Adjoint method in machine learning: A pathway to efficient inverse design of photonic devices

Abstract

Innovative machine learning techniques have facilitated the inverse design of photonic structures for numerous practical applications. Nevertheless, the quantity of data and the initial data distribution are paramount for the discovery of highly efficient photonic devices. These devices often require simulated data ranging from thousands to several hundred thousand data points. This issue has consistently posed a major hurdle in machine learning-based photonic design problems. Therefore, we propose a new data augmentation algorithm grounded in the adjoint method, capable of generating more than 300 times the amount of original data while enhancing device efficiency. The adjoint method forecasts changes in the figure of merit (FoM) resulting from structural perturbations, requiring only two full-wave Maxwell simulations for this prediction. By leveraging the adjoint gradient values, we can augment and label several thousand new data points without any additional computations. Furthermore, the augmented data generated by the proposed algorithm displays significantly improved FoMs. We apply this algorithm to a multi-layered metalens design problem and demonstrate that it consequently exhibits a 343-fold increase in data generation efficiency. After incorporating the proposed algorithm into a generative adversarial network, the optimized metalens exhibits a maximum focusing efficiency of 92.93%, comparable to the theoretical upper bound.