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Browsing by Author "Ziolkowski, R. W."

Now showing 1 - 4 of 4
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    A Bidirectional Traveling Plane-Wave Representation Of Exact-Solutions Of The Scalar Wave-Equation
    Besieris, 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.
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    Localized energy pulse trains launched from an open, semi-infinite, circular waveguide
    Shaarawi, 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.
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    A Novel-Approach To The Synthesis Of Nondispersive Wave Packet Solutions To The Klein-Gordon And Dirac Equations
    Shaarawi, 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.
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    On the evanescent fields and the causality of the focus wave modes
    Shaarawi, 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.