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A hemispherical Luneburg lens (LL) with the focal plane near lens surface is proposed using a transformation optics (TO)-based metamaterial (MTM) lens (metalens) concept for wide-angle beamsteering applications. The TO technique has long been implemented to reduce the longitudinal dimension of an LL. However, the transformed lenses, usually having a long focal length, suffer from limited volume reduction, severe reflection, narrow beamscanning range (BSR), and low capture efficiency. The proposed TO mapping in this article, engendered by transforming the upper and lower parts of the original LL separately, preserves the original beamsteering property of an LL in half a space with the focus retained at its flat surface before exerting any index approximations. The effects of the approximations and the discretization on the performance of the transformed LL are then investigated and analyzed comprehensively. After that, a hemispherical lens with a radius of 60 mm is exemplified at X-band and fabricated using a ten-layered nonresonant gradient index MTM. The designed TO-based LL is fed by a stacked patch antenna linearly shifted at a distance of 4 mm (a focal-to-diameter ratio of 0.03) beneath the lens to achieve a wide beamsteering range of ±41° with a maximum gain of 15.7 dBi and a gain tolerance of 1.7 dB. The proposed TO-based metalens antenna features compactness with a near-surface focal plane, wide BSR, and easy fabrication, which shows potential applications in far-field imaging, radar, and 5G wireless communication.
Xu et al. (Wed,) studied this question.