常规散射矩阵中的因果求和规则

中文摘要 AI 辅助

散射矩阵是光子与电磁器件的标准实验及计算描述。无源特性在常规入射-出射矩阵中明确体现，而因果求和规则通常仅在将响应转换为辅助变量后才被构建。本文证明，通过消除参考域引入的时间超前，这些规则可直接写入常规散射矩阵。利用各通道的最早到达延迟，我们定义了一个域延迟矩阵，该矩阵在保留实频率无源特性的同时恢复了因果时间原点。在明确的解析性、透明性和正则性假设下，该矩阵成为Schur函数，支持Cayley-Herglotz构造。所得的投影界与行列式界约束了相干通道叠加及多通道总损耗。该框架恢复了Rozanov吸收体极限与球多极求和规则，同时将因果界扩展至插入损耗、受抑制奇异值通道、条件无损耗延迟-带宽权衡等可测量量。本研究将基础因果理论与可实验获取的散射数据直接关联，初始理论路径由用于开放式科学发现的AI研究系统Qiushi Engine自主探索，后续经作者验证、完善与拓展，展现了AI-人类混合发现流程。

英文摘要

Scattering matrices are the standard experimental and computational description of photonic and electromagnetic devices. Passivity is explicit in the conventional incoming-outgoing matrix, whereas causality sum rules are usually formulated only after transforming the response into auxiliary variables. Here we show that these rules can be written directly in the conventional scattering matrix by removing the time advance introduced by the reference domain. Using the earliest-arrival delay of each channel, we define a domain-delayed matrix that preserves real-frequency passivity while restoring the causal time origin. Under explicit analyticity, transparency, and regularity assumptions, this matrix becomes a Schur function, enabling a Cayley-Herglotz construction. The resulting projected and determinant bounds constrain coherent channel superpositions and aggregate multichannel loss. The framework recovers Rozanov's absorber limit and spherical-multipole sum rules, while extending causality bounds to measurable quantities including insertion loss, suppressed singular-value channels, and conditional lossless delay-bandwidth trade-offs. Our work directly connects fundamental causality theory with experimentally accessible scattering data. The initial theoretical route is autonomously explored by Qiushi Engine, an AI research system for open-ended scientific discovery, and subsequently verified, refined, and developed by the authors, demonstrating a hybrid AI-human discovery workflow.

发表机构

• Zhejiang University（浙江大学）
• China Jiliang University（中国计量大学）
• Hangzhou City University（浙大城市学院）

机构由 AI 辅助整理，请以论文原文为准。