Field radiated by a leaky wave slot fed by dipole: uniform asymptotic solution

The magnetic current excited by an electric dipole on a slot printed between two different homogeneous media has been derived in analytical form under the non restrictive assumption of small slot width in terms of wavelength (see Neto, A. and Maci, S., Technical Report No D/21321, California Institute of Technology, Jet Propulsion Laboratory). Starting from this magnetic current, we constructed a ray-optical field structure in the denser medium from a space-domain stationary phase approximation (see Neto and Maci, ibid., p.490-3), finding leaky and lateral wave rays emerging from separated points on the slot axis and propagating with the ambient wavespeed along the surface of radiation cones. We derive a rigorous pole saddle point uniform asymptotic solution starting from the continuous spectrum representation of the Green´s function solution. Regarding the lateral wave, its higher radial asymptotic order legitimates its negligibility in the present uniform asymptotic evaluation. The result obtained, and the physical insight gained, from this prototype solution provides a further building block for extension to more general Green´s function problems of open or semi-open waveguiding and leaky structures.