AI 中文总结
本文提出统一矢量衍射理论与误差补偿角谱法，结合GPU加速的全可微形式，实现高精度矢量场计算，成功应用于量子比特门及特定光束传播场景。
AI 中文摘要
自由空间场传播的数值精度和计算效率直接决定了从纳米光子超表面到光寻址量子处理器等场景下可预测的物理现象及可设计的器件。现有方法面临着根本性的精度-速度权衡问题，而在矢量领域这一问题更为复杂——现有主要形式体系零散，缺乏统一的计算框架。本文针对这两项挑战：提出了统一矢量衍射形式体系的理论，以及解决精度-速度权衡的算法，二者相互强化。我们证明，所有主要的矢量衍射形式体系和矢量势初始化方法均源自单一的面等效原理，且可无近似地简化为一系列标量角谱操作。因此，标量传播领域的任何进展都可应用于整个矢量体系。误差补偿角谱法（E-ASM）作为一种快速且精确的标量求解器，相较于最先进的带拓展角谱法，其峰值信噪比增益超过60 dB，速度提升达一个数量级，且观测窗口可自由配置。二者结合后，以GPU加速的全可微形式实现，将此前对宏观距离上的高阶光束而言难以实现的严格矢量场计算，转化为实用的、可用于逆设计的工具。我们在光寻址局域量子比特门，以及矢量厄米-高斯光束、拉盖尔-高斯光束的传播场景中验证了该框架，解决了标量或近似矢量方法无法获取的场结构问题。
英文摘要
The numerical accuracy and computational efficiency of free-space field propagation directly determine what physics can be predicted and what devices can be designed, from nanophotonic metasurfaces to optically addressed quantum processors. Existing methods face a fundamental accuracy-speed trade-off, which is further compounded in the vectorial regime, where major formalisms remain fragmented with no unified computational framework. Here we address both challenges: a theory that unifies the vectorial diffraction framework, and an algorithm that resolves the accuracy-speed trade-off, each reinforcing the other. We prove that all major vectorial diffraction formalisms and vector-potential seeding methods arise from a single surface equivalence principle and reduce, without approximation, to a finite sequence of scalar angular-spectrum operations. Any advance in scalar propagation can therefore be exploited across the entire vectorial ecosystem. The error-compensating angular spectrum method (E-ASM) serves as a fast and accurate scalar solver, delivering peak signal-to-noise-ratio gains exceeding 60 dB over the state-of-the-art band-extended angular spectrum method at order-of-magnitude faster speed, with a freely configurable observation window. Their combination, implemented in a GPU-accelerated, fully differentiable form, turns rigorous vectorial field computation, previously prohibitive for higher-order beams over macroscopic distances, into a practical, inverse-design-ready tool. We demonstrate the framework on optically addressed local qubit gates and on vectorial Hermite-Gaussian and Laguerre-Gaussian beam propagation, resolving field structures inaccessible to scalar or approximate vectorial methods.
Comments91 pages, 25 figures
