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

Abstract

The feasibility of exciting a localized X-wave pulse from a finite aperture is addressed. Also, the possibility of using a finite-time excitation of a dynamic aperture to generate a finite-energy approximation to an X-wave pulse is explored. The analysis is carried out by using a Gaussian time window to time limit the infinite X-wave initial excitation. Huygens' construction is used to calculate the amplitude of the radiated wave field away from the finite-time source. The decay rate of the peak of the X wave is compared to that of a quasi-monochromatic signal. It is shown that the finite-time X-wave propagates to much farther distances without significant decay. Furthermore, the decay pattern of the radiated X-wave pulse is derived for a source consisting of an array of concentric annular sections. The decay behavior of the radiated pulse is similar to that of an X-wave launched from a finite-time aperture. This confirms the fact that time windowing the infinite energy X-wave excitation is a viable scheme for constructing finite apertures. A discussion of the diffraction limit of the X-wave pulse is also provided.

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

“…This is essentially a geometrical interpretation of the spectral coupling between the spatial and temporal frequency components. 7,[19][20][21] Donnelly and Power have argued that for oblique incidence the reflected waveform has an LW structure, while the transmitted waveform does not. The aim of this paper is to clarify this point and to quantify the process of disintegration of the transmitted LW field.…”

“…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.…”

Two Fundamental Representations of Localized Pulse Solutions To the Scalar Wave Equation - Abstract

“…The X-wave has a closed-form expression that appears to be very different from that of the FWM pulse. However, the generation and propagation characteristics of these wavefields show great similarities [61,86,87]. Both are tightly focused, high intensity, pulsed wavefields embedded in an extended background of a much lower magnitude.…”

“…They have extended ranges of localization in the near-to-far field limit and are generated by dynamic apertures for which the size of the active area of the initial excitation is time dependent. Furthermore, it has been shown [61,86,87] that the X-wave and the FWM pulses have very similar spectral structures. They only differ in the way their respective spatial and temporal frequency components are coupled together.…”

Focused X-shaped pulses

“…Moreover, several investigations about constructing and generating approximate X-shaped waves from finite apertures [21,22] have been carried on.…”