Modeling, Design and Performances of Half Maxwell Fish-Eye Lens Antennas

Inhomogeneous lenses with index gradient are usually used to focus electromagnetic waves produced by antennas. They are built by assembling several homogeneous shells, giving them the name of stratified lenses. This paper deals with an inhomogeneous hemispherically stratified lens: the half Mawell fish-eye (HMFE) lens. First, a general method to analyze stratified lenses in terms of radiating properties such as radiation patterns, directivity and electromagnetic field distribution for any kind of incoming electromagnetic field is described. Then, an optimization method, to choose the thickness and permittivity of a stratified HMFE lens, is applied. This technique allows to approach the radial permittivity law as well as possible. Finally, simulation results of an optimized 9-shell HMFE lens antenna in W band are shown.