Light propagation through space-time non-Markovian random media

Accurately modeling light propagation through complex environments, such as atmospheric turbulence, remains a fundamental challenge because standard memoryless approximations do not fully capture intrinsic temporal correlations. To address this, 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 can be mapped onto the hyperbolic Anderson model. This mapping enables the derivation of new, to our knowledge, 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 light phenomena through a generalized colored noise framework, providing crucial insights for free-space optical communication, remote sensing, and coherent imaging.