Scattering of stratified lenses illuminated by any real source

An analytical method to compute the scattering of spherically and hemispherically stratified lens antennas fed by any real source is described. A mode matching technique (MMT) based on spherical wave functions is first used to analyze the scattering by spherically stratified lens antennas. The farfield patterns and directivity obtained are in excellent agreement with commercial software simulations and measurements for a six-shell Luneburg lens at 6 GHz. This MMT is then extended to hemispherically stratified lens antenna analysis. Its validation is carried out by comparisons to both commercial software and measurements for a three-shell half Maxwell fish-eye lens fed by an open-ended waveguide at W-band. The expansion on spherical modes gives a direct access to the field everywhere. To highlight the progressive focusing effect of inhomogeneous lens antennas, the electric field is mapped in terms of magnitude and phase in the neighborhood of the entire structure. One of the originalities of this work stands in the fact that, besides scattering the incident field, the reaction created by the scatterer on the feed is quantified. The particularization of the scatterer to the stratified lens does not affect the generality of the presented procedure. On the top of providing a controlled accuracy, the MMT tremendously reduces both computation time and memory load in comparison to commercial software.