Localized wave representations

Summary form only given. An extension to the bidirectional traveling plane wave decomposition was presented. New basis functions are used in the superposition, resulting in exact, nonseparable, acoustic (scalar-valued) and electromagnetic (vector-valued) wave solutions in a variety of environments (free space, dispersive media, lossy media, metallic waveguides, optical dielectric waveguides). In the bidirectional representation, some of the attractive solutions require smart choices of complicated spectra. In the 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.<>