发表机构
Stanford University; University of California, Berkeley（斯坦福大学; 加州大学伯克利分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文首次将预计算数值格林函数方法用于纳米光子逆向设计，通过线性成本计算和低秩更新实现亚毫秒迭代，设计时间加速超三个数量级，可秒级设计新器件。
AI 中文摘要
逆向设计在纳米光子学中具有变革性，提供了一种自动化实现高性能、非直观器件的方法。然而，现有逆向设计方法的主要瓶颈在于其依赖耗时且计算成本高昂的全波电磁仿真。在本工作中，我们首次将预计算数值格林函数（PNGF）方法扩展到纳米光子逆向设计，将正向问题的评估加速多个数量级，且与全波解相比无精度损失。在单次完全可并行的预计算步骤之后，目标函数及其梯度均可通过简单计算进行评估，其成本随设计区域大小线性增长。一种低秩矩阵更新技术进一步降低了目标函数评估的成本，使得每次迭代的计算时间达到亚毫秒级。使用基于梯度的水平集优化和瓦片翻转直接二进制搜索的设计示例，在设计时间上通常实现超过三个数量级的加速，从而形成一个超快光子逆向设计平台，可在数秒内从零开始设计新器件。
英文摘要
Inverse design has been transformative in nanophotonics, providing an automated means of realizing high-performance, non-intuitive devices. However, the primary bottleneck of existing inverse design approaches is their reliance on time-consuming and computationally expensive full-wave electromagnetic simulations. In this work, we extend the Precomputed Numerical Green Function (PNGF) method for the first time to nanophotonic inverse design, accelerating evaluation of the forward problem by multiple orders of magnitude with no loss in accuracy compared to the full-wave solution. After a single, fully parallelizable precomputation step, both the objective function and its gradient can be evaluated through simple calculations whose cost scales linearly with the size of the design region. A low-rank matrix update technique further reduces the cost of objective function evaluation, yielding sub-millisecond computation times per iteration. Design examples using both gradient-based level-set optimization and tile-flipping direct binary search often achieve more than three orders of magnitude speedup in design time, resulting in an ultrafast photonic inverse design platform that can design new devices from scratch in seconds.
