Pulse return from a sphere

The back scattering of short plane-wave harmonic pulses incident on a perfectly conducting sphere is investigated for both near and far fields. The pulse return is expressed in terms of the inverse Laplace transform of the CW back-scattered field. The inverse transform is calculated for the initial part of the pulse return using a Tauberian theorem. The latter part of the pulse return is given exactly in terms of residues representing the natural oscillations of the spheres. This residue expression converges rapidly for small
ka
or
ka
of the order of 1. However, for
ka\gg1
, the particular residue series is slowly convergent, but the terms which are slowly convergent can again be summed using methods of contour integration to give the CW creeping waves plus transients. Calculations of the pulse return for the case
ka = 1
, indicates that there is significant tail to the pulse return in the "resonance" region. For very large
ka
, the tail of the pulse return is the order of
1/ka
of the head. In the high frequency limit there is no pulse distortion.