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

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.