A Quasi-Direct Method for the Surface Impedance Design of Modulated Metasurface Antennas

A new approach is presented for synthesizing modulated metasurface (MTS) antennas (MoMetAs) with arbitrary radiation patterns, assumed to be given in amplitude, phase, and polarization. The MTS is defined on a circular domain and is represented as a continuous sheet transition impedance boundary condition (IBC) on the top of a grounded substrate. The proposed method relies on an entire-domain discretization of the electric field integral equation (EFIE). Via the dyadic Green's function of the grounded substrate, the desired radiation pattern is translated into the visible part of the surface current spectrum, decomposed into entire-domain and orthogonal basis functions, while the invisible part of the spectrum stems from the solution of the unmodulated sheet problem. The EFIE is then inverted to obtain the sheet impedance, which is constrained to be anti-Hermitian, as required for implementation with lossless patches. The efficiency of the method relies on the precomputation of the reaction integrals between three functions: basis functions for currents and impedances and testing functions for fields. The formulation is presented first for the scalar (isotropic) MTS case and then generalized to the tensorial (anisotropic) MTSs. Several radiation patterns are presented and designed successfully. A full-wave method-of-moment code is used to validate the designed MTSs IBC.