Coupling of paraxial and white-noise approximations of the Helmholtz equation in randomly layered media

Austin McDaniel, Alex Mahalov

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We study the simultaneous paraxial and white-noise limit of the Helmholtz equation in randomly layered media where the refractive index fluctuations are in the direction of propagation. We consider the regime in which the wavelength is of the same order as the correlation length of the random fluctuations of the refractive index. We show that this simultaneous limit can be taken in this regime by introducing into the equation an arbitrarily small regularization parameter. The corresponding paraxial white-noise approximation that we derive is different from that of the previously studied high-frequency regime. Since the correlation length of the refractive index fluctuations due to atmospheric turbulence varies substantially, our results are relevant for numerous different propagation scenarios including microwave and radiowave propagation through various regions of the atmosphere.

Original languageEnglish (US)
Article number132491
JournalPhysica D: Nonlinear Phenomena
Volume409
DOIs
StatePublished - Aug 2020

Keywords

  • Helmholtz equation
  • Paraxial approximation
  • Waves in random media

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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