On the equivalence of two-dimensional and three-dimensional multibeam microwave lenses

This report analyzes the theoretical characteristics of lens-fed multibeam arrays. It is shown that, under proper conditions, it is possible to achieve identical performance from two-dimensional (2D) and three dimensional (3D) lenses with the same number of ports. The proof of this equivalence requires several steps. It is first noted that lenses and multibeam networks can be equivalent in their performance. Then it is shown that multibeam planar arrays can use exactly the same excitations as linear arrays with the same number of elements. This relationship is treated in detail in an appendix. It is then shown that 2D lenses can feed both linear and planar arrays and that 3D lenses can feed both linear and planar arrays. Thus the desired equivalence between 2D and 3D lenses is established. It is shown that this relationship applies to 3D lenses with square and hexagonal planar arrays. The location of the feed array relative to the lens array required to achieve the 2D-3D equivalence is discussed. An experimental demonstration in which a 37-element linear array is fed by a 3D bootlace lens is described. Finally, it is pointed out that the equivalence relationship holds at only one frequency, because the path lengths through the 2D and 3D lenses are different.