# O-Band Grating Couplers Using Silicon Nitride Structures
## 1 Introduction
The experimental outcomes are striking, as the laser emits over 10 mW of continuous wave light at room temperature. Impressively, approximately 10% of this light is effectively directed into the Si\({}_{3}\)N\({}_{4}\) waveguides. This accomplishment highlights the potential of Si\({}_{3}\)N\({}_{4}\) waveguides as a viable stage for integrating semiconductor lasers on a chip, promising significant advancements in integrated photonics technology. When used for testing Si\({}_{3}\)N\({}_{4}\) waveguide signals within a photonic chip, the use of a waveguide converter from Si\({}_{3}\)N\({}_{4}\) to Si can decrease the performance due to a few factors [24; 25]. The difference in the refractive index between Si\({}_{3}\)N\({}_{4}\) and Si can cause mode mismatch and lead to increased coupling losses during the transition [26; 27]. Additionally, the fabrication process and material properties of the waveguide converter can introduce additional losses, such as scattering or absorption, which can further degrade the overall performance [28]. Furthermore, the interface between the Si\({}_{3}\)N\({}_{4}\) waveguide and Si waveguide converter may introduce reflections or mode distortions, affecting signal integrity and transmission efficiency. During the conversion, there is the potential for BR in the system and power degradation, which can affect the accuracy and reliability of the testing results. The need for a waveguide converter from Si\({}_{3}\)N\({}_{4}\) to Si can result in the increased footprint size of the photonic chip. The additional space required for integrating the converter adds complexity and potentially limits the available area for other components or functionalities on the chip. One popular waveguide converter is the mode-size converter [29], which is a device that converts the size of optical waveguide modes. An example of a high-efficiency, wideband fiber-to-waveguide mode-size converter with minimal coupling loss has been validated on nano-scale waveguides on the SOI platform [30]. In this mode-size converter, the goal is to efficiently couple light into a conventional single-mode fiber (SMF) possessing a mode field diameter (MFD) of approximately 9.6 \(\upmu\)m to the nano-scale waveguides with smaller MFD, typically around 500 nm or less [31; 32; 33]. The challenges associated with this mode-size converter include the significant mode mismatch between the larger MFD of the SMF and the smaller MFD of the nano-scale waveguide [34; 35]. This mode mismatch leads to high coupling losses, limiting the efficiency and performance of the converter. To address the challenges mentioned earlier, we propose a GC using Si\({}_{3}\)N\({}_{4}\) on an insulator substrate that operates within the O-band spectrum under a TE polarization mode. The geometric parameters critical for optimal performance were fine-tuned using the finite difference time domain (FDTD) technique to achieve power distribution, modal analysis, and design optimization. This study shows the ability to design an excellent Si\({}_{3}\)N\({}_{4}\) GC with high light efficiency in the O-band spectrum, which can be very useful for testing Si\({}_{3}\)N\({}_{4}\) photonic chips in data center applications.