Diffusion Schr\"odinger Bridges with enhanced posterior sampling for metasurface inverse design

Abstract

Metasurface inverse design is challenged by the intricate relationship between structural parameters and electromagnetic responses, as well as the high dimensionality of the optimization space. Local models, while commonly employed, quickly become infeasible for complex and locally coupled structures. Conventional iterative optimization techniques, on the other hand, are computationally intensive, time-consuming, and susceptible to convergence in local minima. This study explores a versatile generative methodology based on enhanced posterior sampling within the Schr\"odinger Bridge framework. By decomposing posterior sampling into amplitude and directional contributions, we effectively integrated different kind of posterior sampling. This approach is further supported by refined training strategies to enhance performance and reduce the complexity of hyperparameter optimization. The proposed framework demonstrates exceptional accuracy and robustness, representing a significant advancement in metasurface design. Notably, it enables high-precision inverse design for large-scale configurations of up to $350 \times 350$ pillar arrays, despite being trained on significantly smaller arrays of $23 \times 23$ pillars.