High-Q Factor Dual-Layer Anapole Metamaterial

Simulation results and an experimental study are presented for a dual-layer metamaterial exhibiting a resonance with Q-factor of 4000 in the mm-wave frequency range, achieved by combining resonances from two complementary planar metamaterials. The initial layer, which is the original metamaterial, is composed of metallic unit-cells shaped like epsilon letters and is based on a high Q-factor planar toroidal metamaterial [1]. This metamaterial shows significant localization of electromagnetic energy in the near field region rather than in the radiation zone due to the destructive interference of toroidal and electric dipole moments with identical radiation patterns in the far zone. The second layer, which complements the first one, consists of a metallic layer with cutouts in the epsilon letter shape. Individually, the original metamaterial demonstrates a high Q-factor resonance and confines the electric field of the incident wave. Conversely, the inverted structure does not respond to the incident wave but is instead stimulated by near-field interaction with the original metamaterial. The low losses observed can be attributed to the interaction between the two most significant multipoles excited within the metamaterials. In the case of the original metamaterial, this interaction involves destructive interference between toroidal and electric dipole moments, leading to the formation of an anapole. On the other hand, the properties of the inverted metamaterial stem from the interaction between toroidal dipole and magnetic quadrupole moments. Both metamaterials are fabricated as free-standing to avoid dielectric losses from the substrate, which can significantly diminish the resonance’s Q-factor. The simulated metamaterial (Fig.1a) is excited with the wave polarized along the wires of the metamolecules of the original type, allowing for the support of dual loops of currents along the voids, leading to toroidal excitation.