Impulsive Field Near the Second Focus Along the Symmetry Axis of a Prolate-Spheroidal IRA

Summary form only given. This paper is a development of the field focused at the second focus of a prolate-spheroidal reflector. We explore the behavior of the impulse term along the z-axis as one passes through this focus. IRAs have been developed for the transient far field. Now we are going to focus in the near field to focus on a biological application. This paper is an extension of two previous papers. Some analytic approximations were developed" for the focal waveform produced at the second focus of a prolate-spheroidal reflector due to a TEM wave launched from the first focus. In this paper we find the analytic calculation of the fields on the z-axis near the second focus. First of all, we show that the impulsive part of the waveform at the second focus can be described by a delta-like pulse forming for z < z₀ and in the limit as z rarr z₀ gives the required true delta function. This is a physical example of the formation of a delta function. Then, we show that the aperture integral gives the same result (at early time) as the exact incident wave before truncation. This gives confidence in the aperture integration. We can see that the area of the delta-like pulse is the same for both after and before z₀. Finally, we illustrate these results with a graphical example.