线性时不变光子系统中的复合对称性与双重反对称群
Compound symmetries and double antisymmetry groups in linear time-invariant photonic systems
AI总结：
本文提出线性光子系统的复合对称性统一框架，用双重反对称群理论将线性时不变光子系统分为12个对称类别，通过数值示例和基尔霍夫定律应用验证，为光子系统对称性分析与设计提供系统基础。
AI中文摘要：
对称性是光子系统的基础，外部（空间）对称性与洛伦兹互易、能量守恒、时间反演对称性等内部对称性共同约束电磁响应。光子系统还可拥有结合外部与内部变换的复合对称性，宇称-时间（PT）对称性即为典型例子。然而，目前仍缺乏包含互易性、能量守恒和时间反演的通用复合对称性统一框架，导致其分类与物理意义未被探索。本文针对线性光子系统提出该框架，定义复合变换与复合对称性，推导其对电磁场和散射矩阵的约束，证明内部、外部及复合对称性可由双重反对称群理论自然描述；该理论将线性时不变光子系统分为12个对称类别，每个类别对电磁响应施加特征约束。本文用光子晶体平板的数值示例说明两个代表性类别，并将该理论应用于研究旋电球的基尔霍夫热辐射定律，为分析和设计光子系统的对称性提供系统基础。
英文摘要：
Symmetry is fundamental to photonic systems. External (spatial) symmetries and internal symmetries---Lorentz reciprocity, energy conservation, and time-reversal symmetry---constrain the electromagnetic response. Photonic systems can also possess compound symmetries that combine external and internal transformations, exemplified by parity-time (PT) symmetry. However, a unified framework for general compound symmetries involving reciprocity, energy conservation, and time reversal remains lacking, leaving their classification and physical implications unexplored. In this paper, we present such a framework for linear photonic systems. We define compound transformations and symmetries, and derive their constraints on electromagnetic fields and scattering matrices. We show that internal, external, and compound symmetries are naturally described by the theory of double antisymmetry groups. This theory classifies linear time-invariant photonic systems into twelve symmetry categories, each imposing characteristic constraints on the electromagnetic response. We illustrate two representative categories with numerical examples of photonic crystal slabs and apply the theory to examine Kirchhoff's law of thermal radiation for a gyrotropic sphere. Our work provides a systematic foundation for analyzing and engineering symmetry in photonic systems.
