A novel approach to the synthesis of nondispersive wave packet solutions to the Klein–Gordon and Dirac equations

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

doi:10.1063/1.528995

Cited by 65 publications

(33 citation statements)

References 17 publications

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“…, scalar wave [1 -6], Maxwell's [3,7], Klein-Gordon [8] equations) have been reported recently. When compared with traditional monochromatic, continuous-wave (CW) solutions such as Gaussian or piston beams, these localized-wave (LW) solutions are characterized by extended regions of localization; i.e.…”

Section: Introductionmentioning

confidence: 99%

Localized wave physics and engineering

Ziolkowski

1991

Phys. Rev. A

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Issues pertaining to the rate of beam divergence, the beam intensity, and the measured energy eKciency of beams generated by arrays of radiating elements are central to the practical applications of those beams. It will be shown that a localized-wave pulse-driven array can be designed to outperform similar continuous-wave pulse-driven arrays with respect to each of these beam characteristics. This improved performance is quantified by deriving bounds on those beam quantities for the field generated by an arbitrary pulse-driven array. These bounds extend the meaning of near-field distances or diffraction lengths to the situation where the array driving functions can be broad-bandwidth signals. Particular attention is given to transmitting-and receiving-array systems consisting of elements that are not large in comparison to the shortest wavelength of significance contained in the signals driving them. The output signals of such systems are related to the input driving functions by several time derivatives. It is demonstrated that the properties of the resulting beams depend on the higher-order moments of the spectra of the input driving functions and that diffraction degrades the coherence of these higher-order moments more slowly than its lower orders. A properly designed set of input driving signals having a high degree of correlation in the higher-order moments of their spectra will produce a beam that has extended diffraction lengths and localization properties. The localized-wave solutions provide an immediate access to this situation. An alternative type of array is required to realize these localized-wave effects -one that has independently addressable elements. The enhanced localization effects are then intimately coupled to the proper spatial distribution of broad-bandwidth signals driving the array, i.e. , by controlling not only the amplitudes, but also the frequency spectra of the pulse driving the array. Recently reported experimental comparisons between localized-wave and continuous-wave pulse-driven arrays of ultrasonic transducers in water are reexamined in terms of the theoretical developments presented here. It will be shown that the observed performance enhancements of the localized-wave pulsedriven arrays are in agreement with the theoretical predictions.

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Section: Introductionmentioning

confidence: 99%

Localized wave physics and engineering

Ziolkowski

1991

Phys. Rev. A

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“…In a series of subsequent papers [35,36,51,52,53,54], a simple theoretical method was developed, called by those authors "bidirectional decomposition", for constructing a new series of non-diffracting, luminal pulses.…”

Section: Preliminary Remarksmentioning

confidence: 99%

Localized Waves: A Historical and Scientific Introduction

2007

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“…The application of the Bateman-Hillion-like solutions or weakly localized wave packets to quantum field theory was restricted to the formal studies of the localized solutions of the Klein-Gordon and the Dirac equations [14,15]. In contrast to the solitons, the solutions localized due to nonlinearity, which have long been studied in quantum field theory, see e.g.…”

Section: Introductionmentioning

confidence: 99%