A 3-D Printed Broadband Wide-Angle Multi-Beam Flat GRIN Lens Aided by Multifocal Ray-Path Analyses

An analysis of actual optical ray paths in flat gradient-index (GRIN) lenses for multifocal multi-beam radiations is introduced in this paper. The formulation is rigorously established using the conservation of momentum applied to an offset focal point for the extreme beam generation. Assisted by the above analysis, a new lens design approach for GRIN profile synthesis is proposed with two extreme focal points, and then extended to determine a convenient locus of feed that allows for covering the scanning range with minimal overall aperture phase errors. The ray-path errors have been tested and compared with those of previously reported multi-beam GRIN lenses, which were based on a straight, parallel ray-path assumption inside the lens. The superiority and generality of the new design formulas have been proven by comparing lens prototypes from the two different methods. It is demonstrated that the proposed one can enable consistent gain enhancement for multiple beams at different operating frequencies. Finally, the new design method has been validated by implementing an all-dielectric 3-D printed seven-beam flat GRIN lens. A wide beam coverage of ±44° has been realized with measured scanning losses between 1.2-2.93 dB at different frequencies. The measured 3-dB gain bandwidth is 42.8% covering 12.3-19 GHz.