发表机构
Hanyang University; Yale University（汉阳大学; 耶鲁大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对宽带纳米光子逆设计中传统时域实现的内存瓶颈问题，提出奈奎斯特采样时域伴随FDTD方法，通过特定存储和使用方式减少场存储成本，经实验验证该方法能保持梯度保真度并降低内存，为三维纳米光子逆设计提供实用途径。
AI 中文摘要
伴随优化是宽带纳米光子逆设计的基石，但传统时域实现面临严重内存瓶颈，因为它们在每个有限差分时间域（FDTD）时间步都保留正向场历史。本文表明，对于带限设计目标，这种全时间步存储是不必要 的。通过仅在符合奈奎斯特的时间间隔存储正向场，并在反向时间伴随过程中使用由此产生的稀疏场历史，该方法能够在不保留完整正向或伴随场历史的情况下进行实时梯度累积。这种奈奎斯特采样伴随FDTD框架在保持时域伴随优化的双模拟缩放的同时，大幅降低了主要的场存储成本。梯度验证证实，符合奈奎斯特的采样能够以可忽略的误差再现传统全存储伴随梯度，而超出奈奎斯特极限的欠采样会导致混叠引起的梯度退化。在四个二维宽带纳米光子基准和一个全三维超透镜上，该方法在保持梯度保真度和优化器件性能的同时，将主要场存储内存降低了高达107倍。这些结果表明，宽带时域伴随FDTD中的主要内存障碍不是梯度评估 的内在要求，而是冗余时域场存储的结果，为大规模三维纳米光子逆设计开辟了一条实用途径。
英文摘要
Adjoint optimization is a cornerstone of broadband nanophotonic inverse design, but conventional time-domain implementations face a severe memory bottleneck because they retain forward-field histories at every finite-difference time-domain (FDTD) time step. Here, we show that this full time-step storage is unnecessary for broadband design objectives because the underlying fields are band-limited. By storing forward fields only at Nyquist intervals and using the resulting sparse fields during the adjoint pass, the proposed method enables on-the-fly gradient accumulation without retaining full forward-field histories. This Nyquist-sampled adjoint FDTD framework preserves the two-simulation scaling of time-domain adjoint optimization while substantially reducing the dominant field-storage. Because the broadband gradient is evaluated directly in the time domain, with no spectral discretization, the per-iteration cost is independent of the number of frequencies---in contrast to frequency-sampled adjoint formulations, whose cost grows with spectral sampling density. Gradient verification confirms that Nyquist sampling reproduces conventional full-storage adjoint gradients with negligible error, whereas undersampling beyond the Nyquist limit produces aliasing-induced gradient degradation. Across four two-dimensional broadband nanophotonic benchmarks and a fully three-dimensional metalens, the method maintains gradient fidelity and optimized device performance while reducing dominant field-storage memory by more than $100\times$ relative to full-history storage in a prototypical example. These results suggest that the principal memory barrier in broadband time-domain adjoint FDTD is not an intrinsic requirement of gradient evaluation but rather a consequence of redundant temporal field storage, thereby opening a practical route to large-scale three-dimensional nanophotonic inverse design.
Comments36 pages, 8 figures, 2 table and Supporting information, with 1 figure and 4 tables
