Near-field engineering in RIS-aided links: beamfocusing analytical performance assessment

Reconfigurable intelligent surfaces (RISs) are typically utilized in the far-field as an effective means of creating virtual line-of-sight (LOS) links to mediate non-LOS propagation in wireless communications via beamforming. Owing to their large surface and the multitude of scatterers, the use of RISs can be extended in the near-field, to transform the incident beam into a focused beam that is able to address the challenges of high frequencies more efficiently than conventional beamforming. In this paper we explain from a physics' standpoint how the RIS can engineer wavefronts to transform the incident beam into a focused beam targeted at the user, and we employ the angular spectrum representation approach to describe analytically the dynamics of beamfocusing. We derive analytical expressions that provide the necessary insight into the dependencies and trade-offs between crucial parameters, such as the incident beam's footprint on the RIS, the intended focal distance of the reflected beam, and the link topology. To assess the beamfocusing efficiency we provide metrics that are crucial for future applications, including energy efficient communications, wireless power transfer, tracking and localization.