Silicon photonics and integrated optical circuits are pivotal technologies in the post-Moore era, enabling high-speed and low-latency applications. However, the efficient coupling of optical signals from photonic chips to optical fibers remains a significant challenge due to the mismatch in fiber and waveguide dimensions. Grating Couplers (GCs) present a promising solution due to their flexible coupling position selection, compact structure, and ease of wafer-level testing. This paper aims to design a high-efficiency, compact, and cost-effective GC using shape optimization theories and methods to provide an excellent interconnect solution for silicon photonic chips. This paper designs a double-layer grating coupler with different grating teeth and slots formed through two etching processes, enhancing the coupler's directionality. To address the challenge of local optima during the optimization process and enhance the probability of finding the global optimal solution, a random perturbation method is employed to generate a series of initial devices that are uniformly distributed in the solution space. Each element of the parameter vector undergoes random addition or subtraction of a uniformly distributed random number, ensuring that each element is randomized in the same manner, independent of its position in the vector. This approach promotes a more comprehensive exploration of the solution space and facilitates the identification of the global optimal solution. To overcome the inefficiency of optimizing multiple devices simultaneously due to noise addition, a parameter update rate regulation strategy is introduced to accelerate the optimization process. During the initial optimization stage, a larger update rate alpha is employed to achieve rapid convergence. However, as the iteration progresses, alpha is gradually decreased to prevent missing the global optimal solution. This cosine decay strategy allows for swift exploration of the solution space during the early stages of optimization while enabling refined parameter adjustment in the later stages, thereby increasing the likelihood of converging to the global optimal solution. Compared to other decay methods, this strategy demonstrates superior performance in parallel optimization of multiple devices. The adjustment strategy for the update rate is crucial for the design of the optimization algorithm, as it requires balancing convergence speed and stability to ensure efficient and accurate identification of the global optimal solution. The cosine decay strategy not only ensures the stability of model training but also enhances the search capability for the global optimal solution. The decay path of the update rate follows the characteristics of the cosine function, experiencing a rapid decline in the initial stage to capture the preliminary optimization direction and a gradual decline in the later stages for fine-tuning parameters, thereby improving the precision of locating the global optimal solution. The introduction of a dynamic parameter update rate in the shape optimization algorithm primarily involves larger update steps in the early stage and smaller steps in the later stage. This dynamic adjustment offers two main improvements over static updates: rational control of iteration count, reducing the time cost of optimization, and rapid convergence and elimination of instability, facilitating swift convergence in the early stage and preventing instability in later stages. By employing this optimized parameter update rate regulation strategy, the shape optimization algorithm for grating couplers effectively explores the solution space and converges to the global optimal solution with high efficiency and accuracy. The specific steps are as follows: establishing a parametric model of the double-layer grating coupler and forming a parameter vector by recording vertex coordinates; generating a series of initial devices uniformly distributed in the solution space through random perturbation; introducing a parameter update rate regulation strategy, adopting a larger update rate initially for rapid convergence and gradually decreasing it later to avoid missing the global optimal solution; obtaining a grating coupler structure that meets the design conditions through iterative optimization. The designed double-etched grating coupler achieves a high coupling efficiency of 0.887 in the C band with a 3 dB bandwidth of 28 nm. Compared to recently reported silicon-based grating couplers, this design achieves the highest known coupling efficiency on a 220 nm thick SOI platform without the need for additional material layers. In the case of a 10 nm etching depth error, experimental testing results show that the peak single-port coupling efficiency of the double-etched grating coupler is -3.62 dB (43.5%) at 1 548 nm. The proposed design method can achieve a high-efficiency, compact, and cost-effective grating coupler, providing an excellent interconnect solution for silicon photonic chips and offering new insights into the design and application of grating couplers.
