AI 中文总结
本文提出首个支持自动微分与GPU加速的各向异性严格耦合波分析框架，通过精细积分法构造散射矩阵避免本征分解，实现25倍加速，可用于各向异性光子结构的正向分析与逆向设计。
AI 中文摘要
对于具有完整介电张量和磁导率张量以及任意取向光轴的周期性光子结构，我们提出了据我们所知首个支持自动微分和高效GPU加速的各向异性严格耦合波分析框架。该方法将层内传播表述为边值问题，并采用精细积分法直接构造散射矩阵，从而避免了大型非厄米矩阵的本征分解。在精度相当的情况下，所提方法比基于本征分解的方法实现了25倍的加速。其与自动微分的兼容性进一步证明了其在各向异性光子结构拓扑优化中的巨大潜力，该框架为复杂各向异性器件的正向分析与逆向设计提供了高效计算工具。
英文摘要
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.
