Modelling and next-value prediction of beam propagation from grating structures using a simplified transformer model

In this study, a simplified transformer model is used to perform next-value prediction on light coupled out from silicon photonics gratings to free space. Finite-difference time-domain (FDTD) simulation is performed to simulate the electric field (E-field) in laser light coupled from gratings with pitches of 0.6, 0.8, 1.0, 1.2, 1.4 and 1.6 µm, to free-space. Only E-field distribution from 0.6 µm is used in model training, and the trained transformer model is used to predict the E-field from the rest of the gratings. Prediction of accuracy up to 92.5% is obtained. The time taken for model training is 1908.4 seconds, which is significantly shorter than the conventional three-dimensional FDTD simulation that takes up to several hours. To further reduce the training time, transformer models can be trained with stepped datasets, but with compromised prediction accuracies. In summary, we demonstrated that the transformer model can be used to perform next-value E-field prediction using minimal training data. The developed and trained transformer model can be integrated to the state-of-the-art FDTD software to further expedite the existing FDTD simulation.