  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.
