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, singularityfree 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, singularityfree, transverse solutions to Maxwell's equations can only exist if S is a circular cylinder or a (flat) plane.
 Publication:

Naval Research Lab. Report
 Pub Date:
 May 1986
 Bibcode:
 1986nrl..reptS....G
 Keywords:

 Cylindrical Bodies;
 Electromagnetic Wave Transmission;
 Harmonics;
 Maxwell Equation;
 Wave Equations;
 Differential Geometry;
 Topology;
 Wave Fronts;
 Communications and Radar