Light Propagation through Space-Time Non-Markovian Random Media

Here, we introduce a stochastic partial differential equation (SPDE) formulation driven by temporally correlated noise to describe light propagation beyond the standard Markov approximation. By representing the squared refractive index fluctuations as a random field with explicit long-range temporal correlations, we demonstrate that the propagation dynamics map exactly onto the hyperbolic Anderson model. This rigorous mapping enables the derivation of new quantitative scaling relations that connect the environment's non-Markovian memory effects to the statistical properties of the emergent light field. We experimentally validate these analytical predictions in an outdoor atmospheric environment, confirming the memory-dependent statistical signatures of the propagated light. Our results establish a precise physical foundation for understanding memory-driven wave phenomena, providing crucial insights for free-space optical communication, remote sensing, and coherent imaging.