Title: Logarithmically complex rigorous Fourier space solution to the 1D grating diffraction problem Show Chinese title

Title: 对一维光栅衍射问题的对数复杂度严格傅里叶空间解

Abstract: The rigorous solution to the grating diffraction problem is a cornerstone step in many scientific fields and industrial applications ranging from the study of the fundamental properties of metasurfaces to the simulation of photolithography masks. Fourier space methods, such as the Fourier Modal Method, are established tools for the analysis of the electromagnetic properties of periodic structures, but are too computationally demanding to be directly applied to large and multiscale optical structures. This work focuses on pushing the limits of rigorous computations of periodic electromagnetic structures by adapting a powerful tensor compression technique called the Tensor Train decomposition. We have found that the millions and billions of numbers produced by standard discretization schemes are inherently excessive for storing the information about diffraction problems required for computations with a given accuracy, and we show how to adapt the TT algorithms to have a logarithmically growing amount of information to be sufficient for reliable rigorous solution of the Maxwell's equations on an example of large period multiscale 1D grating structures. Show Chinese abstract

Abstract: 严格求解光栅衍射问题是在许多科学领域和工业应用中的关键步骤，从研究超表面的基本特性到模拟光刻掩模的仿真。傅里叶空间方法，如傅里叶模态方法，是分析周期性结构电磁特性的成熟工具，但对于大型和多尺度光学结构来说计算量太大，无法直接应用。这项工作专注于通过适应一种称为张量列车分解的强大张量压缩技术来推动周期性电磁结构严格计算的极限。我们发现，标准离散化方案产生的数百万甚至数十亿个数字在存储给定精度下计算衍射问题所需信息方面本质上是多余的，我们展示了如何适应TT算法，使信息量以对数方式增长，足以在大型多尺度一维光栅结构的例子中可靠地求解麦克斯韦方程。