Electromagnetic modeling of stratified inhomogeneous lenses fed by real sources

An analytical method, the mode matching technique based on spherical wave functions, has been described and applied to both spherically and hemispherically stratified lenses fed by an open-ended waveguide such as respectively, multishell Luneburg and half Maxwell fish-eye lens antennas. A way to deal with any real source as well as to handle hemispherical lenses is explained, yielding to remarkably accurate results. The agreement between the far field radiation patterns and directivity obtained by the analytical method, commercial softwares and measurements are indeed excellent. A semi analytical method, allowing to deal directly with arbitrary shaped stratified lenses, is now under investigation.