## 3 Results
Figure 5 shows a 5 \(\upmu\)m tolerance range from the optimal value for the MMI length for each of the operating wavelengths in order to achieve normalized power (input power is considered to be 100%) of 70-80% (which is \(\pm\)0.24% of the optimal value). We have great fabrication flexibility thanks to this wide tolerance range. In other words, a large error dimension around \(\pm\)250 nm of the MMI coupler length can be easily handled without significantly reducing the power. These fabrication findings are displayed in Figures 3-5 and can be applied to the prototype test construction to better understand the physical fabrication error of the geometrical parameters (L\({}_{\text{mmi}}\), W\({}_{\text{mmi}}\), and height). Figure 6a,b illustrates the intensity profile of the two-channel SiN MMI demultiplexer device for the operating wavelengths in the XZ plane. When Z = 0 in the input waveguide segment, the light enters and passes through the input taper before entering the MMI section, and Z = 2157 \(\upmu\)m is the point that the two wavelengths split (MMI output). The light propagates through the S-bends separately to the two output ports where Z = 2272 \(\upmu\)m. These figures suggest that the SiN MMI coupler has a longer coupling length compared to the Si MMI coupler, resulting in greater footprint size. Figure 7 illustrates the optical spectrum for the two channels over the C-band range (1535-1565 nm) with a spacing of 20 nm. The data were generated by solving the mode for each wavelength over the C-band with 1 nm intervals and finding the output power for the optimal demultiplexer design. The processing of the data was done by using Python code. As shown in Table 1, the insertion losses, crosstalk, and bandwidth were calculated using Equations (4) and (5) alongside the output power for both ports. The bandwidth was between 16.96 nm and 18.77 nm, the crosstalk was between 23.5 dB and 25.86 dB, and the ILs were between 0.895 dB and 0.936 dB. These findings can be used in a WDM system to double the data bitrate without suffering from crosstalk. For all BPM simulations, the optimal grid sizes for the x, y, and z axes were set to 50 nm and 40 nm, respectively, to achieve high computation accuracy. Figure 5: Normalized power as a function of MMI length. To better emphasize the study on SiN MMI coupling parameters and the physical behavior of the coupling length inside the MMI, we investigated the MMI lengths for four different channel spacings over the C-band window. The chosen spacings were 10 nm, 20 nm, 30 nm, and 40 nm. Table 2 shows the wavelength pair values, their corresponding MMI lengths, and ILs for each output channel. It is clear that as the spacing decreases, the device footprint increases, which should be considered when designing a complex, dense WDM system. \begin{table}
\begin{tabular}{c c c} \hline \hline \(\lambda\) **(nm)** & **1540** & **1560** \\ \hline Port & 1 & 2 \\ Crosstalk (dB) & 23.4 & 25.86 \\ IL (dB) & 0.895 & 0.936 \\ Bandwidth (nm) & 16.96 & 18.77 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Crosstalk, IL and, Bandwidth values. Figure 6: Intensity distributions of the two-channel SiN MMI demultiplexer: (**a**) \(\lambda_{1}\) = 1540 nm (port 1); (**b**) \(\lambda_{2}\) = 1560 nm (port 2). Figure 7: Normalized power as a function of wavelength over the C-band range. We chose to use the 20 nm spacing for this device design because it has a good combination of channel separation and is a relatively compact device. This table varies according to the MMI width. Back reflections are another significant aspect of the MMI coupler. They can be quite harmful to the laser beam source because they can introduce unwanted noise to the system and degrade the signal integrity. In this study, we used SiN material to reduce the MMI coupler self-imaging-related back-reflection power.