Tunable toroidal resonance based on hybrid graphene-metal metasurfaces

With the rise of artificial magnetism and metamaterials, toroidal resonance has gained much attention for its special properties. In this paper, we propose a novel hybrid graphene-metal metamolecule consisting of a square bracket-like resonator and two asymmetric U-shaped resonators. By applying various Fermi energies to graphene, the amplitude of electromagnetically induced transparency (EIT) can be efficiently manipulated, and the maximum amplitude modulation depth can attain 81% in the microwave region. Numerical simulations and theoretical analysis demonstrate that the dynamic manipulation is mainly induced by the active tuning toroidal resonance through the recombination effect of the conductive graphene. Also, the maximum group delay of 85 ps can be attained and controlled with the increasing Fermi energy. The proposed hybrid graphene-metal metamolecule and dynamically manipulating mode presents a novel modulating strategy of EIT-like analog based on the toroidal response, which has great application for the design of efficient tunable resonators, filters, and sensors.