Physics-constrained neural networks for surrogate modeling of lossless periodic structures

2026-06-26

AI Summary

This work addresses the high computational cost of conventional rigorous coupled-wave analysis (RCWA), which hinders its use in optical inverse design requiring efficient surrogate models. The authors propose a physics-constrained neural network that models RCWA outputs as Jones matrices and, for the first time, enforces energy conservation in lossless periodic structures as a hard constraint. By employing differentiable symmetric orthogonalization, the network’s output is rigorously confined to the Stiefel manifold, ensuring both physical consistency and gradient differentiability. This approach dramatically improves simulation efficiency and enables rapid, energy-conserving surrogate modeling, as demonstrated in the inverse design of diffractive waveguide combiners for augmented reality eyewear.

Abstract

We introduce a physics-constrained neural network (PCNN) for the rapid prediction of rigorous coupled-wave analysis (RCWA) outputs in the form of Jones matrices. Starting from energy conservation in lossless layered periodic structures, we use the fact that RCWA outputs lie on a Stiefel manifold. This energy constraint is enforced as a hard condition by projecting onto the manifold using differentiable symmetric orthogonalization. The resulting surrogate enforces energy conservation by construction while preserving differentiability for gradient-based inverse design. The performance and generality of the proposed approach are demonstrated through the inverse design of a diffractive waveguide combiner for augmented reality glasses.

Problem

• physics-constrained neural networks
• surrogate modeling
• lossless periodic structures
• energy conservation
• Stiefel manifold

Innovation

• physics-constrained neural network
• Stiefel manifold
• energy conservation
• differentiable surrogate modeling
• inverse design