Elucidating the Design and Behavior of Nanophotonic Structures through Explainable Convolutional Neural Networks

A central challenge in the development of nanophotonic structures and metamaterials is identifying the optimal design for a sought target functionality, and understanding the physical mechanisms that enable the optimized device's capabilities. To this end, previously investigated design methods for nanophotonic structures have encompassed both conventional forward and inverse optimization approaches as well as nascent machine learning (ML) strategies. While in principle more computationally efficient than optimization processes, ML-based methods that are capable of generating complex nanophotonic structures are still 'black boxes' that lack explanations for their predictions. Motivated by this challenge, in this article we demonstrate that convolutional neural networks (CNN) trained to be highly accurate at forward design, can be explained to derive physics-driven insights by revealing the underlying light-matter relationships learned by network. We trained a CNN model with 10,000 images representative of a class of metal-dielectric-metal metamaterial resonators and their corresponding absorption spectra obtained from simulations. The trained CNN predicted the spectra of new and unknown designs with over 95% accuracy. We then applied the Shapley Additive Explanations (SHAP) algorithm to the trained model to determine features that made positive or negative contributions towards specific spectral points, thereby informing which features to create or eliminate in order to meet a new target spectrum. Our results reveal that the physical relationships between a nanophotonic structure and its electromagnetic response can be obtained - and new designs can be achieved - by exposing the valuable information hidden within a machine learning algorithm.