Maxwell Fisheye Lens Based Retrodirective Array

Abstract

A Maxwell fisheye lens using parallel plate index grading is presented in this study to develop a passive retrodirective antenna array. As a proof-of-concept a design frequency of 10 GHz was selected for fabrication and experiment. The design principals of the lens are discussed, which enables 85% energy flow at the drain probe (also referred to as image point) of the lens. It is shown that the image in the Maxwell fisheye lens has a point symmetry with a reverse phase, which makes it possible to realize passive retrodirective action using the lens. This arrangement is significantly more practical than previous passive retrodirective topologies due to the un-constrained number of connections to radiating elements that it can support without the need for multi-layer technology. In the realization described here, a cross-polarized microstrip patch antenna array is connected to the source and drain probes of the lens structure in order to form the retrodirective array. The strategy for selecting the optimal transmission line lengths required to connect the antennas to the lens for maximum re-radiation power is described and implemented. Experimental results for a prototype high efficiency passive retrodirective array based on the theoretical design considerations presented in this paper are reported.

Design and analysis of Maxwell fisheye lens based beamformer

“…Mathematically, ray trajectory can be represented as , where t signifies the parametric variation of the ray. As shown previously in 14 , the rays from a 3D system projects onto a plane without any loss of generality, and this principle can be used to translate a 3D Maxwell fisheye lens on a finite plane.…”

“…In this stereographic projection, the line segments dx and dy can be represented using spherical coordinates, hence the cylindrical lens profile can be represented as where, at the equator of the reference sphere index . Using this principle, the Maxwell fisheye lens profile can be represented by 14 , 17 : where R represents the radius of the reference sphere and is the refractive index at the center of the lens. The traditional methods used to create a refractive index profile for fisheye focusing include thin plates 18 and holy parallel plates 19 .…”