Complex Gaussianity and spatio-frequential memory effect of random wave processes
Analysis of PDEs
2025-10-13 v1 Probability
Optics
Abstract
Wavefield speckle patterns are generated by interference of randomly scattered coherent light. In the weak-coupling regime of the It\^o-Schr\"odinger paraxial model for long-distance wave propagation, we show the following multiscale character: a macroscopic envelope solves a deterministic diffusion equation while the local wavefield (the speckle) is described by a complex Gaussian process both in terms of spatial axial and lateral displacements as well as frequency and angular variations of the incident wavebeam. These results describe speckle patterns and corroborate chromato-spatial memory effects observed in laser light propagation through heterogeneous media.
Cite
@article{arxiv.2510.09402,
title = {Complex Gaussianity and spatio-frequential memory effect of random wave processes},
author = {Guillaume Bal and Anjali Nair},
journal= {arXiv preprint arXiv:2510.09402},
year = {2025}
}