Synthesis of Transmitarrays for Far- and Near-Field Shaping using Convex Optimization

A unified mathematical framework for the analysis and synthesis of the near and far field radiated by a transmitarray antenna is presented. The far-field co-polar component and a scalar near-field component are expressed as formally identical, convex functions of the phases of the transmission coefficients of the transmitarray cells. Far-field and near-field shaping problems are thus solved using the same iterative convex optimization algorithm, based on semidefinite relaxation. The robustness and effectiveness of this phase-only synthesis procedure in handling diverse pattern constraints is numerically demonstrated with the optimization of a shaped-beam transmitarray and a near-field focusing one. The accuracy of the near-field model is proved by comparison with full-wave simulations.