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

130 Citations (Scopus)

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
StatePublished - 1989
Externally publishedYes

Fingerprint

Wave equations
Traveling Wave
Plane Wave
wave equations
Wave equation
plane waves
Exact Solution
Scalar
scalars
Decomposition
Circular waveguides
pulses
Energy transfer
Bessel Beam
decomposition
circular waveguides
Decompose
Spinor
Energy Transfer
Free Space

ASJC Scopus subject areas

  • Organic Chemistry

Cite this

A bidirectional traveling plane wave representation of exact solutions of the scalar wave equation. / Besieris, Ioannis M.; Shaarawi, Amr M.; Ziolkowski, Richard W.

In: Journal of Mathematical Physics, Vol. 30, No. 6, 1989, p. 1254-1269.

Research output: Contribution to journalArticle

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