A bidirectional traveling plane wave representation of exact solutions of the scalar wave equation

Ioannis M. Besieris, Amr M. Shaarawi, Richard W. Ziolkowski

Research output: Contribution to journalArticle

134 Scopus citations

Abstract

A new decomposition of exact solutions to the scalar wave equation into bidirectional, forward and backward, traveling plane wave solutions is described. The resulting representation is a natural basis for synthesizing pulse solutions that can be tailored to give directed energy transfer in space. The development of known free-space solutions, such as the focus wave modes, the electromagnetic directed energy pulse trains, the spinor splash pulses, and the Bessel beams, in terms of this decomposition will be given. The efficacy of this representation in geometries with boundaries, such as a propagation in a circular waveguide, will also be demonstrated.

Original languageEnglish (US)
Pages (from-to)1254-1269
Number of pages16
JournalJournal of Mathematical Physics
Volume30
Issue number6
DOIs
StatePublished - Jan 1 1989

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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