Analytical solution for early-time transient radiation from pulse-excited parabolic reflector antennas

A closed-form analytical solution is developed for predicting the early-time transient electromagnetic fields which are generated by a perfectly conducting parabolic reflector antenna when it is illuminated by a transient step spherical wave due to an elemental Huygen´s source located at the focus. This closed-form time-domain solution, which is valid both near and far from the reflector (and anywhere in the forward region) can be used via the convolution theorem to efficiently obtain the early-time transient fields generated by the same parabolic reflector antenna when it is illuminated by a realistic finite-energy pulse which emanates as a spherical wave from the focus. The transient solution is developed here by analytically inverting, in closed form, the corresponding frequency-domain solution in terms of a radiation integral that employs an asymptotic high-frequency geometrical optics (GO)-based approximation for the fields in the aperture. Numerical results are presented for the transient fields both near and far from the reflector. The fields on boresight exhibit an impulse-like behavior similar to that of the impulse radiating antenna (IRA) introduced by Baum et al. (1989, 1993)