A Transformation-Optics-Based Flat Metamaterial Luneburg Lens Antenna with Zero Focal Length

The transformation-optics (TO) technique has been widely applied in the volume reduction of Luneburg lens (LL) in both optical and microwave regimes. However, it is found that the focus is usually not located on the surface of the transformed LL anymore after applying TO. The focus location shift results in a limited volume reduction, severe reflection from the new lens surface, and limited scanning range with increased spillover loss. This paper theoretically studies and proposes a TO-based LL antenna with zero focal length by considering the phase mismatch caused by the space discontinuity. The study first reveals that the transformation of an LL alone without sustaining the original boundary inherently deteriorates the original focusing property even before exerting any approximation. To validate the idea, a flat metamaterial LL antenna using TO is proposed, approximated, and fabricated using an integrated dielectric and conductive three-dimensional printing manufacturing process. The feeding patch antenna remains on the surface of the transformed lens. The thickness of the proposed antenna is reduced to 1/3 of a traditional LL in its boresight, while a ±20° beam scanning range is achieved with linearly shifted feedings. The study verifies that it is essential to ensure phase matching at the radiation boundary to maintain the original focusing property of an LL. The information derived from the study evidences the conditions of the enforcement of the TO in electromagnetic problems such as dielectric lenses.