Inverse Design of Photonic Crystal Waveguides Using Neural Networks and Dispersion Optimization

Abstract: Photonic crystal waveguides (PCWs) play a critical role in precisely controlling light propagation, enabling high-performance functions in applications such as optical communication and integrated photonics. The design of PCWs traditionally relies on complex numerical methods, including finite-difference time-domain (FDTD) and plane-wave expansion (PWE) methods, which are often inefficient when dealing with high-dimensional parameter spaces, particularly for subwavelength structures. To overcome these challenges, a convolutional neural network (CNN)-based inverse design method is introduced to optimize the structural parameters of PCWs. By simulating band structures under varying line defect widths and air hole radii using MIT Photonic Bands (MPB), a large dataset was generated, mapping structural parameters to corresponding band characteristics. Backpropagation neural networks (BPNN) and CNN models were trained on this dataset to predict key PCW structural parameters. The CNN model demonstrated superior performance in predicting complex geometries, maintaining high accuracy even when extrapolating beyond the training dataset, with precision up to four decimal places. In contrast, the BPNN model exhibited faster training times and higher computational efficiency on smaller datasets, though it performed less effectively on larger datasets. Cross-validation using MPB confirmed the generalization capability and reliability of both models. This study highlights the potential of deep learning techniques in photonic device design, particularly for advancing the development of high-efficiency, low-loss components in integrated photonics and optical communication systems.