Continuous Rectangular Phoenix Cells Mapping for Direct Copolar and Crosspolar Optimization of Quasi-Periodic Reflective Surfaces

This paper proposes a general methodology to enhance the efficiency of the direct optimization of the copolar and crosspolar radiation of large aperture quasi-periodic reflective surfaces (QPRS) antennas by ensuring the layout continuity without abrupt geometrical variation. This is done through the exploitation of the Phoenix cells (PC) properties, by efficiently parametrizing and interpolating PC lookup tables. In particular, the proposed parametrization allows the description of the QPRS layout through continuous functions without losing precision. Indeed, the description of the QPRS through continuous functions, namely B-spline functions, allows for to reduction of the large- scale optimization problem dimensions and naturally ensures the layout smoothness. A use case of a large faceted contour beam reflectarray (RA) is presented, showing a remarkable improvement in both the copolar and the crosspolar discrimination levels compared to classical synthesis techniques and the RA layout smoothness is practically demonstrated.