Focusing characteristics of curvilinear half-open Fresnel zone plate lenses: plane wave illumination

A diffraction field-focusing equation based on a specific conical-segment linearization procedure is derived for the Fresnel zone plate (FZP) lens of arbitrary curved profile and is applied for contrasting plane, spherical, parabolic and conical zone plate lenses, convex-side illuminated by a paraxial plane wave front. Two sets of 100-GHz curvilinear and plane FZP lenses are studied numerically with regards to their dimensions, axial focusing intensity and footprint, and frequency bandwidth. For the first set, where the curvilinear and plane lenses share a common lens base aperture and have equal focal lengths, the following new finding has resulted: regardless of their different in shape profiles the FZP lenses have equal zone numbers and produce similar axial focusing. The second set also consists of plane, spherical, parabolic and conical lenses. They share a common apex, and have equal in diameter base apertures and focal lengths but different thicknesses. For such disposition and proportions, the FZP lenses possess different zone numbers and focusing parameters (gain, efficiency, footprint and bandwidth). The belief that the curvilinear FZP have superior (or inferior) electromagnetic characteristics, compared to those of the plane FZP lens with equal number of zones is not in general true. Their relative focusing qualities can vary significantly depending on the lens positioning and dimensions. Index Terms--Focusing, Fresnel zone-plate (FZP) lenses, lenses, millimeter-wave lenses.