### Abstract

Several new classes of localized solutions to the homogeneous scalar wave and Maxwell's equations have been reported recently. Theoretical and experimental results have now clearly demonstrated that remarkably good approximations to these acoustic and electromagnetic localized-wave solutions can be achieved over extended near-field regions with finite-sized, independently addressable, pulse-driven arrays. We demonstrate that only the forward-propagating (causal) components of any homogeneous solution of the scalar-wave equation are actually recovered from either an infinite- or a finite-sized aperture in an open region. The backward-propagating (acausal) components result in an evanescent-wave superposition that plays no significant role in the radiation process. The exact, complete solution can be achieved only from specifying its values and its derivatives on the boundary of any closed region. By using those localized-wave solutions whose forward-propagating components have been optimized over the associated backward-propagating terms, one can recover the desirable properties of the localized-wave solutions over the extended near-field regions of a finite-sized, independently addressable, pulse-driven array. These results are illustrated with an extreme example-one dealing with the original solution, which is superluminal, and its finite aperture approximation, a slingshot pulse.

Original language | English (US) |
---|---|

Pages (from-to) | 75-87 |

Number of pages | 13 |

Journal | Journal of the Optical Society of America A: Optics and Image Science, and Vision |

Volume | 10 |

Issue number | 1 |

State | Published - Jan 1993 |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Journal of the Optical Society of America A: Optics and Image Science, and Vision*,

*10*(1), 75-87.

**Aperture realizations of exact solutions to homogeneous-wave equations.** / Ziolkowski, Richard W; Besieris, Ioannis M.; Shaarawi, Amr M.

Research output: Contribution to journal › Article

*Journal of the Optical Society of America A: Optics and Image Science, and Vision*, vol. 10, no. 1, pp. 75-87.

}

TY - JOUR

T1 - Aperture realizations of exact solutions to homogeneous-wave equations

AU - Ziolkowski, Richard W

AU - Besieris, Ioannis M.

AU - Shaarawi, Amr M.

PY - 1993/1

Y1 - 1993/1

N2 - Several new classes of localized solutions to the homogeneous scalar wave and Maxwell's equations have been reported recently. Theoretical and experimental results have now clearly demonstrated that remarkably good approximations to these acoustic and electromagnetic localized-wave solutions can be achieved over extended near-field regions with finite-sized, independently addressable, pulse-driven arrays. We demonstrate that only the forward-propagating (causal) components of any homogeneous solution of the scalar-wave equation are actually recovered from either an infinite- or a finite-sized aperture in an open region. The backward-propagating (acausal) components result in an evanescent-wave superposition that plays no significant role in the radiation process. The exact, complete solution can be achieved only from specifying its values and its derivatives on the boundary of any closed region. By using those localized-wave solutions whose forward-propagating components have been optimized over the associated backward-propagating terms, one can recover the desirable properties of the localized-wave solutions over the extended near-field regions of a finite-sized, independently addressable, pulse-driven array. These results are illustrated with an extreme example-one dealing with the original solution, which is superluminal, and its finite aperture approximation, a slingshot pulse.

AB - Several new classes of localized solutions to the homogeneous scalar wave and Maxwell's equations have been reported recently. Theoretical and experimental results have now clearly demonstrated that remarkably good approximations to these acoustic and electromagnetic localized-wave solutions can be achieved over extended near-field regions with finite-sized, independently addressable, pulse-driven arrays. We demonstrate that only the forward-propagating (causal) components of any homogeneous solution of the scalar-wave equation are actually recovered from either an infinite- or a finite-sized aperture in an open region. The backward-propagating (acausal) components result in an evanescent-wave superposition that plays no significant role in the radiation process. The exact, complete solution can be achieved only from specifying its values and its derivatives on the boundary of any closed region. By using those localized-wave solutions whose forward-propagating components have been optimized over the associated backward-propagating terms, one can recover the desirable properties of the localized-wave solutions over the extended near-field regions of a finite-sized, independently addressable, pulse-driven array. These results are illustrated with an extreme example-one dealing with the original solution, which is superluminal, and its finite aperture approximation, a slingshot pulse.

UR - http://www.scopus.com/inward/record.url?scp=0027266705&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027266705&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0027266705

VL - 10

SP - 75

EP - 87

JO - Journal of the Optical Society of America A: Optics and Image Science, and Vision

JF - Journal of the Optical Society of America A: Optics and Image Science, and Vision

SN - 1084-7529

IS - 1

ER -