Closed-Form Expressions of the Axial Step and Impulse Responses of a Parabolic Reflector Antenna

Electromagnetic pulses radiated by parabolic antennas and similar structures are needed in many applications like air and ground penetrating radar or high power microwaves (HPM) weapons. In this paper, an approach based on Skulkin and Turchin's work and on physical optics approximation in the time domain is developed to determine the radiated fields. Closed-form time-domain expressions of the electromagnetic step and impulse responses, along the axis of a classical parabolic reflector antenna, are derived. A closed-form expression of the impulse response duration is also given. The obtained E-field and H-field formula are valid along the axis, both near and far from the reflector. Using these closed-form expressions, the radiated fields are computed by means of a convolution product of the primary source excitation and the impulse response. Numerical results have been obtained in the case of a causal sine and a generalized Gaussian impulse excitations to illustrate some specific transients effects which occur with such an antenna