Accelerating and abruptly-autofocusing beam waves in the Fresnel zone of antenna arrays

We introduce the concept of spatially accelerating (curved) beam waves in the Fresnel region of properly designed antenna arrays. These are transversely localized EM waves that propagate in free space in a diffraction-resisting manner, while at the same time laterally shifting their amplitude pattern along a curved trajectory. The proposed beams are the radiowave analogue of Airy and related accelerating optical waves, which, in contrast to their optical counterparts, are produced by the interference of discrete radiating elements rather than by the evolution of a continuous wavefront. Two dyadic array configurations are proposed comprising 2D line antennas: linear phased arrays with a power-law phase variation and curved power-law arrays with in-phase radiating elements. Through analysis and numerical simulations, the formation of broadside accelerating beams with power-law trajectories is studied versus the array parameters. Furthermore, the abrupt autofocusing effect, that occurs when beams of this kind interfere with opposite acceleration, is investigated. The concept and the related antenna setups can be of use in radar and wireless communications applications