Transformer-based acceleration for near-field 3D simulation of optical beams from silicon photonic gratings

With the continuous development of integrated silicon photonics (SiPh) gratings, more and more studies have used them for optical addressing of trapped ions. However, the ion trapping height decreases as the grating size decreases and eventually falls into the near-field range. To obtain a high-precision 3D electric field, the traditional finite-difference time-domain (FDTD) simulation consumes a lot of time and computer memory. In this study, we use a simplified transformer model to accelerate the simulation of high-precision electric fields starting from low-precision electric fields. The model is trained using FDTD-generated data from a grating with a 60 µm radius and then applied to predict electric fields from gratings with radii of 15, 20, 30, and 40 µm. The model training took about 30 min, and using parallel processing, the entire high-precision 3D electric field prediction with the arithmetic power of two RTX4090 only took about 2 h, compared to more than 12 h for a high-precision FDTD simulation. The predicted field distributions closely match the high-precision FDTD results, with overall average percentage errors well below 10% and errors in the critical focused regions maintained between 0% and 2%.