Electromagnetic analysis of the Fresnel zone plate lens antenna

The Fresnel zone plate has a very long history as an optical lens and promising characteristics as a microwave antenna. Experimental investigations of its radiation properties have demonstrated a narrow main beam and low sidelobes. Previous analyses have been entirely in terms of scalar diffraction theory. Our purpose is to perform a more complete analysis using electromagnetic diffraction theory. Computer software is developed to evaluate the resulting equations and for design and study of this novel lens antenna. The problem is formulated using a vector analog to Green's theorem yielding integral equations in a form convenient for the solution of electromagnetic diffraction by a surface. Since the Fresnel lens antenna is a planar structure having alternating metallic and transparent zones, edge diffraction effects are incorporated into the analytic model. It is demonstrated that the superposition of radiation from the transparent apertures and zone edges yields a total diffracted field that satisfy Maxwell's equations. Solutions are derived for the field patterns of the lens in both near and far-field regions. The near-field solution is used to investigate the diffraction pattern along the lens axis and in the focal plane. The far-field solution is used to characterize the radiation properties of the antenna. In both cases, the field intensities are expressed as definite integrals that are not amenable to closed form solution. Numerical evaluation programs have been developed to investigate the near and far-field performance of the Fresnel lens antenna. Several variations of the design parameters are considered. Computed diffraction patterns are presented and discussed for each Fresnel lens antenna design.