Path Integrals for Waves in Random Media

Abstract

The problem of wave propagation in a random medium is formulated in terms of Feynman's path integral. It turns out to be a powerful calculational tool. The emphasis is on propagation conditions where the rms (multiple) scattering angle is small but the log-intensity fluctuations are of order unity - the so-called saturated regime. It is shown that the intensity distribution is then approximately Rayleigh with calculable corrections. In an isotropic medium, the local or Markov approximation which is commonly used to compute first and second (at arbitrary space-time separation) moments of the wave field is explicitly shown to be valid whenever the rms multiple scattering angle is small. It is then shown that in the saturated regime the third and higher moments can be obtained from the first two by the rules of Gaussian statistics. There are small calculable corrections to the Gaussian law leading to coherence tails. Correlations between waves of different frequencies and the physics of pulse propagation are studied in detail. Finally it is shown that the phenomenon of saturation is physically due to the appearance of many Fermat paths satisfying a perturbed ray equation.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1977
Accession Number
ADA045949

Entities

People

  • Roger Dashen

Organizations

  • SRI International

Tags

Communities of Interest

  • Air Platforms
  • C4I
  • Energy and Power Technologies
  • Space

DTIC Thesaurus Topics

  • Differential Equations
  • Equations
  • Frequency
  • Integrals
  • Intensity
  • Linear Accelerators
  • Mathematics
  • Navy
  • Oceanography
  • Partial Differential Equations
  • Path Integrals
  • Physics Laboratories
  • Random Variables
  • Statistics
  • Two Dimensional
  • Wave Equations
  • Wave Propagation

Fields of Study

  • Physics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Calculus or Mathematical Analysis
  • Wave Propagation and Nonlinear Chaotic Dynamics.

Technology Areas

  • Space
  • Space - Hall-Effect Thruster