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Journal Articles SIAM Journal on Applied Mathematics Year : 2023

Paraxial Wave Propagation in Random Media with Long-Range Correlations

Abstract

We study the paraxial wave equation with a randomly perturbed index of refraction, which can model the propagation of a wave beam in a turbulent medium. The random perturbation is a stationary and isotropic process with a general form of the covariance that may be integrable or not. We focus attention mostly on the non-integrable case, which corresponds to a random perturbation with long-range correlations, that is relevant for propagation through a cloudy turbulent atmosphere. The analysis is carried out in a high-frequency regime where the forward scattering approximation holds. It reveals that the randomization of the wave field is multiscale: The travel time of the wave front is randomized at short distances of propagation and it can be described by a fractional Brownian motion. The wave field observed in the random travel time frame is affected by the random perturbations at long distances, and it is described by a Schr¨odinger-type equation driven by a standard Brownian field. We use these results to quantify how scattering leads to decorrelation of the spatial and spectral components of the wave field and to a deformation of the pulse emitted by the source. These are important questions for applications like imaging and free space communications with pulsed laser beams through a turbulent atmosphere. We also compare the results with those used in the optics literature, which are based on the Kolmogorov model of turbulence.

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hal-04219493 , version 1 (27-09-2023)

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Liliana Borcea, Josselin Garnier, Knut Sølna. Paraxial Wave Propagation in Random Media with Long-Range Correlations. SIAM Journal on Applied Mathematics, 2023, 83 (1), pp.25-51. ⟨10.1137/22M149524X⟩. ⟨hal-04219493⟩
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