Study on Light Propagation through Space-Time Random Media via Stochastic Partial Differential Equations

2026-01-16

AI Summary

This study investigates the propagation dynamics and stochastic characteristics of light fields in spatiotemporally random media. To address the limitations of conventional models in capturing dynamic fluctuations of the medium, the hyperbolic Anderson model is introduced for the first time into optical propagation modeling, treating the fluctuations of the squared refractive index as a random field and establishing a theoretical framework based on stochastic partial differential equations. Building upon this foundation, several novel quantitative metrics are proposed to characterize the statistical properties of light fields, and experimental validation confirms the efficacy of the model. This work provides a more accurate theoretical basis and practical guidance for experimental design in applications such as free-space optical communication, remote sensing, and imaging through complex media.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

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.

Problem

• light propagation
• space-time random media
• stochastic partial differential equations
• refractive index fluctuation
• random phenomena

Innovation

• stochastic partial differential equations
• hyperbolic Anderson model
• light propagation
• random media
• refractive index fluctuations