Discrete Luneburg lens fed by a spherical-circular printed antenna in axisymmetrical mode - accurate analysis by MAR

Research has been carried out on circular microstrip antennas (MA) fed by a probe located at the center to ensure an omnidirectional pattern. Even more attractive are MAs conformally printed on curved surfaces, such as spherical-circular MA (SCMA). Many new applications need sophisticated antennas, which possess a number of special properties. Indeed, data transmissions via low Earth orbit satellites or military tracking X-band radar constrain one to have an agile scanning beam. A very attractive candidate for all these applications is the Luneburg lens (LL). Practically, LL is manufactured as a finite number of concentric homogeneous dielectric shells $this is called a discrete LL. The spherical geometry of both SCMA and LL enables one to simulate them with the same method. Here, we use the method of analytical regularization (MAR) sometimes called semi-inversion method. Generally, it converts a first-kind singular integral or series equation to a well-conditioned second-kind Fredholm matrix equation, and therefore serves as a perfect pre-conditioner of originally ill-posed problem. Then both numerical convergence and efficiency is achieved and matrix-truncation error is controlled.