Design of Circular Array Lenses Through the Quasi-Conformal Transformation Optics

This work presents the design of lenses for directivity enhancement of elements in a circular array antenna. Within a circular array, directive elements can both broaden the stability of the beamformed pattern over frequency and improve its directivity. The lenses are designed through the technique of transformation optics, whereby a desired coordinate transformation on the electromagnetic fields is specified and its effect realized through the introduction of a spatially varying material. Directivity enhancement is achieved by transforming a portion of the circular phase front radiated by an array element into a flat profile, resulting in partial collimation of the resulting radiation. An example of such a transform for an array of four isotropic sources is shown in Fig 1(a).