Meent: Differentiable Electromagnetic Simulator for Machine Learning

TL;DR

Meent introduces a Python-native differentiable electromagnetic simulator based on RCWA to fuse EM modeling with machine learning. It provides automatic differentiation, supports both raster and vector geometry, and offers backends in NumPy, JAX, and PyTorch, enabling end-to-end ML workflows in optics. The authors demonstrate three ML-enabled use cases—neural operators for field prediction, model-based RL for metasurface design, and gradient-based inverse problems in OCD metrology—highlighting improved data efficiency, surrogate capability, and practical invertibility. The work is positioned as a versatile platform that accelerates design, optimization, and analysis in computational optics, with code available under MIT license on GitHub.

Abstract

Electromagnetic (EM) simulation plays a crucial role in analyzing and designing devices with sub-wavelength scale structures such as solar cells, semiconductor devices, image sensors, future displays and integrated photonic devices. Specifically, optics problems such as estimating semiconductor device structures and designing nanophotonic devices provide intriguing research topics with far-reaching real world impact. Traditional algorithms for such tasks require iteratively refining parameters through simulations, which often yield sub-optimal results due to the high computational cost of both the algorithms and EM simulations. Machine learning (ML) emerged as a promising candidate to mitigate these challenges, and optics research community has increasingly adopted ML algorithms to obtain results surpassing classical methods across various tasks. To foster a synergistic collaboration between the optics and ML communities, it is essential to have an EM simulation software that is user-friendly for both research communities. To this end, we present Meent, an EM simulation software that employs rigorous coupled-wave analysis (RCWA). Developed in Python and equipped with automatic differentiation (AD) capabilities, Meent serves as a versatile platform for integrating ML into optics research and vice versa. To demonstrate its utility as a research platform, we present three applications of Meent: 1) generating a dataset for training neural operator, 2) serving as an environment for the reinforcement learning of nanophotonic device optimization, and 3) providing a solution for inverse problems with gradient-based optimizers. These applications highlight Meent's potential to advance both EM simulation and ML methodologies. The code is available at https://github.com/kc-ml2/meent with the MIT license to promote the cross-polinations of ideas among academic researchers and industry practitioners.

Figures (30)

• Figure 1: Summary. Simulation Algorithm depicts the process flow of electromagnetic simulation algorithm, namely RCWA, in meent. Applications present the most representative problems that meent can be utilized.
• Figure 2: Characteristics of each modeling type. In each subfigure, the left side depicts raster while the right side depicts vector. (a) illustrates how the geometry is formed by each method. (b) presents a schematic diagram highlighting the difference between the topological derivative (left) and shape derivative (right). (c) The area enclosed by the blue double line denotes the codomain, while the red dots on the left and red area on right represent the range.
• Figure 3: Metagrating and its abstract representations. (a) An example of metagrating sized 16 cells, where the grating layer is bounded by air and glass layers. The grating pattern periodically repeats along x axis and all layers remains constant along y axis. (b) Abstract matrix representation $u\in {\{1, -1\}}^{k\times k}$, the front view of metagrating. (c) Array representation of the grating pattern, $g\in {\{1, -1\}}^{k}$.
• Figure 4: FNO's approximation of Maxwell's equation. (a) Real part of electric field distribution, of ground truth and prediction from FNO. (b) Test result on higher resolutions of fields, 512$\times$512 and 1024$\times$1024. The models were trained on 256$\times$256 resolution.
• Figure 5: Learning curve across 3 random seeds. Historical maximum efficiencies during training phase are plotted.