### 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) |
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Pages (from-to) | 1254-1269 |

Number of pages | 16 |

Journal | Journal of Mathematical Physics |

Volume | 30 |

Issue number | 6 |

DOIs | |

State | Published - Jan 1 1989 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

*Journal of Mathematical Physics*,

*30*(6), 1254-1269. https://doi.org/10.1063/1.528301