In this work, we investigate the feasibility of applying deep learning to phase synthesis of reflectarray antenna. A deep convolutional neural network (ConvNet) based on the architecture of AlexNet is built to predict the continuous phase distribution on reflectarray elements given the beam pattern. The proposed ConvNet is sufficiently trained with data set generated by array-theory method. With radiation pattern and beam direction arrays as input, the ConvNet can make real-time and fairly accurate predictions in milliseconds with the average relative error below 0.7%. This paper shows that deep convolutional neural networks can ``learn'' the principle of reflectarray phase synthesis due to their inherent powerful learning capacity. The proposed approach may provide us a potential scheme for real-time phase synthesis of antenna arrays in electromagnetic engineering.
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