# O-Band Multimode Interference Coupler Power Combiner Using Slot-Waveguide Structures
## 3 Simulation Results
Thus, by solving the taper mode, the suitable length was found and its value was 50 \(\upmu\)m with a normalized power of more than 97.5% of the total power. Figure 5a shows the light intensity profile of two Gaussian TE fields at the signal of 1.31 \(\upmu\)m at the x-z plane. The Gaussian source was set to be 50% of the total laser power level. It can be noted that the light intensity was combined from two sources to one source at z = 59.81 \(\upmu\)m. The selected gap between the two input laser sources ensured there was no  
Figure 4: Optimizations of the waveguide taper length. Figure 3: Normalized power as a function of the MMI combiner coupler key parameters: (a) \(W_{\text{MMI}}\) (b) L\({}_{\text{MMI}}\). light coupling between them, as can be seen in Figure 5a in the input taper section. After a short light coupling of 109.81 \(\upmu\)m, the combiner efficiency reached 97.6% from the total input power coming from the two sources, as shown in Figure 5b. Thus, the insertion loss could be calculated using Equation (4) at 1310 nm wavelength and the power loss value was only 0.105 dB. Figure 6 shows the normalized power as a function of the wavelength over the O-band spectrum, and it can be seen that a high combiner efficiency range of 94.8-97.6% from the total power was obtained. The wavelength tolerance range over the O-band was 1280 to 1330 nm, which is suitable to transmit more than 96.3% of the total power, as shown in Figure 6. Thus, the proposed combiner could easily handle the laser wavelength drift effect, and heat emissions during the natural working process of a laser. Therefore, this coupler could be suitable for combining lasers and worrying less about the wavelength drift effect over the O-band range. The back reflection coming back from the MMI coupler into the laser source is an undesirable phenomenon because of its potential to amplify noises in the laser system. The back reflection can happen because of the self-imaging mechanism and the high index differences between the index waveguide material and the cover index material. However, in our design, the back reflection was not an issue thanks to SiN slot waveguide technology combined with waveguide tapers, which can easily deal with the reflections coming from the MMI coupler and the SiO\({}_{2}\) cover area. To demonstrate the advance of using this technology, a FDTD simulation was done to calculate the power back reflection of the proposed combiner at the wavelength of 1310 nm. Figure 7a shows the schematic sketch of the FDTD simulation setup, which includes the full 2 \(\times\) 1 combiner design with an additional SiN waveguide segment that is used for setting the monitor. This monitor collects the light reflections coming back into the input waveguide tapers, as shown in Figure 7a. The grid size for all dimensions (\(x\)-axis, \(y\)-axis, \(z\)-axis) was set to 10 nm for obtaining good accuracy in the mesh calculation. Figure 5: 2 \(\times\) 1 combiner intensity light propagation profile under TE mode: (a) plane x-z; (b) \(z\)-axis. In our design, reflections could be produced at the boundaries between the cover area and the SiN slab area, and as a side effect of the self-imaging. From the analysis of the FDTD result, the power back reflection was found and its value was 44.94 dB. Figure 7b shows the power back reflection in dB units as a function of cT. The cT is defined as the light propagation direction, which in our case was the \(z\)-axis. As expected, the proposed device did not suffer from the back reflection effect, thus there was no need for a complex MMI coupler design such as an angled MMI coupler to overcome the back reflection losses [15]. To understand and study the advantages of this design, we compared the proposed combiner design to other combiner devices that were previously published. As shown in Table 1, the main characteristics of the power combiners were compared including dimension (length \(\times\) width), number input of sources (number of sources), operation wavelength band, insertion, loss, and back reflection.