Enhanced Inverse Design of Thin-Film High Reflectors Using a Mixture Density Network and Optimization Framework

Abstract Deep learning (DL) has emerged as a promising tool for photonic inverse design. Despite initial successes in retrieving spectra of modest complexity with near-instantaneous readout, DL-assisted design methods often exhibit lower accuracy compared to advanced optimization techniques and have yet to demonstrate competitiveness in handling spectra of practical relevance. In this work, we introduce a tandem optimization model that integrates a mixture density network (MDN) and a fully connected (FC) network to perform inverse design of practical thin-film high reflectors. The multimodal nature of the MDN provides access to a vast array of candidate designs described by probability distributions, which are iteratively sampled and evaluated by the FC network to facilitate rapid optimization. We demonstrate that the proposed model effectively retrieves the reflectance spectra of 20-layer thin-film structures. Notably, it reproduces high reflectors with periodic structures derived from physical principles with high precision, despite the absence of such information in the training data. Additionally, the model is capable of producing improved designs with extended high-reflectance zones. Our approach combines the high-efficiency advantages of DL with optimization-enabled performance improvements, making it an efficient and on-demand solution for practical inverse design applications.