Numerical analysis of the precursor fields in linear dispersive pulse propagation

Abstract

A fast accurate algorithm for the numerical evaluation of Laplace transform-type integrals is presented and applied to the numerical analysis of the precursor fields in linear dispersive pulse propagation for a Lorentz medium. Both the delta function pulse and the unit step-function modulated signal are considered. These results are compared with the results given by modern asymptotic techniques, demonstrating the ability of this numerical method to resolve accurately the extremely high frequency structure associated with the onset of the Sommerfeld precursor field. This algorithm then provides a useful technique for the investigation of any space–time region of the transient field structure associated with dispersive pulse propagation for any given dispersion relation of appropriate form without the need for performing a complicated asymptotic expansion. It also provides a useful comparison for the asymptotic theory in those important cases that warrant such a detailed analysis.