Efficient inverse design of long-wave infrared metalenses: frequency-domain physics-model-informed neural networks

The design of metalenses is often constrained by the prohibitive computational cost of full-wave electromagnetic solvers. To address this, we introduce a design framework termed FD-PINN-M (Frequency-Domain Physics-Model-Informed Neural Network for Metalenses), in which a neural network learns the frequency-domain input-output mapping of the rigorous coupled-wave analysis (RCWA), thereby creating a high-fidelity surrogate model that avoids solving complex partial differential equations (PDEs). The hybrid architecture, comprising a convolutional neural network (CNN) and a multilayer perceptron (MLP), can process both the macroscopic parameters (e.g., wavelength, size) and the microscopic geometric details (the discretized permittivity matrix) at the same time, thus enabling an efficient mapping between structure and optical response. The trained model predicts meta-atom optical responses over 18 times faster on average than the RCWA solver it emulates. Furthermore, the model achieves a prediction accuracy of over 95% on the test set, significantly outperforming conventional data-driven networks, which show prediction errors exceeding 20% on the same task. The framework's physical reliability is confirmed through a finite-difference time-domain (FDTD) simulation of a 200 µm, F/1 (numerical aperture, NA ≈ 0.45) metalens, which shows close agreement with our predictions. This work presents a powerful surrogate modeling strategy that effectively overcomes the challenges of traditional PDE-based Physics-Informed Neural Networks (PINNs) for three-dimensional electromagnetic problems, offering a novel strategy for developing scalable and accurate frequency-domain physics-model-informed neural networks for the intelligent design of metalenses.