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.

No abstract

Large classes of nonseparable space-time solutions of the equations governing many wave phenomena (e. scalar wave, Maxwell's, Klein-Gordon equations) have been reported recently and w k be reviewed briefly here. When compared with traditional monochromatic, continuous wave (CW) solutions, these localized wave (LW) solutions are characterized by extended regions of localization; i.e., their shapes and /or amplitudes are maintained over much larger distances than their CW analogues. Such solutions represent pulses with highly localized transmission characteristics which may have potential applications in the areas of directed energy applications, secure communications and remote sensing. It has been shown that LW solutions can be obtained from a representation that employs a decomposition into bidirectional traveling plane wave solutions; i.e., solutions formed as a product of forward and backward traveling plane waves. The bidirectional representation does not replace the standard Fourier synthesis, but rather complements it, especially for the LW class of solutions.An extension to the bidirectional traveling plane wave decomposition is presented. New basis functions are used in the su erposition resulting in exact, nonseparable, acoustic (scalar-valued) and electromagnetic (Pvector-valued) wave solutions in a variety of environments (free space, dis ersive media, lossy media, metallic waveguides, optical dielectric waveguides). In the &directional representation, some of the attractive solutions require smart choices of complicated spectra. In the new superposition, these attractive solutions can be obtained more easily due to the freedom of choice of the basis functions used. This is illustrated by a class of interesting pulses known as sling-shot pulses or X waves. An effort is also made to obtain these solutions by applying the above technique directly to the Fourier representation.The complicated internal structure of LW solutions can be probed with techniques based on enerB conservation princi les. Illustrative examples of local energy speeds are given for three L solutions to the scarar wave equation (Focus Wave Mode, Modified Power Spectrum, Sling-Shot). 19