Design of a Discrete Luneburg Lens Fed by Slot-Excited Spherical-Circular Conformal Printed Antenna

This paper deals with an accurate mathematical and numerical analysis of both a Luneburg lens and a spherical-circular printed antenna with a co-axial spherical-circular ground conductor. Consideration is done in terms of the spherical vector wave function expansions in each partial domain. The problem is cast into a coupled set of the dual-series equations for the expansion coefficients, and then to an infinite-matrix equation having favorable features. This is achieved by following the Method of Analytical Regularization, which is based here on the explicit inversion of the static part of the dual-series equations thanks to the Abel integral equation properties. Such a procedure leads to a guaranteed convergence and controlled accuracy of computations.