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. The inverted structure, rotated to complement the original one, does not exhibit excited currents with the wave’s set polarization; instead, it is activated by near-field interaction with the original metamaterial. Transmission spectra of the metamaterials at varying distances are illustrated in Fig. 1b, with optimal results obtained at a distance of 0.8 mm. The metamaterials were fabricated using a xTool laser cutter on a 50nm brass film, with the original and inverted structures comprising 10x10 metamolecules of 1.3 mm radius and periods of 2.60 mm and 2.55 mm, respectively. Experimental transmission spectra (Fig.1c) were measured utilizing a Keysight PNA Network Analyzer with VNA Extenders WR-12. The layers were housed in 3D-printed holders separated by spacers ranging from 0.6 to 2 mm in thickness. The most pronounced resonance, with a Q-factor close to 4000, was observed at a distance of 0.8 mm, similar to the simulation.