Abstract: Several exact, nonseparable, space-time solutions of the scalar wave and Maxwell's equations have been found recently. These localized wave (LW) solutions contain very broad-bandwidth components and can be optimized to exhibit enhanced localization properties. Moreover, by driving an array with these LW solutions, one can generate beams that also exhibit these LW characteristics. A new type of array is required to try to realize these localized wave effects - one that has independently addressable elements. The enhanced localization effects are intimately coupled to the proper spatial distribution of broad-bandwidth signals driving the array; i.e., by shading not only the amplitudes, but also the frequency spectra of the pulses driving the array. A LW pulse-driven array generates a moving localized, interference pattern, i.e., a set of pulses whose shapes are reconstituted as they propagate by the frequency components arriving at different times from the various aperture sources. Analytical bounds on the characteristics of beams generated by an arbitrary pulse-driven array have been derived and are supported by numerical and experimental values. 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. It has been demonstrated theoretically and experimentally that an acoustic array driven with a designed set of localized wave (LW) solutions of the scalar wave equation generates a robust, well-behaved, transient pencil-beam of ultrasound in water that outperforms the beams generated by related continuous wave excitations of the same array. Numerical models predict similar results for an electromagnetic LW pulse-driven array.!
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