Efficient multi-objective design method for optical coatings

•An efficient adaptive multi-objective design method for optical coating design is proposed.•The spectrum, group delay dispersion, and electric field distribution performances are improved simultaneously, achieving higher laser-induced damage threshold.•Gradient based algorithm and Deep learning method are employed to improve the design's universality and efficiency. The modern design of high-performance optical coatings demands a comprehensive consideration of multiple properties. We propose an efficient multi-objective optimization method utilizing an adaptive weighted sum method, exploring the lexicographic optimization and geometry-based adaptive weights determination method. Broadband negative dispersive mirrors have been designed that demonstrates notable improvements in performances of spectrum, group delay dispersion and electric field distribution. In addition, we employ Deep-learning method to enhance the optimization. The mapping between different design parameters and results has been learned, which helps the optimization to directly approach the optimal design. It extends the novel method to diverse designs utilizing the similar kinds of merit functions and subsequently accelerates the design by 120 times.