A bi-dimensional compressed Luneburg lens antenna for miniaturization based on transformation optics

Transformed Luneburg lens has been widely employed to provide aberration -free imaging and high-gain antenna system, but whose focal plane and beam scanning range decrease correspondingly. In this paper, a two-dimensional compressed elliptical cylindrical Luneburg lens is presented based on transformation optics (TO) to achieve miniaturization and wide-angle beam steering. The Jacobian matrix and the permittivity tensor are calculated after supposing formulas to compress the focal plane, while maintaining the lens' inherent performance. The gradient permittivity is achieved by two ring-type periodic unit cells on the basis of the Equivalent Medium Theory. The lens is then attached between a pair of parallel metal plates to further improve its gain and lower the side lobe level (SLL). To demonstrate this assumption, a prototype of this Luneburg lens is manufactured by isotropic material and 3D printing technique. The antenna operates at 3.3-5 GHz with a peak gain of 16.1/15.9 dBi. A 2D beam scanning range of +/- 50 degrees and +/- 20 degrees can be implemented by merelyfive feeds, the side lobe level keeping less than-16.3/-16 dB. Measured results coincide well with theoretical predictions, offering a beneficial transformation mapping to both microwaves and optics.