An analytic solution for early-time transient scattering from a finite parabolic surface illuminated by pulse-excited plane waves

The increasing interest in the use of ultrawideband or short pulse antennas for target identification and remote sensing applications has driven the efforts to obtain direct time domain (TD) solutions in the electromagnetic (EM) analysis. A closed-form analytic solution is thus developed for predicting the early-time transient EM fields scattered from a finite parabolic surface when it is illuminated by a transient step plane wave. Scatters of parabolic surfaces are selected due to the fact that the surface profiles of many general scatters can be locally approximated by parabolic surfaces. This TD solution can be employed via the convolution theorem to efficiently obtain the early-time transient fields generated by the same scatter illuminated by a realistic finite-energy pulse. It is obtained by analytically inverting, in closed-form, the corresponding frequency-domain (FD) solution based on physical optics (PO) integral, and coincidently can be decomposed in terms of reflection and diffraction effects as usually described in high-frequency asymptotic solutions. Numerical examples are presented to demonstrate its utilization.