Directional, nonpropagating, and polychromatic excitations in one-dimensional wave systems.

It has been demonstrated that, in a one-dimensional wave system, monochromatic waves may be generated which are completely localized to the region of excitation or which propagate in only one direction. We further the discussion of such nonpropagating and directional excitations and demonstrate that they can be extended to excitations of an arbitrary finite number of frequencies. Two techniques for mathematically constructing these excitations are discussed. Furthermore, the relation between nonpropagating excitations and nonscattering scatterers is discussed. The results presented here may be useful in the development of devices for one-dimensional and quasi-one-dimensional wave systems.