Focusing characteristics of symmetrically configured bootlace lenses

A symmetrically configured class of bootlace lenses (also known as Gent or Rotman lenses) is analyzed. These trifocal lenses are used to feed haft-wave spaced linear arrays to form a set of multiple beams. The lens dimensions are scaled\´ so that all lenses have transmission characteristics equivalent to those of a Butler matrix with the same number of ports. The relationship between the focusing characteristics and the lens dimensions is calculated, and it is shown that these symmetrically configured lenses form a one-parameter family. Design equations are derived, and a design procedure is described. It is found that, for a wavefront tolerance of , the maximum usable array length varies from to as the ratio of lens width to array length varies from one to 1.6.