General Solutions to Maxwell's Equations for a Transverse Field.

Abstract

The general solution to the wave equation for a transverse field is obtained in terms of the geometry of the wavefront surfaces S. Every solution to Maxwell's equation is a solution to this wave equation, but the converse is not necessarily true. Indeed, by using results from differential geometry and topology, it is found that smooth, singularity-free transverse solutions to Maxwell's equation cannot exist if S is a spheroid, a noncircular cylinder, or a surface or revolution. It is conjectured that smooth, singularity-free, transverse solutions to Maxwell's equations can only exist if S is a circular cylinder or a (flat) plane. Keywords: Electromagnetic propagation; and Harmonic fields.

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Document Details

Document Type
Technical Report
Publication Date
May 30, 1986
Accession Number
ADA169604

Entities

People

  • William B. Gordon

Organizations

  • United States Naval Research Laboratory

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Bessel Functions
  • Classification
  • Coordinate Systems
  • Curvature
  • Differential Equations
  • Differential Geometry
  • Equations
  • Far Field
  • Geometry
  • Intervals
  • Military Research
  • Notation
  • Partial Differential Equations
  • Revolutions
  • Scattering
  • Security
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Electromagnetic Wave Scattering and Antenna Radiation Engineering
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Structural Dynamics.