Note on Transformation-Optics-Based Flat Metamaterial Luneburg Lens Antenna with Zero-Focal Plane

This paper discusses the fundamental issues of the application of transformation-optics (TO) technique to the volume reduction of Luneburg lens (LL). The issue how to keep the invariance of Maxwell’s equation after TO implementation is addressed. The invariance is the key to keep the focal plane of lens on or near the lens surface after the transformation. Well known, the focus location shift away from the lens surface results in a limited volume reduction, severe reflection from the transformed lens surface, and limited scanning range with increased spillover loss. After theoretical study, two designs based on the TO are exemplified to show how to realize zero-focal or near-surface focal LL antennas. One flat LL antenna is first introduced to achieve the volume reduction of whole antenna by 2/3 using three-dimensional printing metamaterials. Then a hemispherical LL antenna is presented to show the wide beamscanning range and easy fabrication using multi-layered metamaterials when a near-surface focal plane is achieved.