Localized wave physics and engineering

Abstract

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.

Acoustic X-wave reflection and transmission at a planar interface: Spectral analysis

“…Eliminating the dependence on ␣ 2 and after some algebraic manipulation, we obtain cos 4 For short distances from the interface the condition z(c 1 /c 2 )⌬()Ӷa is satisfied for all values of ⌬͑͒. Hence, we introduce the hypothesis that the pulse stays localized with peak amplitude ϰ1/a until it reaches the following distance along the direction of propagation of the pulse:…”

“…Studies of the generation of acoustical and optical localized waves ͑LW͒ [1][2][3][4][5][6][7] and their use in high-resolution imaging and target identification [8][9][10] have advanced considerably in the past few years. Because of their large focusing depths and their wideband spectra, LWs have a potential in detecting objects buried at different depths and identifying wide ranges of the parameters characterizing a detected target.…”

Aperture synthesis of time-limited X waves and analysis of their propagation characteristics

“…[1][2][3][4][5][6][7][8][9][10][11][12] A number of these pulsed wave solutions are finite-energy variants of the focus wave mode ͑FWM͒. 13,14 They are usually derived either as superpositions of infinite-energy FWM pulses, [8][9][10][11]14 or by time limiting various FWM-like excitations to construct finite-energy aperture fields. [2][3][4][5][6][7] Alternatively, such LW pulses can be synthesized as superpositions over Bessel beams with appropriately chosen spectra.…”

Spherical scattering of superpositions of localized waves

“…For the CW piston with aperture radius Ra and area A = 1rR;, the diffraction length may be given by the classical Rayleigh distance [Ziolkowski, 1991] (1.1)…”

“…they have associated diffraction lengths which exceed classical Rayleigh distances. These waveforms, called Localized Waves (LWs), were first introduced by Brittingham [1983] and were studied in detail later by Ziolkowski [1985Ziolkowski [ , 1988Ziolkowski [ , 1989Ziolkowski [ , 1990Ziolkowski [ , 1991. In chapter three, the predicted MPS spherical backscatter spectrum is calculated using techniques described in chapter two.…”