Light Propagation through Space-Time Non-Markovian Random Media

TL;DR

This paper develops a new mathematical model for light propagation in non-Markovian random media, linking environmental memory effects to light statistics, and validates predictions through outdoor atmospheric experiments.

Contribution

It introduces an SPDE framework with correlated noise, mapping light propagation to the hyperbolic Anderson model, and derives new scaling relations validated experimentally.

Findings

Memory effects influence light statistics significantly.

Analytical predictions match outdoor atmospheric measurements.

Provides a foundation for advanced optical communication and sensing.

Abstract

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.