ASYMPTOTIC EVALUATION OF HIGH-FREQUENCY FIELDS NEAR A CAUSTIC

AN INTRODUCTION TO MASLOV'S METHOD.

Richard W Ziolkowski, Georges A. Deschamps

Research output: Contribution to journalArticle

95 Citations (Scopus)

Abstract

Geometrical optics (GO) is reviewed briefly and is applied to two examples: plane wave propagation in a linear layer medium and propagation near a cusp caustic in a homogeneous medium. The phase space approach to geometrical optics is discussed. Hamilton's equations and he associated flow, the Lagrangian submanifold, and amplitude half densities are introduced, and their connection with standard GO quantities is made. The canonical operator and the resultant representation of the field are defined. Two alternate descriptions of that representation are also given. Maslov's method is then applied to the aforementioned examples.

Original languageEnglish (US)
Pages (from-to)1001-1025
Number of pages25
JournalRadio Science
Volume19
Issue number4
StatePublished - Jul 1984
Externally publishedYes

Fingerprint

Geometrical optics
Caustics
homogeneous medium
geometrical optics
wave propagation
alkalies
near fields
evaluation
cusps
Wave propagation
plane waves
operators
propagation
method

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Atmospheric Science
  • Computers in Earth Sciences
  • Geochemistry and Petrology
  • Geophysics
  • Instrumentation

Cite this

ASYMPTOTIC EVALUATION OF HIGH-FREQUENCY FIELDS NEAR A CAUSTIC : AN INTRODUCTION TO MASLOV'S METHOD. / Ziolkowski, Richard W; Deschamps, Georges A.

In: Radio Science, Vol. 19, No. 4, 07.1984, p. 1001-1025.

Research output: Contribution to journalArticle

@article{ecd66fcc4b7f45818ac318625b2c2016,
title = "ASYMPTOTIC EVALUATION OF HIGH-FREQUENCY FIELDS NEAR A CAUSTIC: AN INTRODUCTION TO MASLOV'S METHOD.",
abstract = "Geometrical optics (GO) is reviewed briefly and is applied to two examples: plane wave propagation in a linear layer medium and propagation near a cusp caustic in a homogeneous medium. The phase space approach to geometrical optics is discussed. Hamilton's equations and he associated flow, the Lagrangian submanifold, and amplitude half densities are introduced, and their connection with standard GO quantities is made. The canonical operator and the resultant representation of the field are defined. Two alternate descriptions of that representation are also given. Maslov's method is then applied to the aforementioned examples.",
author = "Ziolkowski, {Richard W} and Deschamps, {Georges A.}",
year = "1984",
month = "7",
language = "English (US)",
volume = "19",
pages = "1001--1025",
journal = "Radio Science",
issn = "0048-6604",
publisher = "American Geophysical Union",
number = "4",

}

TY - JOUR

T1 - ASYMPTOTIC EVALUATION OF HIGH-FREQUENCY FIELDS NEAR A CAUSTIC

T2 - AN INTRODUCTION TO MASLOV'S METHOD.

AU - Ziolkowski, Richard W

AU - Deschamps, Georges A.

PY - 1984/7

Y1 - 1984/7

N2 - Geometrical optics (GO) is reviewed briefly and is applied to two examples: plane wave propagation in a linear layer medium and propagation near a cusp caustic in a homogeneous medium. The phase space approach to geometrical optics is discussed. Hamilton's equations and he associated flow, the Lagrangian submanifold, and amplitude half densities are introduced, and their connection with standard GO quantities is made. The canonical operator and the resultant representation of the field are defined. Two alternate descriptions of that representation are also given. Maslov's method is then applied to the aforementioned examples.

AB - Geometrical optics (GO) is reviewed briefly and is applied to two examples: plane wave propagation in a linear layer medium and propagation near a cusp caustic in a homogeneous medium. The phase space approach to geometrical optics is discussed. Hamilton's equations and he associated flow, the Lagrangian submanifold, and amplitude half densities are introduced, and their connection with standard GO quantities is made. The canonical operator and the resultant representation of the field are defined. Two alternate descriptions of that representation are also given. Maslov's method is then applied to the aforementioned examples.

UR - http://www.scopus.com/inward/record.url?scp=0021468666&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021468666&partnerID=8YFLogxK

M3 - Article

VL - 19

SP - 1001

EP - 1025

JO - Radio Science

JF - Radio Science

SN - 0048-6604

IS - 4

ER -