Diffusion model-based inverse design of photonic crystals for customized refraction.

Photonic crystals (PhCs) have demonstrated great potential for use in integrated photonic systems. However, traditional design methods often struggle with low efficiency and limited flexibility. While deep learning approaches offer innovative solutions for the inverse design, existing generative models like generative adversarial network and variational autoencoders still face challenges such as training instability or excessive noise. Here, a novel generative design framework based on the diffusion model is presented to achieve the inverse design of high-precision and customized refraction structures. A comprehensive dataset consisting of operating frequency, refracted angles and corresponding structure patterns is constructed by calculating the equifrequency contours of various PhCs at a resolution of 64 × 64. Based on this dataset, customized PhC structures are successfully generated by using a diffusion model combined with the U-Net model. This design can predict cell patterns with allowable incident and refraction angles ranging from 0°∼80° and -80°∼80°, respectively. And if the types of structures in the dataset are increased, the solution space can be further expanded. A normalized design approach ensures adaptability to multi-scale scenarios. Finite-difference time-domain simulations and numerical analysis indicate that 85 % of the 1000 tested refracted angle errors measured by L2-norm are below 0.1. Such strong correlation between targets and simulated results demonstrates the high stability and precision of our diffusion model-based approach, which may provide a promising avenue for the automated inverse design of photonic devices.