Browsing by Author "Shaarawi, Amr M."
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- Acoustic X-wave reflection and transmission at a planar interface: Spectral analysisShaarawi, Amr M.; Besieris, Ioannis M.; Attiya, Ahmed M.; El-Diwany, Essam (Acoustical Society of America, 2000-01-01)The spectral structure of a three-dimensional X-wave pulse incident on a planar surface of discontinuity is examined. Introducing a novel superposition of azimuthally dependent pulsed plane waves, it is shown for oblique incidence that the reflected pulse has a localized wave structure. On the other hand, the transmitted field maintains its localization up to a certain distance from the interface, beyond which it starts disintegrating. An estimate of the localization range of the transmitted pulse is established; also, the parameters affecting the localization range are identified. The reflected and transmitted fields are deduced for X-waves incident from either a slower medium or a faster one. For the former case the evanescent fields in the second medium are calculated and their explicit time dependence is deduced for a normally incident X-wave. Furthermore, at near-critical incidence the transmitted pulse exhibits significant pulse compression and focusing.
- Aperture synthesis of time-limited X waves and analysis of their propagation characteristicsChatzipetros, Argyrios A.; Shaarawi, Amr M.; Besieris, Ioannis M.; Abdel-Rahman, Mohammad J. (Acoustical Society of America, 1998-05-01)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.
- A Bidirectional Traveling Plane-Wave Representation Of Exact-Solutions Of The Scalar Wave-EquationBesieris, Ioannis M.; Shaarawi, Amr M.; Ziolkowski, R. W. (AIP Publishing, 1989-06-01)A new decomposition of exact solutions to the scalar wave equation into bidirectional, forward and backward, traveling plane wave solutions is described. The resulting representation is a natural basis for synthesizing pulse solutions that can be tailored to give directed energy transfer in space. The development of known free_space solutions, such as the focus wave modes, the electromagnetic directed energy pulse trains, the spinor splash pulses, and the Bessel beams, in terms of this decomposition will be given. The efficacy of this representation in geometries with boundaries, such as a propagation in a circular waveguide, will also be demonstrated.
- Characterization of a nonrigid sphere using the backscattered fields of acoustic X wavesMoawad, Maged F.; Shaarawi, Amr M.; Besieris, Ioannis M. (Acoustical Society of America, 2004-06-01)The scattering of acoustic ultra-wideband X-wave pulses by a nonrigid sphere is simulated for purposes of material identification and characterization. Using the backscattered spectrum of the X-wave pulses, a procedure is described for estimating the radius, speed of sound, and density of-the sphere. The effectiveness of the suggested technique is verified in the case that the peak of the X-wave is incident on the centers of the sphere, as well as for the off-center incidence case.
- Localized energy pulse trains launched from an open, semi-infinite, circular waveguideShaarawi, Amr M.; Besieris, Ioannis M.; Ziolkowski, R. W. (American Institute of Physics, 1989-01-15)A new decomposition of exact solutions to the scalar wave equation into bidirectional, backward and forward traveling plane waves is described. These elementary blocks constitute a natural basis for synthesizing Brittinghamlike solutions. Examples of such solutions, besides Brittingham’s original modes, are Ziolkowski’s electromagnetic directed energy pulse trains (EDEPTs) and Hillion’s spinor modes. A common feature of these solutions is the incorporation of certain parameters that can be tuned in order to achieve slow energy decay patterns. The aforementioned decomposition is used first to solve an initial boundary_value problem involving an infinite waveguide. This is followed by considering a semi_infinite waveguide excited by a localized initial pulse whose shape is related directly to parameters similar to those arising in Ziolkowski’s EDEPT solutions. The far fields outside the semi_infinite waveguide are computed using Kirchhoff’s integral formula with a time_retarded Green’s function. The resulting approximate solutions are causal, have finite energy, and exhibit a slow energy decay behavior.
