General Solutions to Maxwell's Equations for a Transverse Field.
Interim rept. Nov 85-Feb 86,
NAVAL RESEARCH LAB WASHINGTON DC
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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 Maxwells 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 Maxwells 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 Maxwells equations can only exist if S is a circular cylinder or a flat plane. Keywords Electromagnetic propagation and Harmonic fields.
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