Systematic Splitting of Wavefields into Unidirectional Modes: Long-Range Asymptotic Methods for Weakly Uniform Media,

Abstract

A series of pseudo-unitary transforms is devised and applied to the Helmholtz equation for a weakly nonuniform one-dimensional medium, decoupling the wave field in a consistent order-by-order way into counter-propagating modes. The result is a generalized form of d'Alembert decomposition, providing an asymptotic solution without backscatter at arbitrary order. Low-order contributions correspond to the standard WKB approximation. Higher orders provide additional terms of potential importance in applications involving propagation over long ranges, e.g., long time-of-flight measurement and very-long-baseline interferometry. Evidence is presented that this decoupling scheme is equivalent to high-order Born approximations.

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Document Details

Document Type
Technical Report
Publication Date
Aug 08, 1996
Accession Number
ADA317497

Entities

People

  • Robert F. Gragg

Organizations

  • United States Naval Research Laboratory

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Backscattering
  • Born Approximations
  • Decomposition
  • Differential Equations
  • Energy
  • Equations
  • Generators
  • Helmholtz Equations
  • Integral Equations
  • Nonuniform
  • Quantum Mechanics
  • Refractive Index
  • Scattering
  • Splitting
  • Standards
  • Wave Equations
  • Wave Power

Fields of Study

  • Physics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Wave Propagation and Nonlinear Chaotic Dynamics.