Numerical analysis of the precursor fields in linear dispersive pulse propagation

A fast, accurate numerical algorithm based on the Laplace transform is presented. By using this algorithm, the high-frequency structure present at the onset of the precursor field for both the delta-function pulse and the unit-step-function-modulated signal has been resolved. A comparison of the results with those obtained by modern asymptotic techniques demonstrates the ability of this numerical method to resolve the high-frequency structure associated with the onset of the Sommerfeld precursor field.