In this letter, the theory of stochastic partial differential equations is applied to the propagation of light fields in space-time random media. By modeling the fluctuation of refractive index's square of the media as a random field, we demonstrate that the hyperbolic Anderson model is applicable to describing the propagation of light fields in such media. Additionally, several new quantitative characterizations of the stochastic properties that govern the light fields are derived. Furthermore, the validity of the theoretical framework and corresponding results is experimentally verified by analyzing the statistical properties of the propagated light fields after determining the spatial and temporal stochastic features of the random media. The results presented here provide a more accurate theoretical basis for better understanding random phenomena in emerging domains such as free-space optical communication, detection, and imaging in transparent random media. The study could also have practical guiding significance for experimental system design in these fields.

翻译：本文应用随机偏微分方程理论研究光场在时空随机介质中的传播问题。通过将介质折射率平方的涨落建模为随机场，我们证明双曲安德森模型适用于描述此类介质中的光场传播。此外，我们推导出若干控制光场随机特性的新定量表征。进一步地，在确定随机介质的时空随机特征后，通过分析传播光场的统计特性，对理论框架及相应结果进行了实验验证。本文研究结果为更准确理解自由空间光通信、透明随机介质中的探测与成像等新兴领域的随机现象提供了更精确的理论基础。该研究对这些领域的实验系统设计也具有实际指导意义。