标题： 电磁波在随机时变介质中的传播统计规律 显示英文标题

标题： Statistical regimes of electromagnetic wave propagation in randomly time-varying media

摘要： 时间变化介质中的波传播通过时间调制打破能量守恒，从而实现对能量传输的独特控制。 在由此产生的现象中，时间无序——材料参数的随机波动——可以抑制传播并引起局域化，类似于安德森局域化。 然而，这一过程的统计性质仍不完全清楚。 我们对具有随机时间变化介电常数的均匀空间介质中的电磁波进行了全面的分析和数值研究。 利用不变嵌入方法，我们推导出精确的矩方程，并识别出三种不同的统计区域：初始单向输入在早期时间为伽马分布的能量，中期时间为指数行为，长时间为准对数正态分布。 相比之下，对称的双向输入在所有时间尺度上都产生真正的对数正态统计特性。 这些发现通过使用两种互补的无序模型——delta相关高斯噪声和分段常数波动——进行的大规模计算得到验证，表明观察到的统计特性是稳健的，并由输入对称性和时间动力学所支配。 动量守恒进一步限制了长期行为，将初始条件与能量增长联系起来。 我们的结果建立了一个统一的框架，用于理解时变系统中的统计波动力学，并为设计动态可调的光子和电磁器件提供了指导原则。 显示英文摘要

摘要： Wave propagation in time-varying media enables unique control of energy transport by breaking energy conservation through temporal modulation. Among the resulting phenomena, temporal disorder-random fluctuations in material parameters-can suppress propagation and induce localization, analogous to Anderson localization. However, the statistical nature of this process remains incompletely understood. We present a comprehensive analytical and numerical study of electromagnetic waves in spatially uniform media with randomly time-varying permittivity. Using the invariant imbedding method, we derive exact moment equations and identify three distinct statistical regimes for initially unidirectional input: gamma-distributed energy at early times, exponential behavior at intermediate times, and a quasi-log-normal distribution at long times. In contrast, symmetric bidirectional input yields true log-normal statistics across all time scales. These findings are validated by extensive calculations using two complementary disorder models-delta-correlated Gaussian noise and piecewise-constant fluctuations-demonstrating that the observed statistics are robust and governed by input symmetry and temporal dynamics. Momentum conservation further constrains long-term behavior, linking initial conditions to energy growth. Our results establish a unified framework for understanding statistical wave dynamics in time-modulated systems and offer guiding principles for the design of dynamically tunable photonic and electromagnetic devices.