Deep Convolutional Neural Networks to Predict Mutual Coupling Effects in Metasurfaces

Metasurfaces have provided a novel and promising platform for the realization of compact and large-scale optical devices. The conventional metasurface design approach assumes periodic boundary conditions for each element, which is inaccurate in most cases since the near-field coupling effects between elements will change when surrounded by non-identical structures. In this paper, we propose a deep learning approach to predict the actual electromagnetic (EM) responses of each target meta-atom placed in a large array with near-field coupling effects taken into account. The predicting neural network takes the physical specifications of the target meta-atom and its neighbors as input, and calculates its phase and amplitude in milliseconds. This approach can be applied to explain metasurfaces' performance deterioration caused by mutual coupling and further used to optimize their efficiencies once combined with optimization algorithms. To demonstrate the efficacy of this methodology, we obtain large improvements in efficiency for a beam deflector and a metalens over the conventional design approach. Moreover, we show the correlations between a metasurface's performance and its design errors caused by mutual coupling are not bound to certain specifications (materials, shapes, etc.). As such, we envision that this approach can be readily applied to explore the mutual coupling effects and improve the performance of various metasurface designs.