Actively tunable toroidal excitations in graphene based terahertz metamaterials

Toroidal dipoles, unlike electric and magnetic dipoles, are formed due to currents flowing on the surface of a torus along it's meridians. We investigate the toroidal dipole response in a graphene based infinite 2D array of terahertz (THz) metamaterial (MM) and report the active tuning of the toroidal resonances. Each metamolecule in our proposed MM configuration consists of two joint split ring resonators (SRRs) made up of graphene material with two gaps in each resonator. We examine actively tunable response of the toroidal excitations with respect to a change in the Fermi energy of graphene material. The toroidal effect is elaborated using surface current and magnetic field profiles at the resonance frequency of the metamolecule structure. The modulation of the metamaterial's toroidal response and effect on Q factor is further examined by changing the relaxation time of graphene. The excitation of toroidal resonances at terahertz frequencies and their dynamic control could be significant in designing efficient tunable modulators, filters and sensors.