Research on the Enhanced Application of Artificial Neural Network Models in Photonic Crystal Design

Abstract

 Photonic crystals, owing to their ability to precisely control photonic dispersion and localized fields, are extensively utilized in lasers, sensing, and optical information processing. However, their structural inverse design is highly dependent on numerical solvers such as FDTD and PWE, leading to significant computational demands and lengthy optimization cycles. To overcome this bottleneck, this paper proposes combining backpropagation (BP) artificial neural networks with the plane wave expansion (PWE) method to achieve rapid prediction of the dimensions of two-dimensional GaAs-air triangular lattice photonic crystal microcavities. Firstly, based on the defect-free photonic lattice, a two-dimensional GaAs-air triangular lattice model was established using the plane wave expansion method implemented in MIT Photonic-Bands. Subsequently, on the basis of the photonic lattice with a microcavity, the defect-free lattice was replicated in a 5×5 supercell configuration, and an air column with radius r = 0.01a–0.50a was reintroduced at the center as a defect. Then, after cleaning and rearranging the data using MATLAB, a dataset directly applicable for supervised learning was generated, and a three-layer backpropagation (BP) network was constructed. The hidden layer activation function was selected as tansig, the output layer employed purelin, and the training algorithm used was Levenberg–Marquardt. Twenty samples were used for training, and five samples were used for testing. The results indicate that the network reduced the mean squared error of the validation set to 0.00040637 by the third iteration cycle, achieving a computational speed over three orders of magnitude faster than traditional methods; The best generalization performance on the test set achieved a correlation coefficient R² of 0.99987, with an average relative error maintained at approximately 0.8%, fully replicating the rigorous solutions of the PWE method. This study confirmed the feasibility of BP-ANN for rapid inverse design of photonic crystals, offering a low-cost and highly efficient approach for prototype iteration of complex photonic devices such as lasers and sensors.