### 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 language | English (US) |
---|---|

Pages (from-to) | 1254-1269 |

Number of pages | 16 |

Journal | Journal of Mathematical Physics |

Volume | 30 |

Issue number | 6 |

State | Published - 1989 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Organic Chemistry

### Cite this

*Journal of Mathematical Physics*,

*30*(6), 1254-1269.

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

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 30, no. 6, pp. 1254-1269.

}

TY - JOUR

T1 - A bidirectional traveling plane wave representation of exact solutions of the scalar wave equation

AU - Besieris, Ioannis M.

AU - Shaarawi, Amr M.

AU - Ziolkowski, Richard W

PY - 1989

Y1 - 1989

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=36549104582&partnerID=8YFLogxK

M3 - Article

VL - 30

SP - 1254

EP - 1269

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 6

ER -