Deep neural networks with adaptive solution space for inverse design of multilayer deep-etched grating

This article presents an inverse design technique of multilayer deep-etched grating (MDEG) using a deep neural network with adaptive solution space. MDEG is a key component in multispectral imaging, significantly affecting the quality of acquired multispectral images. Inverse design problems with one-to-many mappings from an optical response to multiple structures of MDEG have been addressed using machine learning techniques. Prior efforts, such as the tandem network and convolutional neural network (CNN), approached the problem from a modeling perspective. In this proposed method, a deep neural network is trained using cross-entropy loss for inverse design, predicting the probability distribution across the discretized space. The solution space is then formed by selecting the top K values with the highest probability, enabling evaluation of an optimal solution using the forward modeling network and avoiding the challenges of one-to-many mapping problems. Given the scarcity of optical training data, we explore training the network with reduced datasets of 30,000, 50,000 and 100,000 samples, demonstrating that the network performs well with a small amount of training data. Computational experiments conducted on the generated test dataset demonstrate that the proposed method improves in-band and out-of-band efficiencies by 26% and 12%, respectively, using only one-third of the required data.