Thickness-to-Bandwidth Limit for Impedance Matching Metasurfaces Design According to the Bode–Fano Theorem

In this article, we derive a general form of the thickness-to-bandwidth limit according to the Bode–Fano theorem for the transmissive impedance-matching metasurfaces. It provides guidance for designing thin and broadband metasurfaces by effectively manipulating key parameters, for example, relative permittivity and permeability. Meanwhile, the thickness-to-bandwidth limit clearly reveals the inherent tradeoff between the antireflection bandwidth and the desired thickness of existing impedance matching layer (IML) designs. By utilizing the artificial magnetic conductor (AMC) concept, we optimize two metasurface designs with the reflectance suppressed below 0.1. Specifically, we design a narrowband ultrathin IML with an electrical thickness of $\lambda /120.5$ and a broadband IML with an electrical thickness of $\lambda /12.3$ , significantly outperforming previous IML designs. The performance of both narrowband and broadband metasurfaces is validated through the standard transmission/reflection measurements in the microwave anechoic chamber. The broadband metasurface is further tested via a multiday ground-penetrating radar (GPR) survey. The enhanced spectrum energy (SE) and resolution of parallel buried metallic pipes at a depth of 0.5 m in a highly lossy material-to-match (MTM) confirms the improved detection performance introduced by the broadband IML.