Analytic analysis of transient scattering from a finite second-order surface illuminated by an incident plane wave

A closed-form analytic solution based on a time-domain (TD) physical optics (PO) approximation is developed for the scattering from a finite second-order surface when illuminated by a transient impulsive plane wave. This TD-PO solution can be applied via a convolution to derive the early time transient fields scattered from the same scatterer that is illuminated by a realistic astigmatic finite-energy pulse. The closed form TD-PO solution is obtained by inverting the corresponding frequency-domain PO solution into TD. This solution can be expressed in terms of reflection and diffraction components of the scattering mechanisms as in other conventional high-frequency asymptotic solutions. Numerical examples are presented to demonstrate its physical phenomenon of the scattering mechanisms.