Optimized three-dimensional lenses for wide-angle scanning

Three-dimensional bootlace lens antennas with two and four focal points can be optimized to produce high-quality scanned beams over a wide field of view. For two-dimensional scanning, the planar feed locus is replaced by a curved feed locus designed to minimize path length errors. Comparisons with previous bootlace lens designs demonstrate the advantages of this focal distribution. The bifocal lens shows good scanning performance in both principal and orthogonal planes. The quadrufocal lens performs better in its principal plane than in its orthogonal plane. It is also shown that the quadrufocal lens can be realized with a planar outer surface and a circular focal arc, and improved scanning performance is still achievable. Further optimization of the focal arc and/or relaxation of the planar outer surface condition results in quadrufocal lenses with negligible phase errors in the principal plane.