Relation between the ringing of resonances and surface waves in radar scattering

The exact normal-mode or Mie series for electromagnetic scattering from a conducting sphere has in the previous literature been transformed via the Watson transformation into components corresponding to specularly reflected and to creeping waves, or via the singularity expansion method (SEM) into a series of pole contributions in the complex frequency plane which in the time domain give rise to a series of damped sinusoidal signals. In this work, the connection between the two methods is established by using the Watson transformation for obtaining the specular wave, and by transforming the remainder into the SEM series. From the latter, we obtain the shapes of creeping-wave pulses for the case of an incident -function pulse by evaluating the series via the stationary-phase method.