Speckle Memory Effect in the Frequency Domain and Stability in Time-Reversal Experiments

Garnier, Josselin; Sølna, Knut

doi:10.48550/arxiv.2201.05558

Cited by 1 publication

(2 citation statements)

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“…Starting from equation (4.16), using the asymptotic expansion (4.8), changing variables as s " pz ´z1 q{z and η " Rq, and using definitions (4.18) and (4. 19) we get…”

Section: The Spatial Covariance Functionmentioning

confidence: 99%

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Paraxial wave propagation in random media with long-range correlations

Borcea¹,

Garnier²,

Sølna³

2022

Preprint

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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 Schrödinger-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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“…Starting from equation (4.16), using the asymptotic expansion (4.8), changing variables as s " pz ´z1 q{z and η " Rq, and using definitions (4.18) and (4. 19) we get…”

Section: The Spatial Covariance Functionmentioning

confidence: 99%

“…Therefore, the second and even fourth order statistical moments of the wave field can be calculated using Itô calculus [17]. The study of such moments is an essential part of both the analysis and the development of new methodologies for imaging [5,9,18], time reversal [4,15,19,31] and optical communications applications [7].…”

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confidence: 99%