On the Use of Entire-Domain Basis Functions and Fast Factorizations for the Design of Modulated Metasurface

Entire-domain, spectral basis functions (BFs) have witnessed recent interest in the integral-equation analysis of large metasurface (MS) antennas modeled via homogenized impedance boundary conditions. We present a formulation employing classical Galerkin test via Rao-Wilton-Glisson functions yet assembled to represent entire-domain div-conforming BFs for the shape of interest (e.g., circular/coaxial waveguide modes). On the one hand, the rationale is that entire-domain, spectral BFs afford a significant economy in the number of necessary unknowns; on the other hand, being expressed as combination of Rao-Wilton-Glisson functions, reaction integrals are computed with optimum cost via fast methods. This is applied to reduce the cost of the optimization process used to design MS antennas based on spatially modulated reactance profiles. The authors support the method proposed, presenting criteria to define the entire-domain functions, considering the overall numerical complexity in an optimization framework, and providing a convergence analysis and the numerical results for holographic leaky-wave antennas, relevant in the MS context.