC}}\) for waveguide width (w) of (a) 250 nm, (b) 260 nm, (c) 270 nm, and (d) 280 nm. The normalized H-field distribution in the directional coupler for (e) \(\mathrm{L_{DC}}\) = 4 \(\mathrm{\SIUnitSymbolMicro\meter}\) and (f) \(\mathrm{L_{DC}}\) = 3 \(\mathrm{\SIUnitSymbolMicro\meter}\). Note: The gap between the waveguides is fixed at 100 nm. Red and black lines represent the output power at Output-1 and Output-2, respectively. Whereas the green dashed line indicates the equal power distribution at both output port. typically influenced by various factors such as the physical dimensions of the resonator, including its length, width, and height, as well as the refractive index of the material. Interference dips, a key aspect in MZI structures, signify instances where the output intensity of the interferometer diminishes due to interference between the two optical paths. L\({}_{\text{DC}}\) is varied between 3 \(\upmu\)m and 6 \(\upmu\)m, whereas the other geometric parameters such as w, g, and L are fixed at 250 nm, 100 nm, and 5 \(\upmu\)m, respectively. The transmission of the device is plotted by utilizing the expression \(Transmission\)\((dB)=10\times log\Big{(}\frac{P_{\text{out}}}{P_{\text{in}}}\Big{)}\), where P\({}_{\text{out}}\) and P\({}_{\text{in}}\) are the output and input power, respectively. From Figure 3a-g, it is evident that as L\({}_{\text{DC}}\) increases from 3 \(\upmu\)m to 6 \(\upmu\)m, the FSR of the device decreases from 90 nm to 57 nm, accompanied by a noticeable blueshift in the dips. The extinction ratio (ER) of the device ranges from 19 dB to 27 dB, indicating a robust destructive interference resulting from the interaction of two light waves with opposite phases. For further investigation, L\({}_{\text{DC}}\) is fixed at 6 \(\upmu\)m, which provides a good transmission characteristic in the desired wavelength range. The width (w) of the waveguide in integrated photonic sensors plays an important role in defining the sensitivity of the device. As w approaches the cut-off, even slight variations in factors like material properties, dimensions, or the presence of external elements can cause noticeable alterations in its transmission characteristics. This heightened sensitivity is advantageous for sensing applications because it enables the detection of subtle changes in the environment with greater precision. Consequently, designing a waveguide near the cut-off can enhance the sensitivity of sensors based on waveguide principles, making them more effective for detecting changes in parameters such as temperature, pressure, or chemical composition. The impact of w on the FSR of the device, spanning from 250 nm to 270 nm is determined, as illustrated in Figure 4a-c. While keeping other geometric parameters such as L\({}_{\text{DC}}\), g, and L constant at 6 \(\upmu\)m, 100 nm, and 5 \(\upmu\)m, respectively, a notable trend is observed. Specifically, the FSR exhibited a discernible rise from 57 nm to 92.5 nm with an increment in w from 250 nm to 270 nm.