- A Novel-Approach To The Synthesis Of Nondispersive Wave Packet Solutions To The Klein-Gordon And Dirac EquationsShaarawi, Amr M.; Besieris, Ioannis M.; Ziolkowski, R. W. (AIP Publishing, 1990-08-01)A systematic approach to the derivation of exact nondispersive packet solutions to equationsmodeling relativistic massive particles is introduced. It is based on a novel bidirectional representation used to synthesize localized Brittingham‐like solutions to the wave and Maxwell’sequations. The theory is applied first to the Klein–Gordon equation; the resulting nondispersive solutions can be used as de Broglie wave packets representing localized massive scalar particles. The resemblance of such solutions to previously reported nondispersive wave packets is discussed and certain subtle aspects of the latter, especially those arising in connection to the correct choice of dispersion relationships and the definition of group velocity, are clarified. The results obtained for the Klein–Gordon equation are also used to provide nondispersive solutions to the Dirac equation which models spin 1/2 massive fermions.
- Numerical Reconstruction and Applications of Acoustic and Electromagnetic Ultra-Wideband Localized Pulses Generated by Dynamic Aperture AntennasAbdel-Rahman, Mohamed A. (Virginia Tech, 1997-12-17)A study is undertaken of the numerical reconstruction of acoustic and electromagnetic (EM) localized waves (LWs). The latter are carrier-free ultra-wideband pulses characterized by large focusing depths and extended ranges of localization. Special emphasis is placed on finite energy LWs that can be generated by dynamic aperture antennas with independently addressable elements. The reconstruction techniques are based on Huygens and Rayleigh-Sommerfeld integral I and II representations, both in the time and frequency domains. In contradistinction to the Weyl representation,they lend themselves to the physical realization of space-time aperture sources capable of generating localized wave solutions propagating away from the aperture plane. A detailed comparison of the three reconstruction techniques has been carried out in connection with LW solutions to the scalar wave equation, especially with respect to their handling of acausal components incorporated in the aperture excitation fields. In addition, a study is presented of the characteristic properties of LWs propagating through dispersive media modeled by the Klein-Gordon equation. It is demonstrated that contrary to expectation, the depletion of the spectral components of the LW Klein-Gordon field may be slower than that associated with the free space scalar field. Previous work by Power et al. [73] is extended by studying the acoustic bistatic scattering of a modified power spectrum (MPS) pulse from rigid and compressible spheres. The analysis allows the extraction of the radius of a sphere from the backscattered data. Finally, a special class of electromagnetic (EM) LWs, referred to as azimuthally polarized X waves (APXWs), is derived and their reconstruction is addressed, both in the time and frequency domains.
- On the evanescent fields and the causality of the focus wave modesShaarawi, Amr M.; Ziolkowski, R. W.; Besieris, Ioannis M. (AIP Publishing, 1995-08-01)The diverging and converging field components of the source-free focus wave modes are studied within the framework of both the Whittaker and Weyl plane wave expansions, It is shown that, in the Weyl picture, the evanescent fields associated with the diverging and converging components of the focus wave mode solution cancel each other identically, The source-free focus wave modes are, hence, composed solely of backward and forward propagating components of the Whittaker type, It will also be shown that no evanescent fields are associated with the causal excitation of an aperture by an initial focus wave mode field. The diverging field, however, is composed solely of causal components that propagate away from the aperture. With a specific choice of parameters, the field generated by the aperture is a very good approximation to the source-free solution. Under the same conditions, the original focus wave mode solution is composed predominantly of causal forward propagating fields. (C) 1995 American Institute of Physics.
- Paraxial Localized Waves in Free SpaceBesieris, Ioannis M.; Shaarawi, Amr M. (Optical Society of America, 2004-07-01)Subluminal, luminal and superluminal localized wave solutions to the paraxial pulsed beam equation in free space are determined. A clarification is also made to recent work on pulsed beams of arbitrary speed which are solutions of a narrowband temporal spectrum version of the forward pulsed beam equation. (C) 2004 Optical Society of America.