# O-Band Grating Couplers Using Silicon Nitride Structures
## 3 Simulation Results
These findings provide valuable insights incorporated within the exact design criteria that are essential for attaining the intended GC performance, encompassing study manufacturing processes. Figure 6 provides a detailed analysis of the coupling efficiency in relation to the angle of the SMF, which is located at a distance of 2.6 \(\upmu\)m from the GC, specifically focusing on an operational wavelength of 1310 nm. The angle, denoted as \(\theta\), has been meticulously chosen to optimize the coupling efficiency between the GC and SMF. By utilizing the principles of Bragg conduction, alongside the FDTD simulations, the optimal angle has been found to be 7.5 degrees, as shown in Figure 6. Additionally, the figure also showcases a tolerance range spanning from 6.6 to 8.6 degrees. This range is particularly noteworthy as it demonstrates that even within this wide span of angles, the coupling efficiency is over  
Figure 4: Coupling efficiency as a function of etch depth. Figure 5: Coupling efficiency as a function of thickness: (a) T\({}_{\text{SiO}_{2}}\), (b) T\({}_{\text{Si}_{3}\text{N}_{4}}\). 24%. This observation further emphasizes the robustness and effectiveness of the proposed design technology. Figure 7 illustrates the scattered light within the GC directed towards the SMF at the x-z cross-section. The associated simulation depicts the intensity profile of the light being transmitted through the GC. A red arrow indicates the direction of the input signal, pointing towards the GC structure denoted by a white arrow, while a green arrow symbolizes the SMF. When examining the graph, it is evident that when the laser source transmits, the light scatters through the grating structure. Some of the light is absorbed by the SiO\({}_{2}\) layer, while a portion propagates through the grating. The phenomenon of light transmission through the grating can be observed in the middle of the graph where wave patterns emerge. These waves exhibit varying intensities, ranging from 0 (gray) to 1 (light blue), with the light blue color indicating higher intensity. Figure 6: Coupling efficiency with respect to the angle from the SMF. Figure 7: Description of the intensity light propagation from the GC into the SMF: (**a**) x-z plane, (**b**) zoom into the GC area. The greater the intensity of these waves, the more light can be captured by the SMF. The process of light scattering through the GC is known as the Bragg effect, where there is a partial matching of phases between the incident wave and the scattered wave. As the waves propagate from the GC towards the SMF, their intensity increases, as indicated by a lighter shade of blue, and the coupling efficiency also improves. This implies that the integral overlap between the mode of the GC and the mode of the SMF increases. To better see the diffracted light coming from the GC into the SMF and the light scattering into the air, a zoom in on Figure 7a is conducted, as shown in Figure 7b. The output electric field from the FDTD monitor was extracted and used as a launch field to simulate and study the physical mechanism of the electric field distribution over the SMF, as shown in Figure 8. It can be seen that strong light confinement is achieved inside the SMF core, which ensures that all the light coupled from the GC can be utilized to test the signals at the output SMF. Figure 9 provides a comprehensive analysis of the coupling efficiency in relation to the SMF location from the GC. The graph illustrates two areas with strong coupling efficiency that can be utilized for the measurement of the chip signal. Additionally, the graph indicates a decrease in the coupling efficiency as h increases, which is clearly expected because of the absorption of the light in the free-space (air) zone. Thus, from a testing view, it will be better to use area 1 or area 2 to obtain good stability for dealing with mechanical errors, such as the shifting or vibrations of the SMF in the optical setup. Area 1 is located where h is between 2.2 and 3 \(\upmu\)m, and \(\theta\) is between 6.6 and 8.6 degrees.