In this work we present an automatic, deterministic procedure to fully design a metasurface antenna, self-consistently including the metallic feeding structure. The impedance pattern has full spatial variability in two dimensions, to allow designs otherwise difficult. The design is based on the integral-equation formulation with a current-only approach, in which the surface 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; it does not require any assumption on the impedance profile. We also show how a 3D feed can be accounted for in a hybrid scheme partially employing commercial 3D simulation software. Application examples address centerfed circular metasurface antennas, in which the feed is not connected to the metasurface, and rectangular "strip-like" leakywave antennas where the metasurface is electrically connected to the feeding surface. In all cases, the design is carried out up to the final layout, and the full antenna is simulated to verify the design.

We present an automatic procedure to fully design a metasurface antenna, including the feeding structure. This feature is achieved by performing preliminary full-wave simulations of the feeding structure and by properly modelling PEC regions inside a current-based numerical design method. The synthesized metasurface antennas are implemented and simulated with a fullwave commercial solver, showing excellent agreement with the predicted performances.

We present a 3D method to numerically design a realizable metasurface, which transforms a given incident field into a radiated field that satisfies mask-type (inequality) constraints. The method is based on an integral equation formulation, with local impedance boundary condition (IBC) approximation. The procedure yields the spatial distribution of the impedance, yet the process involves the synthesis of the equivalent current only. This current is constrained to correspond to a realizable surface impedance, i.e., passive, lossless, and with reactance values bounded by practical realizability limits. The current-based design avoids any solution of the forward problem, and the impedance is obtained from the synthesized current only at the end of the process. The procedure is gradient-based, with the gradient expressed in closed form. This allows handling large metasurfaces, with full spatial variability of the impedance in two dimensions. The method requires no a priori information, and all relevant operations in the iterative process can be evaluated with O(N logN) complexity. Application examples concentrate on the case of on-surface excitation and far-field pattern specifications; they show designs of circular and rectangular metasurface antennas of 20 wavelengths in size, with pencil- and shaped-beam patterns, and for both circular and linear polarization.