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.

在这项研究中，使用了一个简化的变压器模型来预测从硅光子学光栅耦合到自由空间的光线的下一个值。通过有限差分时域（FDTD）模拟，仿真了由间距为0.6、0.8、1.0、1.2、1.4和1.6 µm的光栅耦合出的激光光的电场（E-field）。模型训练中仅使用了来自0.6 µm间距光栅的电场分布，而经过训练的变压器模型被用来预测其余光栅的电场。达到了高达92.5%的预测准确率。模型训练所花费的时间为1908.4秒，这比传统的三维FDTD模拟所需的时间要短得多，后者可能需要数小时才能完成。为了进一步缩短训练时间，可以使用阶梯数据集对变压器模型进行训练，但这样会牺牲一定的预测准确性。总之，我们证明了变压器模型可以在仅用最少的训练数据的情况下用于电场下一个值的预测。开发和训练出的变压器模型可以集成到最先进的FDTD软件中，以进一步加速现有的FDTD模拟。