Localized energy pulse trains launched from an open, semi-infinite, circular waveguide

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.