Efficient Analysis of Planar, Arbitrarily Shaped, and (Bi)-Anisotropic Metasurface Antennas

An efficient method of moments (MoM) scheme is presented for the analysis of planar, possibly cascaded metasurfaces (MTSs) implementing high-impedance surfaces. The MTS can be designed on an arbitrarily shaped domain and is accounted for as a set of cascaded electric sheet impedances. In the proposed method, the shaped MTS is included in a larger rectangular domain meshed with rooftop basis functions, resulting in a Toeplitz-block Toeplitz structure for the substrate impedance matrix, which enables fast Fourier transform (FFT)-based acceleration of matrix-vector products. The basis functions lying in the rectangular domain but outside the MTS are disabled by including zeros in the impedance matrix. The obtained linear system of equations is well conditioned, does not require any specific near-field treatment, and can be solved iteratively using the generalized minimal residual (GMRES) method. It has been demonstrated that the algorithm is able to handle efficiently any MTS antenna shape in single-layer or multilayer configuration with almost linear complexity. It is shown that the high-impedance sheets improve the convergence rate. MTSs with more than 40 wavelengths size, meshed with more than 1 million basis functions, can be analyzed on a conventional computer in less than 15 min. A very good agreement is shown through comparison with results from other software packages.