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Fourth-Moment Analysis for Wave Propagation in the White-Noise Paraxial Regime

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Abstract

In this paper we consider the Itô–Schrödinger model for wave propagation in random media in the paraxial regime. We solve the equation for the fourth-order moment of the field in the regime where the correlation length of the medium is smaller than the initial beam width. In terms of applications we prove that the centered fourth-order moments of the field satisfy the Gaussian summation rule, we derive the covariance function of the intensity of the transmitted beam, and the variance of the smoothed Wigner transform of the transmitted field. The second application is used to explicitly quantify the scintillation of the transmitted beam and the third application to quantify the statistical stability of the Wigner transform.

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Authors and Affiliations

  1. Laboratoire de Probabilités et Modèles Aléatoires, Laboratoire Jacques-Louis Lions, Université Paris Diderot, 75205, Paris Cedex 13, France

    Josselin Garnier

  2. Department of Mathematics, University of California, Irvine, CA, 92697, USA

    Knut Sølna

Authors
  1. Josselin Garnier
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  2. Knut Sølna
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Correspondence to Josselin Garnier.

Additional information

Communicated by F. Otto

This work is partly supported by AFOSR Grant # FA9550-11-1-0176.

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Garnier, J., Sølna, K. Fourth-Moment Analysis for Wave Propagation in the White-Noise Paraxial Regime. Arch Rational Mech Anal 220, 37–81 (2016). https://doi.org/10.1007/s00205-015-0926-2

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  • DOI: https://doi.org/10.1007/s00205-015-0926-2

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