Precursor wave in a layered waveguide.

The precursor wave (often called the first arriving signal) in a layered waveguide is investigated. It is known that the velocity of such a signal is close to the velocity of the fastest medium in the waveguide, and it may be bigger than the fastest group velocity given by the dispersion diagram of the waveguide. Usually the precursor pulse decays with the propagation distance. A model layered waveguide is studied in the paper. It is shown that the precursor is associated with the pseudo-branch structure of the dispersion diagram. The velocity of the precursor is determined by the slope of the pseudo-branch. The decay is exponential and it depends on the structure of the pseudo-branch. Three approaches to precursors are described in the paper: the Miklowitz-Randles approach based on analytical continuation of the dispersion diagram, the leaky wave approach, and the approximate technique based on the properties of the real dispersion diagram.