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arXiv · 2608.06185

Differentiable eigendecomposition-free RCWA for full-tensor anisotropic photonics

Enbo Yang·Qiang Song·Weiwei Cai
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Abstract

Full-tensor anisotropy transforms rigorous coupled-wave analysis (RCWA) into a large, fully coupled non-Hermitian eigenproblem, making eigendecomposition expensive and difficult to differentiate. We introduce a differentiable, eigendecomposition-free RCWA framework for spatially patterned media with fully coupled permittivity tensors, using boundary fields rather than internal eigenmodes as the layer representation. A boundary-value cascade constructs scattering operators directly from these fields, enabling automatic differentiation and efficient GPU execution. Benchmarks against finite-element and transfer-matrix solutions show close agreement in scattering responses, while automatic-differentiation gradients agree with finite differences and enable topology optimization. At 529 Fourier harmonics, layer construction is 22.8 times faster than conventional eigendecomposition on the same GPU. Our framework offers a general computational route toward scalable forward modeling and inverse design in anisotropic photonic systems.

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Enbo Yang, Qiang Song, Weiwei Cai. 2026-08-06. Differentiable eigendecomposition-free RCWA for full-tensor anisotropic photonics. https://arxiv.org/abs/2608.06185

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