Theoretical Modeling of Substrate-Integrated Impedance Surfaces

Substrate-integrated impedance surfaces (SIISs) or substrate-integrated metasurfaces (SIMSs) have recently been proposed to tailor the dispersion and eigenmodes of waveguides, resonators, and cavity antennas, as well as to develop reconfigurable epsilon-near-zero (ENZ) channels with enhanced supercoupling, electric field localization, and sensitivity to perturbations. Here, we present a compact analytical model for calculating the effective surface impedance of the capacitive SIIS formed by a 1-D array of blind vias embedded in a substrate-integrated waveguide (SIW). The analytical model is validated using numerical examples and simulations, achieving good accuracy even for SIISs consisting of the non-diluted and dense array of blind vias. Our theoretical results may be beneficial for SIIS-loading techniques and SIWs, which are critical to realizing the full potential of the next-generation microwave/millimeter-wave communication, sensing, and cavity quantum electrodynamics (cQED) systems.