Deep Learning Techniques for Lossless and Passive Metasurface Design–a Review

Metasurfaces are powerful tools for manipulating electromagnetic (EM) waves. Their design typically involves macroscopic and microscopic stages, which can be achieved using different techniques including gradient based optimization, lookup tables, or deep learning (DL) approaches. An important advantage of DL techniques is their rapid prediction performance, which is important for dynamic beam shaping scenarios. Herein, we review our recent progress in developing DL techniques for the design of lossless and passive transmissive metasurfaces. For the macroscopic design stage, our DL technique determines an appropriate aperture field that (i) fulfills the desired far-field (FF) specifications such as FF lower and upper masks, and (ii) meets the local power conservation (LPC) constraint with respect to a known incident field (Epstein and Eleftheriades, IEEE Trans. Antennas Propag., vol. 64, 2016). Since building a labeled dataset is challenging when considering these two requirements, unsupervised learning is a natural choice. This requires integrating a forward solver into the DL framework, which computes the aperture field and FF. This then allows us to assess the satisfaction of LPC and FF requirements. (The aperture field can support auxiliary surface waves to redistribute power, thereby satisfying the LPC constraint.) Since the forward solver is part of the DL framework, it needs to be differentiable, allowing its derivatives to be computed either manually or using frameworks such as PyTorch as is the case in our implementation. (If differentiability is not achievable, alternative DL methods like reinforcement learning can be used.) Another aspect of the macroscopic design stage is to ensure that the aperture field remains Maxwellian and that the field variation between adjacent unit cells is sufficiently smooth to be consistent with the local periodicity assumption typically used in the microscopic design stage. To this end, our approach trains the neural network to generate the so-called synthetic source arrays, which serves as an auxiliary step to compute the required aperture field before being discarded. This method offers two key advantages: (1) the aperture field is inherently Maxwellian and (2) its smoothness can be controlled to some extent. We have noticed that our neural network may get stuck in LPC local minima, thus, degrading FF performance. To resolve this, we have implemented a dynamic weighting strategy, which starts with a low LPC weight and gradually increases it to a baseline value.

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