Light Propagation through Space-Time Non-Markovian Random Media

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.

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References in corpus (19)

• Measuring the Transmission Matrix in Optics : An Approach to the Study and Control of Light Propagation in Disordered Media
• Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
• Light fields in complex media: mesoscopic scattering meets wave control
• Experimental control of the transition from Markovian to non-Markovian dynamics of open quantum systems
• Cascades and transitions in turbulent flows
• Quantum channels and memory effects
• Adaptive Optics for Astronomy
• Three-dimensional ghost imaging ladar
• Correlated imaging through atmospheric turbulence
• Refractive Index of Humid Air in the Infrared: Model Fits
• Light in correlated disordered media
• Impact of turbulence in long range quantum and classical communications
• Identification of intermittent multi-fractal turbulence in fully kinetic simulations of magnetic reconnection
• Ultra-stable Free-Space Laser Links for a Global Network of Optical Atomic Clocks
• Fourth-moment Analysis for Wave Propagation in the White-Noise Paraxial Regime
• Rayleigh-Taylor turbulence is nothing like Kolmogorov turbulence in the self similar regime
• Influence of Phase Diffuser Dynamics on Scintillations of Laser Radiation in Earth Atmosphere: Long-Distance Propagation
• A fractional Brownian motion model for the turbulent refractive index in lightwave propagation
• Quantum turbulence, superfluidity, non-Markovian dynamics, and wave function thermalization