Physics-driven tandem inverse design neural network for efficient optimization of UV–Vis meta-devices

Abstract

This paper presents two tandemly stacked forward and inverse deep neural networks to model and optimize cylindrical shaped transmissive meta-atoms for UV–Vis regime. Conventional modeling of these subwavelength meta-atoms calls for repetitive solution of Maxwell equations over each instance of a mesh grid using some high-end commercial EM simulator. In contrast, Deep Learning (DL)-based approaches can significantly expedite this process owing to their abilities to intelligently learn and approximate Maxwell's equations without explicitly solving them, hence anticipating the electromagnetic (EM) response of a given meta-atom within a split-second. Despite of the advantages of DL-based solutions for metasurface design and optimization, dataset collection for training DL models still requires time-tedious conventional approaches. Here, we aim to enhance the learning performance while reducing the dataset requirements and the complexity of the proposed forward and inverse networks by enriching them with more underlying physical facts and substantial knowledge of a particular problem. Therefore, in addition to the list of geometrical parameters of the cylindrical meta-atoms, the proposed forward neural network is also fed with some additional material and physics related parameters as a part of its input, including EM spectral information, material type (dielectric or plasmon), maximum height (based on the fabrication constraints), and period of the cylindrical rod. This results in enhancing the model's performance while utilizing minimum training samples, and predicting the EM transmission amplitude and phase with negligible error tolerance, i.e. MSE: 2.1 × 10−3, for a given dielectric or plasmonic meta-atom at various operating wavelengths (within the targeted regimes). Optimization of such meta-structures is another challenging task that requires hit and trial intuitive guesses, lengthy parametric sweeps and time taking conventional intelligent algorithms. Therefore, an inverse design neural network is stacked behind the trained forward modeling network and their tandem assembly is trained together to predict the best set of dimensions and the most suitable material to achieve the desired response. The inverse design network is also fed with the same additional information including all the aforementioned parameters, as the forward mapping network. In order to assess the impact of incorporating this supplementary problem specific information, a comparative study regarding the number of hidden layers and the amount of training dataset size is carried out for the forward and tandem inverse neural networks. This comparative analysis shows that the loss is greatly decreased, and the networks learns efficiently using the proposed scheme with more knowledge about the problem under consideration. As a result, we show that even with a smaller training dataset and lesser number of hidden layers, the model can realize an appropriate MSE.

Keywords

• Deep learning
• Nano-structures
• Tandem inverse design neural network
• Model reduction