Automated deterministic full design of tensor metasurfaces for field manipulation

We present an automatic, deterministic procedure for the complete design of tensor metasurfaces, fulfilling field manipulation specifications and physical realizability constraints. Radiated field specifications are of the mask-type (inequalities). The tensor impedance pattern has full spatial variability in two dimensions, without any assumption on the tensor components or spatial variation envelope, yielding maximum flexibility. In particular, the choice of purely capacitive (or inductive) tensor impedances can be enforced. A compact representation of the impedance tensors allows to set independent bounds on the tensor components derivable from the chosen unit cell database: this ensures the synthesis of practically realizable structures. The design is based on the integral-equation formulation with a current-only approach, in which the tensor impedance profile is derived only after the optimal current is found; this allows to avoid the solution of the forward problem at all steps of the algorithm, with a drastic reduction of computational resources. 3-D metallic feeding structures are self-consistently accounted for in the design process (when present). An innovative process to optimally realize the whole set of unit cells is also described that allows to implement the full design without even computing the impedance distribution. Application examples address center-fed circular metasurface antennas, for broadside pencil beam and shaped cosecant beam with linear polarizations, and a rectangular metasurface operating as an anomalous reflector. In all cases, the design is carried out up to the final layout, and the full structure is simulated to verify the design. The method to enforce design bounds, and the impedance-free unit cell design can also be employed in design methods which are not current-based.