Volumetric metamaterials versus impedance surfaces in scattering applications

Artificially created media allow employing material parameters as additional valuable degrees of freedom in tailoring electromagnetic scattering. In particular, metamaterials with either negative permeability or permittivity allow creating deeply subwavelength resonant structures with relatively high scattering cross-sections. However, the equivalence principle allows replacing volumetric structures with properly designed curved impedance surfaces, ensuring the same electromagnetic properties. Here, we examine this statement from a practical standpoint, considering two structures, having a dipolar electric resonance at the same frequency. The first realization is based on arrays of inductively loaded electric dipoles printed on stacked circuit boards (a volumetric metamaterial), while the second structure utilizes a 4-wire spiral on a spherical surface (surface impedance realization). An intermediate conclusion is that the surface implementation tends to outperform the volumetric counterparts in the scenario when a single resonance is involved. However, in the case where multiple resonances are overlapping and lossy materials are involved, volumetric realization can have an advantage. The discussed structures are of significant importance to the field of electrically small antennas, superdirective antennas, and superscatterers, which find use in wireless communications and radar applications, to name just a few.