A 3-D-Printed Flat-Bottom Luneburg Lens Antenna Based on Transformation Optics for Wide-Angle Conical Coverage

A compact flat-bottom Luneburg lens antenna with 2-D beam scanning capability is developed and implemented using 3-D printing techniques based on the transformation optics (TO) method. A transformation method that maps coordinates only along the direction normal to the flat bottom of the lens is proposed. Compared to the conventional quasi-conformal TO (QCTO) method, the proposed mapping method can achieve a smaller relative permittivity range for transverse electric (TE) polarization. A fourth-order polynomial function related to the normalized lens radius is then introduced to directly calculate the continuous relative permittivity distribution, eliminating time-consuming lens modeling, simulation, and optimization, and thereby streamlining the overall design process. Accordingly, a 2-D beam-scanning flat-bottom Luneburg lens, fed by 19 patch antennas displaced along the focal plane, has been successfully simulated, fabricated, and measured. The measured results show that the proposed lens antenna operates from 12 GHz to 14.5 GHz. It achieves wide conical beam coverage of about ±55° with scan losses ranging from 0.6-2.3 dB. The measured peak realized gain is 17.7 dBi at 14.1 GHz, with an aperture efficiency of 71.3%.