Analysis and Design of Holographic Reflectarray Antennas Using Collective Polarizability Tensors of Patch Scatterers

This paper presents an analytical approach for designing holographic reflectarray (HRA) antennas using polarizability tensors of patch scatterers. First, the behavior of patch scatterers is described using collective polarizability tensors as their characteristic parameters. The polarizability components of the patch scatterers are then extracted using a retrieval approach. Next, the analytical input admittance of HRA elements, containing patch scatterers, a dielectric substrate, and a ground plane, is derived as a function of incident angle and collective polarizabilities of patch scatterers, which depend on the patch dimensions. This is achieved by applying the collective polarizability tensors of patch scatterers in an equivalent circuit model. A design procedure is then developed to determine the distribution of scatterers on the reflectarray surface. This approach utilizes a closed-form formulation to calculate input admittances, expressed as a function of the incident angle and polarizability components. It takes into account the variations in incident angles for elements positioned at different locations. By adopting this approach, both the computational load and the time required for input admittance calculations are significantly reduced compared to previous methods based on numerical approaches. Additionally, in this method, increasing the number of elements or altering the feed antenna’s position has no impact on the calculation time. Finally, a practical example of an HRA antenna is designed using the proposed approach. Since the proposed approach requires neither extensive full-wave simulations nor an optimization procedure, it can pave the way for fast and accurate design of HRAs. To validate the proposed approach, a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$20\,cm \times 20\,cm$ </tex-math></inline-formula> linearly polarized HRA is manufactured and tested at 15 GHz. The simulation and experimental results show good agreement. The experimental peak gain and aperture efficiency at 15 GHz are found 26.8 dBi and 38%, respectively. Additionally, 1-dB gain bandwidth is 22.22%, from 14 GHz to 17.5 GHz.