AI 中文总结
该博士论文针对超表面逆向设计面临的难题，分三阶段应对。先评估求解器可靠性，再用局部相位近似等消除计算瓶颈，最后在通用协议下测试三种策略，通过多种方法提升超表面设计的保真度，实现多样且抗制造误差的设计。
AI 中文摘要
超表面是亚波长纳米柱的二维排列，可对光的相位进行局部控制，实现超越传统折射元件的平面光学功能。其逆向设计面临设计空间维度巨大和严格电磁模拟成本高昂的问题，无法在器件尺度上进行详尽探索。本论文分三个阶段应对这一挑战。第一阶段评估严格麦克斯韦求解器的可靠性：比较RCWA中Li因式分解规则的三种实现方式，发现光谱收敛并不保证物理保真度。FDTD不受此类伪影影响，被用作整个过程的基准。第二阶段消除计算瓶颈：局部相位近似模型及在大尺寸柱形超表面的FDTD模拟上训练的全卷积替代模型能几乎即时预测近场。利用问题对称性使训练数据库增加四倍，替代模型可推广到更大孔径且保持可微性。第三阶段在通用FDTD协议下对三种策略进行基准测试：Gerchberg - Saxton检索和局部模型（\(R^2\approx0.925\)）、基于替代模型和启发式初始化的梯度下降（\(R^2\approx0.975\)）以及基于扩散模型和薛定谔桥的生成框架。混合后验采样和幅度约束可在比训练尺寸大230倍以上且具有多样、抗制造误差设计特征的表面上恢复尺度不变保真度。数据库增强将每种方法提升到\(R^2\approx0.97\)。
英文摘要
Metasurfaces, two-dimensional arrangements of subwavelength nanopillars, provide local control over the phase of light, enabling flat optical functions beyond conventional refractive components. Their inverse design, finding the pillar distribution producing a target response, faces two obstacles: the immense dimensionality of the design space and the prohibitive cost of rigorous electromagnetic simulations, precluding exhaustive exploration at device scale. This thesis addresses the challenge in three stages. The first assesses the reliability of rigorous Maxwell solvers: comparing three implementations of Li's factorization rules for RCWA shows that spectral convergence does not guarantee physical fidelity, as these rules implicitly distort the simulated permittivity, most severely in the plasmonic regime. FDTD, immune to such artifacts, is retained as ground truth throughout. The second stage removes the computational bottleneck: a local phase-approximation model, then fully convolutional surrogates trained on FDTD simulations of large pillar metasurfaces, predict the near field almost instantaneously. Exploiting problem symmetries quadruples the training database, and the surrogates generalize to much larger apertures while remaining differentiable. The third stage benchmarks three strategies under a common FDTD protocol ($R^2$ between realized and target far fields): Gerchberg-Saxton retrieval and Local Model ($R^2\approx0.925$), surrogate-based and heuristic-initialized gradient descent ($R^2\approx0.975$), and a generative framework based on diffusion models and Schrödinger bridges. Hybrid posterior sampling and amplitude constraints restore scale-invariant fidelity on surfaces over 230 times larger than training, with diverse, fabrication-tolerant designs. Database enhancement lifts every approach to $R^2\approx0.97$.
